Power Transformers Cooling Design: A Comprehensive Review

Abstract

Efficient cooling technologies for power transformers are critical to modern power systems, ensuring reliability, performance, and AN extended lifespan. This review systematically analyses advancements, challenges, and opportunities in cooling systems for power transformers. Oil-immersed transformers, widely used due to their superior insulation and effective cooling, require efficient thermal management to prevent overheating and ensure operational stability. This review evaluates key cooling strategies across oil-natural air-natural (ONAN), oil-natural air-forced (ONAF), oil-directed air-forced (ODAF), and oil-forced air-forced (OFAF) systems. It highlights innovations in radiator design, such as top-mounted radiators and chimney caps, and explores sustainable alternatives, including biodegradable esters, nanofluids, and hybrid ventilation methods. Advanced computational tools like Computational Fluid Dynamics (CFD) and artificial intelligence (AI), particularly neural networks, are identified as transformative for optimising cooling performance, predicting thermal behaviour, and enabling real-time monitoring. Despite progresses, challenges persist in radiator optimisation, airflow dynamics, and scalability of innovative cooling methods. By offering a comprehensive review and identifying critical areas for improvement, this study provides a foundation for developing cost-effective, reliable, and environmentally sustainable cooling systems, aligning with the growing demand for efficient energy infrastructure.

1. Introduction

The transition to renewable energy sources is a cornerstone of global efforts to enhance electricity production, driven by technological advancements, economic incentives, and environmental imperatives [1,2]. Studies highlight the pivotal role of improved efficiency in renewable technologies [3], decreasing costs [4], and the sector’s contribution to economic growth and job creation [5]. Additionally, reduced greenhouse gas emissions [6] and the impact of public awareness alongside supportive policies [5] underscore the comprehensive benefits of adopting renewables. To sustain this progress, resistance to infrastructure development must be addressed [7,8]. Transformers play a crucial role in modern electrical infrastructure, enabling the efficient conversion of voltages between different power levels to meet the demands of energy transmission and distribution [9,10,11]. Among the various types of transformers, oil-immersed models stand out due to their widespread use and the advantages associated with their insulation and heat dissipation capabilities [12,13,14]. The insulating oil in transformers is an essential component, fulfilling the dual role of protecting windings and the core against electrical failures and facilitating the dissipation of heat generated during operation. This process is critical to maintaining equipment reliability and minimising risks of failures or premature degradation of insulation [1]. The circulation of oil between the tank and radiators, combined with air convection cooling the external fins, constitutes a continuous cooling cycle essential for efficient thermal management. However, heat management in oil-immersed transformers remains a significant challenge. Excessive temperatures can compromise the integrity of insulating materials, leading to reduced lifespan and increased risk of catastrophic failures [15,16,17]. Thus, the cooling system’s efficiency directly influences the transformer’s ability to operate under high loads without overheating. In recent years, significant advancements have been made in the thermal management of oil-immersed power transformers, particularly in optimising radiator systems [1,2,10,18,19,20]. However, no quantitative review comprehensively compiles efforts in evaluating the thermal performance of transformers under primary cooling methods, including oil-natural air-natural (ONAN), oil-natural air-forced (ONAF), oil-directed air-forced (ODAF), and oil-forced air-forced (OFAF). Additionally, studies systematically addressing optimising radiator configurations and cooling systems using natural and forced ventilation remain limited. Currently, the field has only two notable reviews. Guo et al. [8] provideD a qualitative overview of temperature prediction methods for oil-immersed transformers, categorising their principles, advantages, limitations, and challenges. Jin et al. [9] deliverED an in-depth review of condition monitoring methodologies, focusing on fault diagnosis and predictive maintenance. While these contributions are valuable, they do not address the pressing need for a quantitative review integrating detailed metrics and data to evaluate and optimise transformer cooling systems. This article fills this critical gap by presenting the first systematic review of quantitative data on advancements in cooling systems for power transformers. It focuses on radiators, oil circulation systems, and thermal dynamics, evaluating analytical, numerical, and experimental methods to enhance cooling efficiency, reliability, and lifespan. The study highlights innovative strategies, including hybrid ventilation methods, alternative cooling fluids, and optimised radiator designs, emphasising their impact on thermal management and sustainability. By providing a comprehensive analysis of the current technologies and innovations, this review serves as a foundation for guiding future research and supporting decision-makers in adopting efficient, cost-effective, and eco-friendly cooling solutions for power transformers. This review is structured into four main sections: the Introduction, which outlines the context and significance of transformer cooling systems; the Methodology, detailing the systematic approach to literature analysis; the Discussion, providing an in-depth analysis of key findings related to cooling technologies, radiator designs, and sustainability; and the Conclusion, summarising insights and proposing directions for future research

2. Methodology

A comprehensive review of the existing literature was conducted using leading international interdisciplinary research platforms, including ScienceDirect, Scopus, and Web of Science. The search employed a strategic combination of the following keywords: Thermal Modelling, Biodegradable Fluids, Radiator Optimization, CFD Simulation, and Heat Management. The review followed a “semi-systematic” approach, as proposed by [21]. This method was selected to balance comprehensiveness with flexibility. It allows the review to focus on the most relevant and impactful studies within a vast and evolving field. This approach provides a robust yet adaptable framework for analysing transformer cooling technologies by synthesising diverse methodologies and accommodating rapid advancements. This review highlights significant advancements in the design and optimisation of cooling systems for power transformers, underscoring the critical role of effective thermal management in improving performance, extending lifespan, and ensuring reliability. It comprehensively analyses analytical, numerical, and experimental methods, detailing their strengths, limitations, and practical applications for enhancing cooling efficiency. The review encompasses the literature published in the past decade, containing a total of 113 research articles that were carefully examined. The article is organised into six sections: (2) Methodology, detailing the research approach; (3) Power Transformers, covering their key components and thermal challenges; (4) Radiator Systems, focusing on performance and enhancement strategies; (5) Radiator Modelling Approaches, exploring analytical, numerical, and experimental techniques; and (6) Conclusions, summarising the study’s key findings and implications. The following section discusses the fundamentals of power transformers, setting the stage for understanding the complexities of their cooling systems.

3. Power Transformers

Based on their structural design and flux path, oil-immersed power transformers are classified into two main categories: core-type and shell-type transformers, as represented in Figure 1. Additionally, both categories can be classified as single-phase for lower loads, and three-phase systems when higher loads are required.

Core-type transformers have windings surrounding the core limbs, with magnetic flux following a single path through the core. The low-voltage winding is closest to the core, while the high-voltage winding surrounds it. This arrangement causes flux leakage, inducing eddy currents in the tank, increasing stray losses [22].

Shell-type transformers, with a central and two outer limbs, offer balanced, low-reluctance flux paths and better efficiency. The low and high-voltage windings alternate around the central limb. Shell-type transformers have significantly lower flux leakage compared to core-type, reflecting superior magnetic coupling [23,24,25,26]. However, core-type transformers remain prevalent in high-voltage, high-power applications due to their lower cost and easier maintenance [24].

3.1. Heat Generation in Transformers Windings

When a transformer operates beyond its rated capacity, an increase in leakage flux around the core raises the temperature of metallic parts, impacting the thermal dynamics of the system. Elevated temperatures can alter the chemical composition of insulation oil, increasing its gas content and further affecting heat distribution within the transformer [27]. Additionally, transformer losses, such as ohmic losses in the windings, core losses, and stray losses, contribute to temperature rises. A particularly critical aspect of this thermal behaviour is the hotspot, a localised region within the windings where the temperature peaks due to concentrated heat generation, further limiting dissipation. This non-uniform heat distribution results from current and magnetic flux variations and is influenced by factors such as loading conditions, ambient temperature, and the cooling system’s efficiency. The temperature at the hotspot ultimately dictates the thermal capacity of the transformer, making it a primary consideration in cooling system design. Standards (e.g., the EEE Std. C57.12.00–2015 [28]) specify that the average winding temperature rise above ambient conditions should not exceed 65 °C, with a maximum hotspot temperature (HST) of 80 °C at the rated load. This standard is based on tests performed by IEEE Std. C57.12.90 under controlled ambient conditions (i.e., 40 °C for air-cooled transformers and 30 °C for water-cooled transformers) [29]. However, typical transformer operation rarely occurs under such constant conditions. Ambient temperature variations are common, often resulting in significantly different loading dynamics [30].

When the ambient temperature is lower than the rated baseline, transformers can accommodate higher loads without accelerating the insulation ageing process. Dynamic rating leverages real-time environmental conditions to safely enhance transformer capacity within established safety margins, offering significant cost savings by postponing the need for investment in new transformer infrastructure [31]. Dynamic rating is particularly beneficial in colder climates where peak demand coincides with low temperatures, allowing for increased load capacity during high-demand periods without increasing ageing risks [32].

Accurate knowledge of HST is essential in developing effective cooling strategies that prevent the transformer from exceeding recommended thermal limits. Exceeding the limits outlined by manufacturers and standards [27] accelerates insulation ageing and reduces transformer lifespan [33]. These thermal limits vary according to transformer type and cooling strategy, highlighting the importance of managing HST to enhance reliability and longevity. For routine cyclic loading, the recommended maximum temperatures are 120 °C for windings, 130 °C for the inner core, 140 °C for metallic hotspots, and 105 °C for top oil [27].

To predict transformer lifespan, standards such as IEEE Std C57.91 [27], IEEE Std C57.100 [34], and IEC 60076-7 [35] provide models that calculate insulation ageing rates based on temperature, recognising that thermal exposure is the primary factor influencing the insulation’s rate of degradation over time [36]. The HST is thus crucial for estimating the transformer’s life expectancy. The relationship between insulation deterioration, time, and temperature variations are captured by the ageing acceleration factor $F_{AA}$, which serves as a vital parameter in determining insulation longevity and transformer durability under different thermal stresses [36]. Analytically, the $F_{AA}$ can be calculated according to Equation (1).

$$F_{AA}=e^{\left[{\displaystyle \frac{15000}{{\theta }_{HS,ref}+273}}-{\displaystyle \frac{15000}{{\theta }_{HS}+273}}\right]}$$

(1)

The reference HST, denoted as ${\theta }_{HS,\mathrm{ref}}$, is established at 110 °C. The actual HST, ${\theta }_{HS}$, can be estimated from oil temperature measurements using the IEEE/IEC loading guides [34,35]. These guidelines facilitate the correlation of oil temperature to the HST, according to Equation (2).

$${\theta }_{HS}={\theta }_{TO}+K·\Delta {\theta }_{HR}{\left({\displaystyle \frac{I}{I_R}}\right)}^{2m}$$

(2)

In this context, ${\theta }_{TO}$ represents the oil temperature recorded at the top of the transformer. At the same time, $\Delta {\theta }_{HR}$ indicates the temperature differential between the hotspot and the top oil temperature, as determined during a heat run test conducted at the transformer’s rated power. The winding exponent, denoted as m, is an empirical value suggested by the loading guide. These parameters, along with the actual load current, I, the rated current, $I_R$, and the HST, can be interpolated [36,37]. Furthermore, a correction factor (K), dependent on the transformer’s design specifications, is applied to enhance the accuracy of the interpolation [36]. To determine the transformer lifespan, L, one divides the everyday insulation life ($L_n$), corresponding to this reference temperature of 110 °C, by the $F_{AA}$, according to Equation (3).

$$L={\displaystyle \frac{L_n}{F_{AA}}}$$

(3)

This calculation allows for adjusting the expected insulation longevity based on the operational conditions and thermal stresses experienced by the transformer, thereby providing a more accurate estimation of its pratical service life. As an alternative approach, discussed in [36], the Loss of Life, LoL, during a defined operational period, top, quantifies the proportion of the everyday insulation life utilised within that specific timeframe. Its value can be computed using Equation (4).

$$LoL={\displaystyle \frac{F_{AA}{t}_{op}}{L_n}}$$

(4)

This methodology enables determining the transformer’s remaining useful life, especially in cases where the HST exhibits temporal variability.

IEC Standard 60076-7 [38] offers two distinct methodologies for calculating HST: an exponential equation tailored for factory testing to determine heat transfer parameters and a differential equation approach more suited for real-time monitoring. These methods are widely adopted for dynamic transformer ratings in diverse applications. Furthermore, Jalal et al. [39] have extended these models to incorporate additional variables, such as tap position and cooling states, which enhance the accuracy of HST and insulation life estimations.

The presence of nonlinear loads introduces additional complexities due to harmonic distortions, further elevating HST. In response, Das et al. [40] proposed a model integrating harmonic considerations into the IEC framework, allowing utilities to conduct dynamic ratings under unbalanced, distorted loading conditions while mitigating transformer failure risks.

Determining the HST in compliance with IEEE/IEC loading guides requires comprehensive data on the correction factor pertinent to transformer design and the measured temperature gradients, such as those from the winding to the oil under rated load conditions. Unfortunately, end users may frequently lack access to this critical information, hindering their ability to accurately evaluate the HST and the remaining operational life of the transformer using this methodology. Additionally, it should be noted that the winding exponent serves as an empirical variable, and the design-dependent correction factor provided in the standards has been criticised for being insufficiently robust, often yielding values that are too conservative when compared to actual winding temperature readings, as highlighted in [41].

Instrumentation-based methods for monitoring HST in transformers primarily include infrared thermography (IRT), fibre optic sensors, and thermocouples or resistance temperature detectors (RTD).

Infrared thermography offers a non-invasive approach that captures thermal data from transformer surfaces. Using high-resolution infrared cameras, IRT provides real-time thermal imaging that identifies temperature discrepancies and reveals potential hotspots in transformers [42]. This method is advantageous for its simplicity and ease of deployment, particularly during on-site inspections where direct access to internal windings is impractical [42]. However, the accuracy of IRT is inherently limited by its reliance on external measurements. External environmental factors, such as emissivity variations and reflections from the transformer oil or tank walls, can significantly influence the readings, leading to potential inaccuracies [43]. Furthermore, IRT only detects surface temperatures, making it less effective for precise internal monitoring.

In contrast, fibre optic sensors, particularly Fibre Bragg Grating (FBG) sensors, provide highly accurate, localised temperature measurements within the transformer windings. FBG sensors work by detecting temperature-induced shifts in the wavelength of light transmitted through the fibre, providing continuous and interference-free data collection [44]. This method is notably advantageous in high electromagnetic fields, where traditional electrical sensors might fail. These sensors offer durability and precision under harsh operating conditions and are increasingly used in high-value assets that require stringent monitoring [45]. Fibre optic sensors face significant barriers to widespread adoption despite these benefits due to installation complexity and high initial costs. Retrofitting these sensors into existing transformers is technically challenging, as it requires substantial modifications to accommodate the fibre cables within the transformer structure [46]. Additionally, ruggedising fibre optic components to withstand oil immersion and high temperatures adds to the operational costs, limiting their application primarily to newly manufactured transformers.

While they are well-suited to provide point-specific temperature data, their limited spatial coverage makes it difficult to obtain a comprehensive thermal profile of the transformer. Moreover, the physical contact required by RTDs and thermocouples exposes them to accelerated degradation from transformer oil, temperature fluctuations, and mechanical stress. Over time, sensor calibration can drift, necessitating regular maintenance to ensure accuracy. While RTDs remain a reliable solution for routine monitoring, their use is often constrained by their limited durability in high-temperature environments, especially in locations with severe electromagnetic interference instrumentation methods are often limited by technical and economic factors [47].

High installation costs, especially for fibre optic sensors, and maintenance challenges for RTDs deter widespread implementation, particularly in older transformer models. Integrating fibre optic sensors, while ideal for precise, real-time monitoring, requires extensive modifications incompatible with existing transformer designs. Consequently, instrumentation methods for HST monitoring remain underutilised in the industry, with preference given to methods that balance cost, installation simplicity, and operational robustness.

This underutilisation highlights the necessity for alternative modelling techniques to predict HST in transformers accurately. A range of such techniques has been investigated. These approaches, which vary from numerical simulations to thermal circuit models, offer different insights and accuracies for HST estimation. Finite element modelling (FEM) is a commonly used technique for simulating HST, particularly in scenarios with varying load and harmonic conditions. For instance, Huang et al. [48] applied a three-dimensional FEM model to examine how high-order harmonics affect magnetic flux leakage, resulting in a temperature rise of approximately 7 °C. Similarly, other researchers have used FEM-based simulations to evaluate transformer losses and predict lifespans under harmonic loads, with one study [49] explicitly focusing on oil-filled and dry-type transformers. Zhang et al. [50] further refined FEM by establishing a quantitative relationship between winding temperature rise, harmonic content, and frequency, showing that HST can increase from 0.3 °C to 18.7 °C as harmonic content rises from 1% to 10%. While FEM-based models deliver high accuracy in capturing the effects of harmonics, they tend to be computationally intensive and may not be suited for real-time monitoring applications.

Thermal circuit models represent another category of HST estimation techniques. These models leverage the duality of electrical and thermal phenomena, using equivalent circuits based on heat transfer theories to calculate HST. By modelling transformers as thermal circuits, these approaches incorporate convective and conductive heat transfer mechanisms to estimate temperature rise, as demonstrated in several studies [51]. While thermal circuit models provide practical insights and are relatively straightforward to implement, they often omit critical parameters, such as the heat dissipation capacity of the transformer tank and oil, which limits their accuracy.

Computational Fluid Dynamics (CFD) has gained traction as a method for HST estimation, mainly due to advances in numerical calculation techniques. CFD-based models enable detailed simulations of temperature distribution and oil flow velocity within transformers, accounting for complex variables such as winding configuration and the electromagnetic-fluid-thermal coupling process [52,53]. With the finite volume method, researchers can analyse the winding-fluid thermal distribution, providing highly accurate visualisations of heat dissipation and fluid behaviour. This approach also enables precise calculation of losses, including load losses, no-load losses, eddy current losses, and stray losses within the transformer tank. However, CFD-based models are computationally demanding and require advanced computer hardware, especially for real-time applications. Additionally, achieving accurate results with CFD requires detailed geometric modelling, including the transformer conservator, corrugated tank walls, and core stacking, making it challenging to implement in complex transformer structures. Despite these limitations, CFD-based models offer high accuracy in assessing HST distributions, making them valuable for scenarios where precision is critical.

Other predictive models for HST focus on utilising minimal data inputs to maintain practicality and scalability in diverse operational settings. Rommel et al. [54] developed a virtual twin-based approach for estimating HST based solely on voltage and current measurements. This method constructs a virtual model using only the transformer nameplate data, simplifying it and making it accessible for cases where detailed information is unavailable. While this approach can effectively estimate winding temperature, it must account for ambient temperature or other environmental factors like solar radiation, limiting its accuracy in outdoor applications. Conversely, Sun et al. [55] used a support vector regression (SVR) technique to predict HST in distribution transformers by integrating inputs such as ambient temperature, load rate, historical HST data, and cooling fan status. This approach achieved high prediction accuracy. However, it applies only to dry-type transformers and requires access to historical data, constraining its adaptability across transformer types and operational conditions.

Artificial intelligence (AI) techniques have increasingly been employed to improve HST prediction accuracy, streamline input requirements, and address limitations inherent in other methods. Juarez-Balderas et al. [56] developed an artificial neural network (ANN)-based model for predicting HST. Validated with FEM simulations and experimental data, the model achieved high accuracy with an average prediction error of just 2.71%. However, this ANN model was explicitly designed for medium-voltage/low-voltage (MV/LV) transformers tested indoors, making it less applicable to outdoor transformers. Moreover, it did not account for ambient temperature and required substantial computational resources, thus limiting its scalability. Another AI-based method, proposed by Zhang et al. [57], combined fuzzy information granulation with a chaotic particle swarm-optimised wavelet neural network to predict winding HST fluctuations. This model showed strong predictive accuracy, though the authors noted that additional research would be required to refine its applicability to practical engineering environments. Beyond neural networks, other AI methods, such as fuzzy logic, metaheuristic algorithms, and clustering, have been explored for transformer health management, thermal parameter estimation, and enhanced design for optimal thermal performance [58].

Figure 2 and

Table 1. Modelling windings heat generation.

Criteria	Analytical Methods	Numerical Methods	AI-Based Methods
Examples	Thermal circuit models	FEM, CFD	Neural networks, SVR, Fuzzy logic
Accuracy	Moderate	High	High
Computational Demand	Low	High	Medium to high
Real-time Applicability	Good, suitable for real-time	Limited due to computational intensity	Moderate, depending on model complexity
Data Requirements	Low	Moderate (detailed design parameters)	High (historical data and environmental factors)
Implementation Complexity	Low	High (requires advanced setup)	Moderate to high
Cost of Deployment	Low	High	Medium
Typical Use Cases	Routine HST monitoring	Detailed simulation under load variations	Predictive maintenance, fault prevention
Limitations	Limited precision, static models	High computational demand	Dependent on data quality, computational cost

summarise the research effort concerning modelling the windings heat generation.

3.2. Transformers Oils: Types and Properties

Transformer oils are vital in power transformers’ insulation and cooling systems, affecting their lifespan and reliability. Mineral oil has been the long-established standard for insulating fluid due to its compatibility with cellulosic solid insulation and adequate heat dissipation properties. However, its drawbacks, such as poor biodegradability, high toxicity, and susceptibility to oxidation, have led to the development of alternative insulating fluids, including natural and synthetic esters [59,60].

These esters, known for their biodegradability and improved thermal and oxidative ageing resistance, have shown potential as sustainable alternative. While esters offer numerous benefits, they also present technical challenges. Their higher viscosity, which can be up to three times the viscosity of mineral oil, can slow coolant flow and impact heat transfer rates, requiring adjustments in transformer design to optimise thermal management [60]. Additionally, while exhibiting analogous dielectric properties to mineral oils under quasi-uniform fields, esters are more prone to fleeting discharges in high electric stress areas, requiring insulation system modifications.

Silicone oils have also been studied as potential alternatives to mineral oils for use in power transformers, as they offer advantages such as enhanced biodegradability and fire resistance [61]. However, a recent study reported significant fluctuations in electrical properties due to the development of colloidal formations [62].

The ageing of mineral and ester oils reduces breakdown strength, with mineral oil exhibiting more significant degradation due to increased moisture content, acid formation, and power factor fluctuations. Yu et al. [63] highlighted that increased ester content in oil mixtures raises breakdown voltage (BDV) and improves physicochemical properties like dynamic viscosity, acidity, and pour point. The elevated fire and flash points of ester mixtures enhance their suitability for transformer applications. Synthetic ester mixtures are also known to slow transformer oil ageing. At the same time, Dombek and Gielniak’s [64] findings suggest that the ester content in oils influences parameters such as relative permittivity, dissipation factor, and net calorific value.

Recent advancements in transformer technology have introduced enhanced transformer oils with nanoparticles to improve insulating fluid performance further. These so-called nanofluids exhibit higher thermal conductivity and BDV than base oils.

Metal oxide nanoparticles such as TiO₂, Al₂O₃, and ZnO are widely used for their affordability, stability, and dielectric properties [65]. Studies have shown that smaller nanoparticles at higher concentrations enhance dielectric strength by trapping free electrons more effectively, though excessive concentrations can cause agglomeration, diminishing these benefits [65,66]. Additionally, surfactants preserve fluid stability by avoiding nanoparticle clumping and guaranteeing uniform dispersion [65].

However, despite these advances, a nanoparticle that meets all performance criteria for transformer applications has yet to be identified. Continued research is essential to achieve an optimal solution for nanoparticle-enhanced natural ester-insulating fluids. Additionally, as evidenced in [67], the potential of natural esters as alternatives to mineral oils is notably enhanced by incorporating nanoparticles.

To fully quantify the potential of transformer oils and their alternatives, it is essential to model their time-dependent thermo-physical properties, such as density ($\rho$), thermal conductivity (k), specific heat capacity (cp), and dynamic viscosity ($\mu$), as they significantly influence heat transfer and flow behaviour.

Table 2. Transformer oils time-dependent properties modelling.

Fluid	Source	Property	Equation
Mineral Oil	[68]	Density	$\rho \left(T\right)=1098.72-0.712T$
		Conductivity	$k\left(T\right)=0.1509-7.101\times {10}^{-5}T$
		Specific Heat	$c_p\left(T\right)=807.163+3.58T$
		Viscosity	$\mu \left(T\right)=0.08467-0.0004T+5\times {10}^{-7}{T}^2$
Synthetic Ester Oil	[69]	Density	$\rho =1185-0.7333\mathrm{T}$
		Conductivity	$\mathrm{k}=9.71\mathrm{E}-2+3.74\mathrm{E}-4\mathrm{T}-7.2503\mathrm{E}-7{\mathrm{T}}^2$
		Specific Heat	${\mathrm{C}}_{\mathrm{p}}=1242.4+2.198\mathrm{T}$
		Viscosity	$\mu =0.2565-1.2963\mathrm{E}-3\mathrm{T}+1.6761\mathrm{E}-6{\mathrm{T}}^2$
Natural Ester Oil	[70]	Density	$\rho =1118.1-0.6737\mathrm{T}$
		Conductivity	$\mathrm{k}=0.2241-2.1174\times {10}^{-4}\mathrm{T}$
		Specific Heat	$C_p=986.78+3.9658\mathrm{T}$
		Viscosity	$\mu =1.19\times {10}^{-4}exp(924/(\mathrm{T}-147))$

presents the relationships of these properties, offering a framework to set thresholds that guarantee effective thermal management in transformer systems.

The substantial potential of these advancements can only be realised through a rigorous techno-economic analysis. However, given the nascent stage of research on the implementation of nanofluids in power transformers, no comprehensive studies providing such an assessment have been found in the literature. One of the major challenges in large-scale production is ensuring the long-term stability of these fluids, as maintaining uniform nanoparticle dispersion over extended periods remains a critical issue that requires further investigation to determine their viability for widespread industrial application.

3.3. Oil Circulation Systems and Cooling Methods

There are three principal oil circulation systems: oil natural (ON), oil forced (OF) and oil directed (OD). They differ primarily in their method of oil movement and cooling efficiency. These systems are crucial for maintaining the transformer’s temperature and ensuring performance. Figure 3 provides a simplified representation of power transformers’ different oil circulation systems.

The main characteristic of the ON system mode is that it operates without the assistance of oil pumps, relying on natural convection to circulate the oil, unlike OF and OD systems. The oil heats inside the tank and is cooled in the radiators, creating density changes causing the oil to flow, also known as the thermosiphon effect. Due to having less active parts, these systems are the most reliable, as they require less maintenance [72].

In contrast, OF uses an oil pump to enhance oil circulation velocity. The oil pump placement can change between the inlet and outlet of the radiator, depending on the power transformer. Furthermore, using pumps implicates more maintenance and an increased risk of failure; if the pump fails, systems relying on forced oil circulation cannot operate in natural mode. In OF systems, oil is forced into the transformer, flowing with the least resistance path. As a result, much of the oil bypasses the active components within the tank, instead flowing along the tank walls, which limits the oil flow through the windings, even when the pump provides higher flow rates.

OD systems utilise internal ducts between the oil pump and winding inlet to direct the cooled oil into the windings, resulting in a higher oil velocity in the active parts. As a result, the oil outside the ducts at the bottom of the tank and on the sides of the active parts have a very low velocity and become almost stagnant. This system has the same problems associated with pumps like OF, but on the other hand, it has the highest lifespan due to the oil directed to the windings [10,73].

Oil circulation systems play a crucial role in determining temperature distribution within power transformers. Thermal analyses conducted by [10,72] rank these systems by cooling capacity: oil-directed systems are the most effective, followed by oil forced systems, with oil natural systems being the least effective.

OD and ON systems exhibit a linear temperature distribution, with colder oil at the bottom and hotter oil at the top. However, ON systems rely on natural convection, creating distinct temperature layers, while OD systems achieve a more homogeneous temperature profile due to higher oil velocity. This homogeneity reduces winding temperature peaks, as observed in [74]. In contrast, ON systems have the highest temperatures, limiting transformer load capacity due to the natural convection’s slower oil velocity [72].

OF systems differ by lacking a linear temperature distribution, maintaining near-uniform temperatures throughout most of the tank. However, a “top oil position” forms, where hot oil from the windings mixes with cold oil from the tank walls, creating a localised high-temperature zone. This mixing can cause sensor readings at this position to misrepresent winding conditions.

Table 3. Flow rate and circulation systems from barious authors.

Authors	Oil Circulation System	Air Circulation System	Flow Rate Radiator Inlet (m3/s)
[72]	OD	AF	0.400 (m/s)
[75]		AF	25.000 × 10−3
		AF	16.667 × 10−3
[76]		AF	18.056 × 10−3
		AF	22.222 × 10−3
[77]		-	19.444 × 10−3
[73]		AF	0.400 (m/s)
		AF	0.700 (m/s)
[78]		AN	3.300 × 10−3
		AN	4.200 × 10−3
[10]		AN	1.490 × 10−3
[72]		AN	0.400 (m/s)
[74]		AN	0.250 (m/s)
[72]	OF	AN	0.400 (m/s)
		AF	0.400 (m/s)
[2]		AF	0.740 × 10−3
		AF	2.210 × 10−3
		AF	3.690 × 10−3
		AF	5.160 × 10−3
[10]		AN	1.490 × 10−3
[79]		AF	0.302 × 10−3
[80]	ON	AF	1.700 × 10−3
[78]		AN	-
[10]		AN	-
[74]		AN	0.100 (m/s)
[19]		AN	0.016 × 10−3
		AN	0.022 × 10−3
		AN	0.028 × 10−3
		AN	0.032 × 10−3
		AN	0.038 × 10−3
		AN	0.041 × 10−3
		AN	0.044 × 10−3
[19]		AN	0.030 × 10−3
		AN	0.040 × 10−3
		AN	0.050 × 10−3
		AN	0.100 × 10−3
		AN	0.500 × 10−3
[81]		AN	0.157 × 10−3
[82]		AN	0.004 × 10−3
[1,83]		AN	0.019 × 10−3
		AN	0.031 × 10−3
[79]		AN	0.173 × 10−3
[80]		AN	1.444 × 10−3

presents a comprehensive overview of power transformers’ oil and air circulation systems, highlighting the oil flow rate of different system configurations.

OD systems have received significant attention in the literature [10,72,73,74,77,78], reflecting their superior cooling capacity, especially when paired with forced air circulation. These systems typically operate with oil flow rates between 1.490 and 25.000 × 10⁻³ m³/s, a wide range influenced by pump capabilities and differing experimental or numerical setups.

OF systems are less frequently studied [10,72,79], with oil flow rates ranging from 0.302 to 2.210 × 10⁻³ m³/s. Despite using pumps like OD systems, the higher flow rates in OF systems do not proportionally improve cooling capacity, leading to reduced flow rates and efficiency compared to OD systems. OF systems are often paired with AF systems to enhance cooling.

ON systems, extensively investigated in passive cooling scenarios [1,10,74,78,79,80,81,82,83,84], are typically combined with natural air cooling. This setup is suitable for applications with lower cooling demands. ON systems have the lowest oil flow rates, ranging from 0.004 to 1.700 × 10⁻³ m³/s, reflecting their reliance on natural convection.

4. Radiator Systems

Removable radiators are mandatory for air-cooled units in high-capacity oil-immersed power transformers with cooling systems. Compliance with the IEC 60076-22-2 standard [85] ensures radiator quality. The standard specifies steel with a minimum thickness of 1 mm, although 1.2 mm is recommended for better mechanical performance. Radiator fin heights must range between 800 mm and 3500 mm, as the standard outlines. Radiators are primarily categorised into FG (radiators with square flanges and elements of equal length) and FR (radiators with square flanges and a lowered upper head). These two designs are the most common, although alternative designs are also described in the IEC 60076-22-2 standard [85]. Among these, the FG model is the simplest and most frequently analysed in the literature [1,2,77,83], making it a popular choice for various transformer applications. Its straightforward design contributes to ease of manufacturing and maintenance, further solidifying its prevalence in transformer cooling systems.

4.1. Effect of Dimensions on Radiator Performance

Radiators in power transformer cooling systems are composed of multiple fins grouped into radiators, forming radiator blocks. Key geometric characteristics (Figure 4) such as fin height (L), fin count/number of fins (N), and fin spacing/distance between fins (D) impact heat transfer efficiency and cooling power.

Traditionally, cooling systems were over-designed, adding extra radiators to exceed thermal requirements. Current trends, however, favour efficient, lightweight designs that reduce weight, size, costs, and carbon footprint while maintaining performance [1].

Table 4. Parametric study of L (mm), D (mm), and N and their effect on radiator cooling performance.

Author	${\mathit{T}}_{{\mathit{oil}}_{\mathit{in}}}$ [°C]/ ${\mathit{T}}_{{\mathit{amb}}_{\mathit{air}}}$ [°C]	Case	L [mm]	N	D [mm]	${\mathit{T}}_{{\mathit{oil}}_{\mathit{out}}}$ [°C]	Cooling Power/Cost [kW/€]	Cooling Power [kW]
[86]	75/27	1	750	40	25.0	-	-	12.46
	75/27	2	1500	20	45.0	-	-	10.91
[1]	55/15	3	2000	18	50.0	-	5.72	6.80
	55/15	4		20		-	5.74	7.56
	55/15	5		22		-	5.38	7.78
	55/15	6		24		-	5.25	8.28
	55/15	7		26		-	5.09	8.69
	55/15	8		28		-	4.95	9.09
	55/15	9		30		-	4.74	9.33
	55/15	10	2200	18	50.0	-	5.48	7.21
	55/15	11		20		-	5.31	7.75
	55/15	12		22		-	5.09	8.17
	55/15	13		24		-	4.92	8.59
	55/15	14		26		-	4.77	9.03
	55/15	15		28		-	4.62	9.42
	55/15	16		30		-	4.49	9.80
	55/15	17	2400	18	50.0	-	5.28	7.64
	55/15	18		20		-	5.09	8.17
	55/15	19		22		-	4.85	8.55
	55/15	20		24		-	4.69	9.00
	55/15	21		26		-	4.54	9.44
	55/15	22		28		-	4.40	9.84
	55/15	23		30		-	4.26	10.22
	55/15	24	2500	18	50.0	-	5.18	7.82
	55/15	25		20		-	4.96	8.32
	55/15	26		22		-	4.73	8.71
	55/15	27		24		-	4.59	9.21
	55/15	28		26		-	4.44	9.64
	55/15	29		28		-	4.29	10.04
	55/15	30		30		-	4.15	10.40
	55/15	31	2600	18	50.0	-	5.04	7.94
	55/15	32		20		-	4.82	8.42
	55/15	33		22		-	4.64	8.91
	55/15	34		24		-	4.48	9.38
	55/15	35		26		-	4.33	9.81
	55/15	36		28		-	4.19	10.21
	55/15	37		30		-	4.06	10.59
	55/15	38	2800	18	50.0	-	4.88	8.30
	55/15	39		20		-	4.64	8.78
	55/15	40		22		-	4.47	9.28
	55/15	41		24		-	4.30	9.75
	55/15	42		26		-	4.15	10.17
	55/15	43		28		-	4.01	10.58
	55/15	44		30		-	3.87	10.95
	55/15	45	3000	18	50.0	-	4.68	8.58
	55/15	46		20		-	4.47	9.10
	55/15	47		22		-	4.30	9.61
	55/15	48		24		-	4.13	10.06
	55/15	49		26		-	3.99	10.52
	55/15	50		28		-	3.85	10.93
	55/15	51		30		-	3.71	11.29
	55/15	52			35.0	48.80	-	3.02
	55/15	53	1000	11	42.5	48.78	-	3.03
	55/15	54			50.0	48.74	-	3.05
	55/15	55			35.0	42.77	-	5.96
	55/15	56	1000	23	42.5	42.72	-	5.99
	55/15	57			50.0	42.61	-	6.05
	55/15	58			35.0	37.22	-	8.67
	55/15	59	1000	35	42.5	37.14	-	8.71
	55/15	60			50.0	36.94	-	8.81
	55/15	61			35.0	46.56	-	4.11
	55/15	62	2000	11	42.5	46.52	-	4.14
	55/15	63			50.0	46.39	-	4.20
	55/15	64			35.0	38.96	-	7.82
	55/15	65	2000	23	42.5	38.87	-	7.86
	55/15	66			50.0	38.63	-	7.98
55/15	67			35.0	32.70	-	10.87
55/15	68	2000	35	42.5	32.53	-	10.95
55/15	69			50.0	32.17	-	11.12
55/15	70			35.0	43.47	-	5.62
55/15	71	3000	11	42.5	43.37	-	5.67
55/15	72			50.0	43.18	-	5.76
55/15	73	3000	23	35.0	35.64	-	9.43
55/15	74			42.5	35.31	-	9.60
55/15	75	3000		50.0	34.89	-	9.81
55/15	76			35.0	29.19	-	12.59
55/15	77	3000	35	42.5	28.75	-	12.80
55/15	78			50.0	28.16	-	13.08
[83]	65/30	79	2000	16	50.0	-	-	2.73
	65/30	80	2200			-	-	2.95
	65/30	81	2400			-	-	3.19
	65/30	82	2500			-	-	3.31
	65/30	83	2600			-	-	3.42
	65/30	84	2800			-	-	3.65
	65/30	85	3000			-	-	3.88
	65/30	86	2000	18	50.0	-	-	3.07
	65/30	87	2200			-	-	3.32
	65/30	88	2400			-	-	3.59
	65/30	89	2500			-	-	3.72
	65/30	90	2600			-	-	3.85
	65/30	91	2800			-	-	4.10
	65/30	92	3000			-	-	4.36
	65/30	93	2000	20	50.0	-	-	3.42
	65/30	94	2200			-	-	3.69
	65/30	95	2400			-	-	3.99
	65/30	96	2500			-	-	4.13
	65/30	97	2600			-	-	4.27
	65/30	98	2800			-	-	4.56
	65/30	99	3000			-	-	4.85
	65/30	100	2000	22	50.0	-	-	3.76
	65/30	101	2200			-	-	4.06
	65/30	102	2400			-	-	4.39
	65/30	103	2500			-	-	4.55
	65/30	104	2600			-	-	4.70
	65/30	105	2800			-	-	5.02
	65/30	106	3000			-	-	5.33
	65/30	107	2000	24	50.0	-	-	4.10
	65/30	108	2200			-	-	4.43
	65/30	109	2400			-	-	4.78
	65/30	110	2500			-	-	4.96
	65/30	111	2600			-	-	5.13
	65/30	112	2800			-	-	5.47
	65/30	113	3000			-	-	5.82
	65/30	114	2000	26	50.0	-	-	4.44
	65/30	115	2200			-	-	4.80
	65/30	116	2400			-	-	5.20
	65/30	117	2500			-	-	5.40
	65/30	118	2600			-	-	5.56
	65/30	119	2800			-	-	5.93
	65/30	120	3000			-	-	6.30
	65/30	121	2000	28	50.0	-	-	4.78
	65/30	122	2200			-	-	5.17
	65/30	123	2400			-	-	5.58
	65/30	124	2500			-	-	5.79
	65/30	125	2600			-	-	5.98
	65/30	126	2800			-	-	6.38
	65/30	127	3000			-	-	6.79
	65/30	128	2000	30	50.0	-	-	5.12
	65/30	129	2200			-	-	5.53
	65/30	130	2400			-	-	5.98
	65/30	131	2500			-	-	6.20
	65/30	132	2600			-	-	6.41
	65/30	133	2800			-	-	6.84
	65/30	134	3000			-	-	7.27

compares three parametric studies, all using a consistent fin width of 520 mm. These parameters are critical as they influence the radiators’ heat transfer efficiency and overall cooling capacity. The data allows for an in-depth analysis of how variations in each parameter affect performance metrics, such as the inner heat transfer coefficient and cooling power output, helping identify optimal configurations for thermal management in power transformer systems. While Anishek et al. [86] reported typical oil flow rates of 1–2 dm³/s, Koca et al. [1,83] applied a fixed 0.25 kg/s rate in their CFD simulations to evaluate radiator performance.

Studies in the literature have evaluated L between 750 to 3000 mm, fins between 11 and 40, and fin spacing from 10 to 50 mm. Some values are excluded in Table 4 due to the lack of corresponding cooling power values for comparison.

Increasing radiator height generally enhances cooling capacity, as indicated by higher cooling power (kW) values linked to greater fin height, according to Koca et al. [1]. Similarly, Anishek et al. [86] found that the heat transfer coefficient peaks within the first 750 mm of the fins and stabilises at lower levels beyond this point, highlighting reduced efficiency in the lower sections of the fins.

Correlations between fin height and the cooling power have been established under a fixed number of fins. Additionally, increasing the number of fins improves cooling power, as shown in Figure 5. However, the literature does not define specific optimal parameter values. Factors such as manufacturing, transportation, and installation should also be considered alongside cooling performance to identify practical solutions.

Koca et al. [83] further investigated the effects of varying fin height on cooling power while keeping the fin count constant and examined how changing the number of fins influences cooling power with a fixed fin height. These findings are summarised in

Table 5. Correlations created by Koca et al. [83].

N	Correlation	L (mm)	Correlation
18	Qt = 1.520 L	2200	Qt = 170.75N
20	Qt = 1.6749 L	2400	Qt = 184.57N
22	Qt = 1.8244 L	2500	Qt = 199.33N
24	Qt = 1.9816 L	2600	Qt = 206.62N
26	Qt = 2.1371 L	2800	Qt = 213.67N
28	Qt = 2.2911 L	3000	Qt = 228.01N
30	Qt = 2.4426 L	2000	Qt = 242.39N

and presented as key correlations.

The distance between the fins can influence a radiator’s performance in terms of airflow development and resistance. However, data from Koca et al. [1] reveal that its impact on cooling power is minor compared to the number of fins and fin height, as shown in Figure 6.

Anishek et al. [86] found that a fin spacing of 25 mm yielded the highest heat transfer coefficient in their analysis of distances between 10 and 50 mm. In contrast, Koca et al. [1] observed higher cooling power for more considerable distances (35–50 mm), likely due to differing simulation methodologies (2D versus 3D). In a hybrid system combining AN with AF modes, the effect of fin spacing becomes more significant with increased airflow. Fin height and the number of fins are the most influential parameters on a radiator’s cooling power.

Koca et al. [1] developed correlations for cooling power and radiator costs based on these parameters, enabling the optimisation of radiator designs for maximum efficiency:

$${\mathrm{Q}}_{\mathrm{T}}=-2219+2.10\mathrm{L}+326\mathrm{N}-1.52\times {10}^{-4}{\mathrm{L}}^2-3.27{\mathrm{N}}^2+0.0193\mathrm{L}\times \mathrm{N}$$

(5)

$$\mathrm{Cos}\mathrm{t}=22.73\times 1.09\times {10}^{-3}\mathrm{L}-6.97\mathrm{N}+{10}^{-7}{\mathrm{L}}^2+1.2\times {10}^{-3}{\mathrm{N}}^2+0.0358\mathrm{L}\times \mathrm{N}$$

(6)

Researchers concluded that reducing fin height enhances cooling capacity per unit cost more effectively than simply increasing the number of fins. Radiators with shorter fins and a significant number of them are more cost-efficient for the same cooling performance, as indicated in Table 3. Anishek et al. [86] proposed a radiator design that reduces fin height from 1500 mm to 750 mm while doubling the number of fins from 20 to 40. This design improved cooling performance by approximately 14% and, based on Koca et al.’s [1] correlations, was 66% more cost-effective. However, it is worth noting that the parameter ranges used in these studies differ. The analysis does not account for radiator blocks with multiple radiators, which could introduce additional variables. Furthermore, ventilation impacts should be examined, as airflow direction may influence whether increasing fin height or fin count yields better performance, particularly under air-natural systems. Comparisons between studies reveal significant differences in cooling power for identical radiator configurations, underscoring the influence of environmental and operational factors. For example, studies [1,83] show a discrepancy in cooling power of 40–60%, with [86] reporting higher values. This difference is likely due to a lower ambient temperature of 15 °C [1] compared to 30 °C [83], as well as a slightly lower oil inlet temperature (55 °C in [1] versus 65 °C in [83]). These findings highlight the critical role of ambient temperature in cooling capacity, which is becoming increasingly relevant in global warming. Cooling systems must be designed with local temperature conditions in mind to ensure optimal performance.

4.2. Optimal Placement and Configuration of Radiators

As power transformers reach higher load levels, radiators become essential for effective heat dissipation. Traditionally, they are installed separately from the oil tank and placed adjacent to it. However, alternative radiator configurations must be considered in urban or near-city scenarios where land area is critical.

Table 6. Different radiator configurations.

Authors	Representation	Radiator Block	Load	Tamb [°C]	Results
[87]		L = 1500 mm; W = 520 mm; N = 38; e = 8 mm	3400 kVA	25	50% land mass reduction; 15% efficiency increase
[88]		-	150 MVA	-	38% area reduction in radiator; 40% oil flow rate increase

highlights the limited research on this topic, focusing on the radiator position and design modifications for radiators in ONAN mode.

The possibility of a top-mounted radiator configuration was explored in [87], where the radiator is directly above and attached to the oil tank through a connecting hole. This design employs Rayleigh–Bérnard convection, a natural and efficient mechanism. In this process, hot oil from the windings rises to the top of the radiator due to its reduced density, and as the oil goes through the radiator, it cools down and descends into the tank. This is a very efficient process due to the stable circulation of the oil, which creates structured patterns called Rayleigh cells. Furthermore, this configuration eliminates the need for an oil storage bank, instead employing venting holes connected to gas collection tubes to prevent any oil circulation from being blocked by air bubbles. This power transformer configuration showed a great reduction in land mass (50%) and an efficiency increase of 15% compared to other older top-mounted configurations. In a different approach, ref. [88] studied the impact of the thermal head (elevation difference between the centre of the coils and the centre of the radiators) by reducing the length of the radiator. Several scenarios were investigated, and it was concluded that when the thermal head was increased by 90%, the oil flow rate raised by 40%, having a positive impact on the cooling power of the radiator, and enabling a reduction of 38% in the heat transfer area, a rather important factor when considering land occupation limitation. In conclusion, both studies presented size reductions, one in area land mass and the other in the heat transfer area. For the latter, it would be useful to understand how the radiator reduction would impact the land area occupation of the power transformer. Furthermore, it would be helpful for both studies to analyse the impact of these different configurations and considerations on the cooling power of the radiator.

4.3. Techniques to Enhance Oil Cooling Efficiency

Air-cooled systems used in oil-immersed power transformers are classified into air natural (AN) and air forced (AF) cooling systems. Additionally, hybrid systems are used, which allow cooling fans to be turned on or off based on electric demand and variations in ambient temperature. Furthermore, variable speed fans are studied to adjust their velocity according to the heat generated [89].

AN cooling relies on natural convection to dissipate heat, providing quiet and stable operation without the need for external devices [90]. While effective in low heat loss scenarios, its passive nature limits its capability under high thermal loads, posing challenges in managing elevated cooling demands [91,92].

AF cooling employs fans to enhance airflow, significantly improving heat dissipation for high-powered transformers [2,71,79,93]. Compared to AN systems, it reduces hot-spot temperatures by approximately 9% [72] and increases radiator cooling power by 181% [71], ensuring consistent and efficient performance under varying conditions. Additional benefits include lowered winding, top-oil, and tank surface temperatures [94].

In specialised applications, alternative cooling strategies enhance efficiency and address specific operational challenges. For example, hydro-power plants utilise pumps to circulate water, effectively regulating oil temperatures and maintaining system stability [95]. Another innovative approach leverages geothermal energy, where microenergy piles dissipate heat from transformer oil, providing high efficiency and reduced operational costs [96]. Two-phase cooling systems have also been explored, employing phase change fluids between the oil and air. However, these systems demonstrated inferior performance compared to conventional cooling methods, limiting their practical application [97]. In urban settings, indoor and underground substations are increasingly used to address space constraints. While these configurations are viable for city applications, they present unique challenges. Cooling performance is often compromised, necessitating the use of more powerful fans, which in turn increases noise levels. Recent studies have focused on optimising cooling efficiency and mitigating noise issues in such environments [98,99,100].

4.3.1. Ventilation Design: Fan Types, Placement, and Airflow Dynamics

Key parameters influencing forced air systems in radiator cooling include fan placement, airflow direction, fan velocity (which affects airspeed), and fan diameter. Additional factors, such as the number of blades and the presence of a fan casing, are occasionally mentioned, but lack comprehensive evaluation in existing studies. Some studies analyse the effects of fan placement in detail, particularly when fans are positioned beneath radiators (see Figure 7).

Findings indicate that the airspeed is greater in the area above the fan, which increases the convective heat transfer coefficient. For instance, Wang et al. [90] reported that fins directly above the fan experienced an increase in cooling capacity from 200 W (non-ventilated areas) to 850 W (ventilated areas), yielding an average improvement of 132.25% in radiator cooling capacity, from 4.86 kW to 11.29 kW. Under forced convection, the average temperature difference between inlet and outlet oil temperatures was 15.42 K, compared to 9.01 K under natural convection. The fan-generated airspeed was 4 m/s, significantly higher than the 0.9 m/s observed under natural convection.

Similarly, Garelli et al. [79] found that, when using a 700 mm diameter fan, only 14 out of 26 fins were impacted by airflow; however, these fins contributed 8.6 kW to the total cooling power of 13.4 kW. The remaining 4.8 kW was attributed to non-ventilated fins, showing that ventilated fins dissipated twice as much heat due to increased air velocity.

Li et al. [13] studied fans with 500 mm and 630 mm diameters, examining airflow rates from 4.200 to 11.000 m³/h and inlet velocities ranging from 5.7 to 9.8 m/s. Their results showed that larger fan diameters and higher airflow rates increased air velocity on ventilated fins, enhancing convective heat transfer and radiator cooling power. Notably, a 630 mm diameter fan improved convective heat transfer on the fins from 4.7 W/m²·K to 14.6 W/m²·K, a 210.6% increase. While larger fan diameters reduced average airspeed on individual fins, they affected a more significant number of fins, a trade-off not explicitly analysed in the study, but crucial for design optimisation. Figure 8 illustrates the schematic of the radiator block under the ventilation setup used in the following tables.

Table 7. Analysed cases comparing vertical and horizontal directional ventilation effects on radiator performance.

Author	Scheme	Fans	Radiator Block	Oil Flow Rate [m3/s]	Cooling Power [kW]	Heat Transfer Coefficient [W/m2·K]	Factor of Merit
[101]		$T_{\mathrm{amb}}$ = 33.7 °C; 2 fans; 4 blades/fan; 550 RPM	$T_{\mathrm{oil},\mathrm{in}}$ = 55.8 °C; Nr = 5 radiators; L = 2000 mm; D = 50 mm; N = 27	0.294 kg/s	46.24	-	-
		$T_{\mathrm{amb}}$ = 33.7 °C; 2 fans; 4 blades/fan; 550 RPM	$T_{\mathrm{oil},\mathrm{in}}$ = 55.8 °C; Nr = 5 radiators; L = 2000 mm; D = 50 mm; N = 27	-	43.58	-	-
[80]		$T_{\mathrm{amb}}$ = 50 °C; 3 fans; Diameter: 500 mm; 7 blades; 940 RPM; with casing	$T_{\mathrm{top},\mathrm{rad}}$ = 93 °C; Nr = 4 radiators; L = 2600 mm; D = 50 mm; N = 14	-	67.5	14.4	-
		$T_{\mathrm{amb}}$ = 50 °C; 3 fans; Diameter 500 mm; 7 blades; 1130 RPM; with casing	$T_{\mathrm{top},\mathrm{rad}}$ = 93 °C; Nr = 4 radiators; L = 2600 mm; D = 50 mm; N = 14	-	78	16.5	-
		$T_{\mathrm{amb}}$ = 50 °C; 3 fans; Diameter 610 mm; 4 blades; 700 RPM; no casing	$T_{\mathrm{top},\mathrm{rad}}$ = 93 °C; Nr = 4 radiators; L = 2600 mm; D = 50 mm; N = 14	-	61	13.4	-
		$T_{\mathrm{amb}}$ = 50 °C; Diameter: 610 mm; 3 fans; 4 blades; 900 RPM; no casing	$T_{\mathrm{top},\mathrm{rad}}$ = 93 °C; Nr = 4 radiators; L = 2600 mm; D = 50 mm; N = 14	-	75	16	-
		$T_{\mathrm{amb}}$ = 50 °C; 3 fans; Diameter: 500 mm; 7 blades; 940 RPM; with casing	$T_{\mathrm{top},\mathrm{rad}}$ = 93 °C; N = 4 radiators; L = 2600 mm; D = 50 mm; N = 14	-	73	15.1	55.2
		$T_{\mathrm{amb}}$ = 50 °C; 3 fans; Diameter 500 mm; 7 blades; 1130 RPM; with casing	$T_{\mathrm{top},\mathrm{rad}}$ = 93 °C; Nr = 4 radiators; L = 2600 mm; D = 50 mm; N = 14	-	84.5	14	39.8
		$T_{\mathrm{amb}}$ = 50 °C; 3 fans; Diameter 610 mm; 4 blades; 700 RPM; no casing	$T_{\mathrm{top},\mathrm{rad}}$ = 93 °C; Nr = 4 radiators; L = 2600 mm; D = 50 mm; N = 14	-	65	17.4	66.5
		$T_{\mathrm{amb}}$ = 50 °C; Diameter: 610 mm; 3 fans; 4 blades; 900 RPM; no casing	$T_{\mathrm{top},\mathrm{rad}}$ = 93 °C; Nr = 4 radiators; L = 2600 mm; D = 50 mm; N = 14	-	80	16.8	40
		$T_{\mathrm{amb}}$ = 50 °C; Diameter: 610 mm; 2 fans; 4 blades; 900 RPM; no casing	$T_{\mathrm{top},\mathrm{rad}}$ = 93 °C; Nr = 4 radiators; L = 2600 mm; D = 50 mm; N = 14	-	65.4	-	46
		$T_{\mathrm{amb}}$ = 50 °C; Diameter 610 mm; 3 fans; 4 blades; 900 RPM; no casing; Offset = 50 mm	$T_{\mathrm{top},\mathrm{rad}}$ = 93 °C; N = 4 radiators; L = 2600 mm; D = 50 mm; N = 14	-	82.4	-	40.6
[102]		Diameter 1000 mm; 2 fans; 7 blades; 860 RPM; no casing	$T_{\mathrm{oil},\mathrm{in}}$ = 33.7 °C; Nr = 4 radiators; L = 3000 mm; D = 50 mm; N = 30	-	65.5	17.8	-
		Diameter 1000 mm; 2 fans; 7 blades; 860 RPM; no casing	$T_{\mathrm{oil},\mathrm{in}}$ = 33.7 °C; Nr = 4 radiators; L = 3000 mm; D = 50 mm; N = 30	-	65	17.5	-
[71]		$T_{\mathrm{amb}}$ = 20 °C; Diameter 600 mm; 6 fans; 4 blades; 550 RPM; Power consumption unit: 122.58 W	$T_{\mathrm{oil},\mathrm{in}}$ = 75 °C; Nr = 5 radiators; L = 2500 mm; D = 60 mm; N = 30	0.00074 0.00221 0.00369 0.00516	209.9 299.87 320.85 329.79	10.17 14.59 15.61 16.05	269.6/60.5 * 482.5/133.8 * 544.2/153.5 * 564.5/162.6 *
		$T_{\mathrm{amb}}$ = 20 °C; Diameter 600 mm; 6 fans; 4 blades; 550 RPM; With casing; Power consumption unit: 122.58 W	$T_{\mathrm{oil},\mathrm{in}}$ = 75 °C; Nr = 5 radiators; L = 2500 mm; D = 60 mm; N = 30	0.00074 0.00221 0.00369 0.00516	223.06 324.19 349.82 361.22	10.85 15.77 17.02 17.58	308.3/73.6 * 550.7/158.2 * 616.13/182.5 * 646.5/194.0 *

* Calculated value using Equation (7).

summarises 22 cases from five studies that specifically examine the impact of fan placement on radiator blocks while also considering other parameters. The performance metrics evaluated include cooling power [kW], heat transfer coefficient [W/m²·K], and factor of merit. In these studies, the fins typically have a width of 520 mm, and the airflow direction from all the fans is from outside the radiator to inside the radiator.

The studies analysed configurations with two to six fans, radiator blocks containing three to five radiators, fin heights ranging from 2000 to 2600 mm, fin counts from 14 to 30, and fin spacing between 35 and 60 mm. For fans, the studies considered diameters from 500 to 1000 mm, speeds ranging from 550 to 1130 RPM, and designs with or without casings. However, the parameters and conditions across the studies are not entirely uniform. Ambient and inlet oil temperatures, oil flow rates, air velocities, fan speeds, and the factor of merit are not consistently reported, making direct comparisons between studies challenging.

Factor of Merit

Several studies [2,71,80] propose a performance indicator, the factor of merit (FOM), which relates the added cooling power from fans to the electrical power used to operate them. While it may not be ideal to directly compare thermal cooling power with electrical power, the cooling power reflects the transformer’s waste energy, making the indicator somewhat viable. A primary energy ratio would, however, be a more accurate metric. The $FOM$ is calculated as Equation (7).

$$FOM=\left(Q_{AF}-Q_{AN}\right)/P_{AF}$$

(7)

where:

$Q_{AF}$ is the cooling power [kW] in AF mode;

$Q_{AN}$ is the cooling power [kW] in AN mode; and

$P_{AF}$ is the electric power consumed by cooling fans [kW].

In Kim et al. [71], discrepancies were noted in the FOM values reported in the bar chart compared to the provided data. Table 7 includes both the reported values and recalculated ones for clarity. Assuming the FOM’s validity, it is applied in this analysis.

Oil Flow Rate and Fan Speed Management

The cooling power strongly influences the merit factor in AN mode. It has been observed that as the oil flow rate increases, the factor of merit also rises. Higher oil flow rates improve the FOM because the AN system cannot efficiently dissipate heat at lower flow rates. Low oil flow rates for AF systems result in lower FOM values, indicating inefficiency. Optimising performance requires balancing oil flow rates with cooling fan operation. As studied by Janic et al. [89], variable-speed fans offer a promising solution by adjusting fan speed to meet cooling demands.

Only Directional Ventilation: Horizontal vs. Vertical

Numerous studies compare the cooling performance of horizontal and vertical ventilation. Figure 9b illustrates that horizontal ventilation improves cooling power by 1% to nearly 9% compared to vertical ventilation under the same conditions, as shown in Figure 9a.

Under identical ventilation conditions, horizontal configurations achieve a higher merit factor than vertical setups due to reduced air waste. In vertical ventilation, a significant portion of airflow escapes to the sides of the radiator block. While horizontal ventilation also experiences some airflow deviation, its impact is less pronounced because of lower air velocities and reduced lateral airflow loss [80,102]. In the AF-vertical cooling model, airflow is driven by a combination of forced convection (from cooling fans) and natural convection (caused by buoyancy due to temperature differences). These forces enhance the upward flow of cooling air along the exterior surfaces of the radiators. However, as the distance from the cooling fans at the base of the radiators increases, air velocity decreases while air temperature rises. In the AF-horizontal cooling model, a similar trend is observed. As the distance from fans on the radiators’ right side increases, air velocity decreases, and the temperature rises. Additionally, air exhibits slight upward deflection due to natural convection effects caused by temperature differences. As the air moves from the bottom to the top of the radiator assembly, its temperature rises, primarily driven by natural convection [71].

The cooling power distribution differs significantly between horizontal and vertical ventilation systems. In vertical ventilation, cooling power is relatively consistent across all radiators in the block. However, variations can occur depending on the number and placement of fans. For instance, if the fans fail to impact the inner radiator significantly, its cooling power may be lower. Similarly, their performance might decline if the fans do not effectively cool the outer radiators. Despite these variations, natural convection and lateral air loss help minimize differences. In contrast, horizontal ventilation exhibits a distinct pattern. The radiator closest to the fans achieves the highest cooling power, progressively decreasing performance for radiators farther from the fans. The farthest radiator may have cooling power up to 33% lower than the nearest radiator, accompanied by a reduced heat transfer coefficient [2,71,101].

The location of the fresh air intake relative to the oil inlet is another critical factor. In horizontal ventilation, fresh air enters with high velocity near the radiator’s upper section, directly cooling the hottest oil from the top-mounted inlet. In vertical ventilation, fresh air enters from the bottom, exchanging heat with the coldest oil before reaching the hotter oil. This arrangement resembles a counterflow heat exchanger, where oil flows downward while air flows upward, theoretically enhancing performance. However, CFD simulations indicate that the crossflow generated in horizontal ventilation produces improved results.

Conversely, through experimental methods, Rogora et al. [104] demonstrated that vertical ventilation provides better cooling performance than horizontal ventilation. However, they emphasized that this should not be regarded as a general conclusion, particularly when considering variations in the height of the plates. For shorter plates using the same fans, it is expected that the efficiency of both orientations might equalize, and in some cases, horizontally blowing fans could even achieve greater efficiency.

Not-Only Directional Ventilation

In addition to horizontal or vertical directional ventilation, various configurations of fan placements were studied.

Table 8. Summary of analysed cases with non-unidirectional ventilation setups.

Author	Scheme	Fans	Radiator Block	Oil Flow Rate [m3/s]	Cooling Power [kW]	Heat Transfer Coefficient [W/m2·K]	Factor of Merit
[102]		$T_{\mathrm{amb}}$ = 39.8 °C; Diameter 1000 mm; 2 fans; 7 blades; 860 RPM; no casing	$T_{\mathrm{top},\mathrm{rad}}$ = 56.1 C; Nr = 4 radiators; L = 3000 mm; D = 50 mm; N = 30	-	63	16.8	-
				-	59.5	16	-
[2]		$T_{\mathrm{amb}}$ = 20 °C; Diameter 600 mm; 2 fans; 4 blades; 550 RPM; With casing; Power consumption unit: 122.58 W	$T_{\mathrm{oil},\mathrm{in}}$ = 75 °C; Nr = 5 radiators; L = 2348 mm; D = 35 mm; N = 30	0.00074 0.00221 0.00369 0.00516	165.27 216.22 225.44 228.68	8.11 10.52 10.97 11.13	674.13 881.96 919.56 932.78
				0.00074 0.00221 0.00369 0.00516	189.32 250.20 261.60 265.10	9.21 12.17 12.73 12.92	772.23 1020.56 1067.06 1082.34
				0.00074 0.00221 0.00369 0.00516	195.76 257.73 269.77 273.55	9.49 12.53 13.12 13.40	798.50 1051.27 1110.38 1115.80
				0.00074 0.00221 0.00369 0.00516	183.26 242.52 254.91 258.85	8.92 11.80 12.40 12.59	747.51 989.23 1039.77 1055.84
				0.00074 0.00221 0.00369 0.00516	194.10 259.60 273.53 278.07	9.48 12.63 13.31 13.53	791.73 1058.90 1115.72 1134.24
				0.00074 0.00221 0.00369 0.00516	201.29 263.73 278.81 279.64	9.79 12.83 13.57 13.65	821.06 1075.75 1137.26 1140.64
				0.00074 0.00221 0.00369 0.00516	164.64 222.04 234.38 238.69	8.01 10.80 11.40 11.61	671.56 905.69 956.03 973.61
				0.00074 0.00221 0.00369 0.00516	181.36 243.52 259.06 263.46	8.82 11.85 12.60 12.82	739.76 993.31 1056.70 1074.65
				0.00074 0.00221 0.00369 0.00516	190.16 253.26 267.50 271.79	9.25 12.32 13.02 13.22	775.66 1033.04 1091.12 1108.62

summarises eleven cases from two different studies examining non-unidirectional ventilation setups.

An analysis of the table reveals that the studies evaluated configurations with two to six fans and radiator blocks containing four or five radiators. The fin heights ranged from 2348 mm to 3000 mm, with 30 fins per radiator and fin spacing between 35 mm and 50 mm. Regarding the fans, diameters varied from 600 mm to 1000 mm, operating at speeds of 550 to 850 RPM, with both cased and uncased designs included in the analysis.

Paramane et al. [102] tested horizontal opposite airflow in two configurations: aligned and vertically displaced fans. In the aligned configuration, the airflow is directed outward to the top and bottom of the radiator block, resulting in significant leakage and forming a vertical airflow pattern in the middle radiators. This symmetrical pattern resembles a “wall” dividing the radiator group at its centre. In the vertically displaced configuration, the left fan directs airflow toward the lower portion of the radiator, while the right fan targets the upper section. The two air streams meet at the radiator’s centre, creating a slightly inclined flow: downward from the left fan and upward from the right. Compared to purely one-directional ventilation, the study concluded that opposite fan placement, whether aligned or displaced, reduces heat dissipation efficiency.

Kim et al. [2] proposed a novel approach by testing hybrid directional fan placements, utilising fans for both vertical and horizontal ventilation simultaneously. Typically, AF cooling for transformers places fans on one side of the radiator for easy manufacturing and transportation. However, as transformer capacity increases, effective cooling becomes more challenging, often requiring over-designed systems with more radiators due to limited fan placement space. To address this, the study introduced a hybrid cooling system using an ODAF cooling system, with fans positioned on both the horizontal and vertical sides of the radiator to improve efficiency. The study evaluated nine configurations, varying fan positions across three locations at the bottom for vertical ventilation and on the right side for horizontal ventilation. Configurations with fans placed close to each other generated counterflow, where airflow directed away from the radiator opposed the intended airflow. Although most air still moved toward the top of the radiator, where temperatures are higher due to the oil inlet, this counterflow reduced efficiency. Conversely, configurations with fans placed further apart avoided counterflow, minimising air waste and improving cooling performance. Two specific setups demonstrated enhanced cooling power: one with a fan at the bottom centre of the radiator block and another with a side fan positioned near the bottom and middle. The latter configuration showed the best cooling power despite creating some counterflow, likely due to the larger blown area around the radiator. These effects were consistent across all oil mass flow rates tested, ranging from 0.74 × ${10}^{-3}$ to 5.16 × ${10}^{-3}$ m³/s.

Offset Between Fans Centres

Paramane et al. [102] explored the impact of fan positioning by examining two configurations: one with fans aligned and another with a 50 mm offset between the centres of the first and last fans. The offset configuration resulted in a 3% increase in cooling power and a 1.5% improvement in the merit factor. These results suggest that adjusting fan alignment could offer a low-cost improvement with modest but worthwhile benefits, warranting further investigation.

Fan Speed and Diameter

Data from Paramane et al. [102] (Table 7) highlight the influence of fan speed and diameter on radiator performance. For fans of the same diameter, increasing fan speed from 940 RPM to 1130 RPM (or from 700 RPM to 900 RPM) led to an average 15.7% improvement in cooling power for three 500 mm diameter fans, alongside a 20.2% increase in fan speed. For three 610 mm diameter fans, the cooling power improved by approximately 23%, with a 28.6% increase in fan speed, indicating a positive correlation between cooling power and fan speed. Another test involved two 610 mm diameter fans operating at 900 RPM in horizontal ventilation. This setup achieved cooling power comparable to three 610 mm diameter fans operating at 700 RPM under the same conditions. While using two fans is more cost-effective, employing three fans may provide excellent reliability in case of a malfunction.

Furthermore, a different study evaluated the fan diameter in vertical ventilation, assuming the same airflow from different diameter fans, from 800 to 1500 mm; the findings noticed an advantage of using smaller fans with higher quantities over bigger fans with smaller quantities [105].

Fan Malfunction

A primary concern in fan-based cooling systems is the potential for malfunctions. If a fan fails, the radiator’s cooling efficiency diminishes, potentially causing damage to the power transformer. While various methods have been developed to detect fan failures [93,106,107], it is equally important to understand the impact of these failures on the radiator block’s overall cooling performance.

Table 9. Summary of cases analysing fan malfunctions in single-directional horizontal and vertical ventilation configurations.

Scheme	Fans	Radiator Block	Cooling Power [kW]
	$T_{amb}$ = 50 °C; Diameter 500 mm; 3 fans; $v_{\mathrm{air}}$ = 7 m/s.	Nr = 4 radiators; L = 2600 mm; N = 14.	39.4
			40.2
			36.7
			40.7

summarises four cases that tested different malfunction scenarios in a three-fan configuration, considering vertical and horizontal single-directional ventilation setups [103].

The study presented in the four scenarios of Table 9 revealed that the failure of one fan significantly impacts the cooling efficiency of the radiator block, depending on the position of the non-operational fan and the type of ventilation (horizontal or vertical). When the middle fan fails, cooling efficiency decreases by approximately 23% in the vertical and 28% in the horizontal systems. Conversely, the failure of the third fan (from left to right) in the vertical system, corresponding to the bottom fan in the horizontal system, results in a reduction of approximately 29% and 27%, respectively.

In the horizontal ventilation system, the upper portion of the radiator is the hottest, making the middle fan particularly critical for maintaining performance. In contrast, in the vertical ventilation system, the impact of the middle fan’s failure is less pronounced due to airflow from the outer fans, which partially compensates for the absence of the central fan. However, the failure of one of the outer fans has a more detrimental effect, as the radiator directly above the non-operational fan receives no airflow, significantly reducing the cooling capacity of the radiator block.

4.3.2. Passive Cooling Strategies for Improved Performance

ONAN-type transformers rely on natural convection for cooling, without the use of fans or other active devices. While research has focused on improving passive cooling performance, a significant gap in the literature persists, underscoring the need for further investigation.

Table 10. Influence of radiator’s enhancements.

Author	Enhancement Representation	Radiator Block	Enhancements	${\mathit{T}}_{\mathrm{amb}}$ [°C]	Toil [°C]	Impact on Power Cooling [kW]
[20]		L = 1200 mm; W = 520 mm; N = 14; e = 6 mm	ChimneyWind Deflector	25	-	(+14.76%)
[81]		L = 1200 mm; W = 520 mm; N = 14; e = 6 mm; d = 45 mm	ChimneyWind Deflector	24.85	69.9	(+26.54%)
[82]		L = 1800 mm; W = 500 mm; N = 26; e = 8 mm	Turbulators used in the middle of the oil channel	29.85	69.85	-
[82]		L = 1800 mm; W = 500 mm; N = 26; e = 8 mm	Wall indentators	29.85	69.85	(+36%)
[18]		L = 2400 mm; W = 979 mm; N = 18; e = 11.9 mm	Trapezoidal radiator + panel area expansion	25.5	69.89	12.9 (+16.9%)
[18]		L = 2400 mm; W = 979 mm; N = 18; e = 11.9 mm	Trapezoidal radiator	25.5	69.89	12.2 (+10.2%)
[18]		L = 2400 mm; W = 979 mm; N = 18; e = 11.9 mm	ChimneyTrapezoidal radiator + panel area expansion	25.5	69.89	15.4 (+39.5%)
[13]		-	Water film on the outer wall of the heat exchanger	25	-	-

summarises various enhancement methods and their impact on cooling capacity.

The use of a chimney cap is one of the most widely adopted strategies, as researched in [18,20,81]. This approach leverages the chimney effect, where pressure differences naturally increase airflow, improving heat transfer from radiator walls to the surrounding air. Chimney caps can also be combined with other features to boost cooling efficiency further. For example, studies in [18,20] examined the addition of wind deflectors, which enhance pressure differences along the radiator’s length, resulting in cooling capacity improvements of 14.76% and 26.54%, respectively. Further analysis in [18] evaluated profiling the bottom edge of the radiators at a 30° angle to the ground. This adjustment alone improved cooling capacity by 10.2%. When combined with a 12.9% increase in panel surface area, the improvement rose to 16.9%. Adding a chimney cap to these modifications increased the overall cooling capacity to 39.5%. Pairing these modifications with a chimney cap significantly increased the overall cooling capacity, reaching 39.5%. These findings highlight the considerable impact of chimney caps on cooling performance.

Research in [82] explored the use of turbulators inside radiator channels and indentations on the walls. While turbulators improved cooling by inducing secondary flows, they also impeded oil flow in ON systems, limiting their practicality. Conversely, triangular-prismatic wall indentations enhanced the thermo-fluid dynamic performance of the oil channels by 36%, making them a more effective solution.

A different approach in [13] investigated applying a water film to the outer radiator wall. Although the study did not quantify cooling capacity improvements, it reported significant reductions in top oil and hotspot temperatures (31.2 °C and 28.7 °C, respectively). It increased the air-side heat transfer coefficient to 50 W/(m²·K).

Research on passive cooling enhancements for ONAN transformers highlights several strategies to improve performance without active components. Combining chimney caps, trapezoidal radiator profiles, and increased panel area has emerged as the most impactful solution (+36%). Additionally, wall indentations and water films show substantial potential, though further research is needed to optimise their application fully. These findings underscore the effectiveness of integrating external and internal modifications to achieve superior cooling performance.

5. Radiator Modelling Approaches

Understanding and predicting the thermal behaviour of the radiators is essential for ensuring the efficiency and reliability of power transformers. To this end, various modelling approaches have been employed, including numerical, analytical, and experimental methods.

Calculating the heat transfer coefficient is critical in numerical and analytical models, as it determines the rate at which energy is dissipated between interacting surfaces or fluids. Improving this coefficient directly translates to a better cooling capacity for the radiator.

Table 11. Summary of heat transfer coefficient calculation methods.

Author	Radiator Block	Heat Transfer Coefficient and Nusselt Number
[19]	Convective; Oil	$h=1.3\times {(T_{\mathrm{avg}}-T_{\mathrm{amb}})}^{0.41}$
[91]	Convective; Oil	$h=N{u}_{\mathrm{oil}}\times (k_{\mathrm{oil}}/D_{\mathrm{h}})$ $N{u}_{\mathrm{oil}}=0.85\left(0.74R{e}_{\mathrm{oil}}^{0.2}{\left(P{r}_{\mathrm{oil}}G{r}_{\mathrm{oil}}\right)}^{0.1}P{r}_{\mathrm{oil}}^{0.2}\right)$
[77]	Convective; Oil; End-fins	$h_1=N{u}_{\mathrm{L}}\times (k_{\mathrm{oil}}/L)$ $N{u}_1={(0.85+{\displaystyle \frac{0.387R{a}_{\mathrm{L}}^{1/6}}{(1+{(0.492/Pr)}^{9/16})8/27}})}^2$
[77]	Convective; Oil; Inner-fins	$h_2=N{u}_{\mathrm{L}}\times (k_{\mathrm{oil}}/S)$ $N{u}_2={\displaystyle \frac{1}{24}}R{a}_2(S/L)$, for S/L = 0
[90]	Convective; Overall	$h=({(1/\rho c_{\mathrm{p}}Q)}_{\mathrm{oil}}-{(1/\rho c_{\mathrm{p}}Q)}_{\mathrm{air}})$
[91]	Convective; Air	$h_{\mathrm{conv}}=N{u}_{\mathrm{air}}\times (k_{\mathrm{air}}/L)$ $N{u}_1={(0.85+{\displaystyle \frac{0.387R{a}_{\mathrm{L}}^{1/6}}{(1+{(0.492/Pr)}^{9/16})8/27}})}^2$
[91]	Conduction; Steel	$h_{\mathrm{cond}}=K_{\mathrm{steel}}/t$ $N{u}_1={(0.85+{\displaystyle \frac{0.387R{a}_{\mathrm{L}}^{1/6}}{(1+{(0.492/Pr)}^{9/16})8/27}})}^2$
[19]	Radiation	$h_{\mathrm{rad}}=(A_{\mathrm{out}}/A)\times ϵ\times \sigma \times (T_{\mathrm{avg}}^2+$ $T_{\mathrm{amb}}^2)(T_{\mathrm{avg}}+T_{\mathrm{amb}})$
[91]	Overall	$h^{-1}=h_{\mathrm{oil}}^{-1}+h_{\mathrm{steel}}^{-1}+h_{\mathrm{air}}^{-1}$

Where: h, Heat Transfer Coefficient (W/(m²K)); T_avg, Average liquid temperature (°C); T_amb, Ambient temperature (°C); Nu, Nusselt Number; Re, Reynold Number; Pr, Prandtl Number; Gr, Grashof Number; Ra, Rayleigh Number; S, Gap between fins (mm); L, Length of the fin (mm); t, Fin thickness (mm); ρ, Fluid density kg/m³; c_p, Specific heat capacity (J/(kg·K)); and Q, Fluid flow rate (m³/s).

presents a comparative analysis of the different methods and considerations to calculate this coefficient.

Most studies treat the convective heat transfer coefficient as the overall heat transfer coefficient. This simplification often neglects the conduction through the fin material, radiation losses, or even both, as it is typically assumed that the thickness of the fin wall is negligible and the radiation losses are minimal. However, it has been concluded in [19] that the conduction and the radiation losses represent 10% and up to 21.9% (depending on the cooling system) of the total heat dissipation process, so ignoring these two processes can lead to inaccurate prediction of the radiator’s cooling capacity. For instance, in [90,91], the overall heat transfer coefficient is calculated by considering both the conduction of the steel walls and the convection of oil and air, whereas in [19], only the convection of the oil and the radiation losses are considered. Even with different heat transfer processes taken into consideration, the most common way to calculate this coefficient is to consider the radiator as a whole unit; however, in [78], a distinction is made between the end-fins located at each extremity of the radiator, and inner fins, located between extremities. The radiator is considered a vertical flat plane for the end fins, the same consideration used by [90,91]. On the contrary, in the inner fins, the airflow is assumed to be fully developed, and the boundary layers are merged due to the extended length of the radiator compared to the distance between fins. Despite variations in the processes considered, most studies rely on empirical equations to calculate the heat transfer coefficient and the Nusselt number. An exception is shown in [19], which employs CFD to estimate the convective heat transfer coefficient.

5.1. Analytical Modelling Techniques

Analytical models for radiators have garnered limited attention in the literature [78,84], making them a relatively under-explored area of study. While the number of available studies is modest, some researchers have made significant strides in developing models to predict critical radiator parameters, including outlet temperature ($T_{\mathrm{outlet}}$), inlet temperature ($T_{\mathrm{inlet}}$), and overall heat dissipation. Additionally, the literature highlights alternative reduced analytical models, which offer simplified yet effective approaches to understanding radiator performance [90,91]. These contributions provide a foundational framework for further research and practical applications in thermal management systems.

Table 12. Analytical heat exchanger models.

Author	Category	Inputs	Fluid Properties
[84]	Oil	$T_{\mathrm{amb}}=[20-25.3]$ °C $T_{\mathrm{inlet}}=[37.8-76.2]$ °C $\dot{m}=[0.0134-0.0370]\mathrm{kg}/\mathrm{s}$ $O=$ N.S.	-
[78]	Oil	$T_{\mathrm{amb}}$ = 20 °C; $T_{\mathrm{inlet}}$ = 75 °C $Q_{\mathrm{oil}}=[1-4]\times {10}^{-3}{\mathrm{m}}^3/\mathrm{s}$ $N=40$; $L=3300\mathrm{mm}$; $D=45\mathrm{mm};$ $O=\mathrm{N}.\mathrm{S}.$	$\rho =1067.75-0.6376T\left[{\mathrm{kg}/\mathrm{m}}^3\right]$ $k=15217-7.16\times {10}^{-5}T\left[\mathrm{W}/\mathrm{m}\mathrm{K}\right]$ $c_{\mathrm{p}}=821.19+3.563T\left[\mathrm{J}/(\mathrm{kg}\mathrm{K})\right]$
[90]	Oil	$T_{\mathrm{amb}}$ = 22 °C; $T_{\mathrm{inlet}}$ = 62 °C $L=2700\mathrm{mm}$; $W=520\mathrm{mm}$ $D=50\mathrm{mm}$; $A=325{\mathrm{mm}}^2$; $O=\mathrm{N}.\mathrm{S}.$	-

summarizes the input conditions and fluid properties used in the studies that developed analytical models.

Table 13. Summary of analytical models developed for calculating oil flow rate, temperature, and heat dissipation.

Author	Flow Rate (m3/s)	Temperature Prediction (°C)	Heat Dissipation (W)
[84]	-	$T\left(z\right)=T_{\mathrm{amb}}+(T_{\mathrm{top}}-T_{\mathrm{amb}})e^{{\displaystyle \frac{-h\times O\times z}{m\times c_{\mathrm{p}}}}}$ $T_{\mathrm{inlet}}=T\left(0\right)=T_{\mathrm{amb}}+(T_{\mathrm{top}}-T_{\mathrm{amb}})=T_{\mathrm{top}}$ $T\left(L\right)=T_{\mathrm{amb}}+(T_{\mathrm{top}}-T_{\mathrm{amb}})e^{{\displaystyle \frac{-h\times O\times L}{m\times c_{\mathrm{p}}}}}$	$P=(T_{\mathrm{inlet}}-T_{\mathrm{outlet}})\times \dot{m}\times c_{\mathrm{p}}$
[78]	$Q_{\mathrm{oil}}\left(N\right)=(1.409-0.031N+0.000416N^2){\displaystyle \frac{Q_{\mathrm{total}}}{Ntotal}}$		On individual fins $P_{\mathrm{fin}}\left(N\right)=(T_{\mathrm{top}}-T_{\mathrm{amb}})(1-e^{{\displaystyle \frac{hfO}{p{c}_{\mathrm{p}}{Q}_{\mathrm{oil}}\left(N\right))}}L})$ Overall $P_{\mathrm{total}}=p\times c_{\mathrm{p}}\times Q_{\mathrm{oil}}(T_{\mathrm{top}}-T_{\mathrm{amb}})((1-e^{{\displaystyle \frac{hfO}{p{c}_{\mathrm{p}}{Q}_{\mathrm{oil}}\left(N\right))}}L})$
[90]	$Q_{\mathrm{oil}}={\displaystyle \frac{\Delta p}{L}}\times {\displaystyle \frac{1/}{\rho \times v_{\mathrm{oil}}}}\times {\displaystyle \frac{32A^3}{\eta \times P{e}^2}}$	-	$P={(\rho \times c_{\mathrm{p}}\times Q\times \Delta T)}_{\mathrm{oil}}$

presents the analytical models developed in the same studies for oil flow rate calculations, temperature, and heat dissipation. The key parameters used in these models include oil mass flow rate ($\dot{m}$) in kg/s, radiator outlet temperature ($T_{\mathrm{outlet}}$200B) and inlet temperature ($T_{\mathrm{inlet}}$200B) in °C, circumference of the radiator cross-section (O) in meters, radiator overall passage perimeter ($P_e$200B) in meters, and overall passage area (A) in square meters, for parameters not specified the nomenclature (N.S) was used. Other important variables are air flow rate ($Q_{\mathrm{air}}$200B) and oil flow rate ($Q_{\mathrm{oil}}$200B) in cubic meters per second, average air velocity ($U_{\mathrm{air}}$200B) and oil velocity ($U_{\mathrm{oil}}$) in meters per second, a dimensionless constant ($\eta$) dependent on the channel section shape, and pressure difference ($\Delta p$). Additionally, the models consider heat transfer coefficient of a fin ($h_f$200B) in watts per square meter-kelvin, total cooling capacity (P) in kilowatts, and cooling capacity of a fin ($P_{\mathrm{fin}}$200B) in kilowatts.

An analysis of the table reveals that many analytical approaches share similarities, though the sources and input parameters can vary across studies. For example, input parameters such as $T_{\mathrm{amb}}$, $T_{\mathrm{inlet}}$, and $\dot{m}$ are often derived from experimental data [84]. In some cases, $T_{\mathrm{amb}}$ and $T_{\mathrm{inlet}}$ are defined to ensure compliance with a temperature rise limit of 55 °C between $T_{\mathrm{amb}}$ and $T_{\mathrm{inlet}}$ [78,108,109]. However, Wang et al. do not specify the sources of these input parameters [90].

Calculating fluid properties, such as density, thermal conductivity, and specific heat, also exhibits slight variations. For instance, Kim et al. [78,91] employ the same model, while [90] uses a different approach. However, the rationale behind the selection of these models is not discussed in the studies [90].

Regarding oil flow rates, one approach derives a function from a CFD model to calculate the flow rate for each fin, enabling a detailed flow distribution analysis as described by Kim et al. [78]. Another method, presented by Wang et al. [90], directly calculates the total flow rate.

A commonly used method to calculate oil temperatures within the radiator involves a function that depends on the vertical height from the top to the bottom of the radiator, as illustrated in Figure 10. This approach facilitates the determination of both inlet ($T_{\mathrm{inlet}}$) and outlet ($T_{\mathrm{outlet}}$) temperatures [78,84]. One iterative method uses input parameters such as ambient temperature ($T_{\mathrm{amb}}$), inlet temperature ($T_{\mathrm{inlet}}$), and an initial average oil temperature ($T_{\mathrm{avg}}$) in analytical calculations to derive coefficients including the heat transfer coefficient (h), radiative heat transfer coefficient ($h_{\mathrm{rad}}$), and convective heat transfer coefficient ($h_{\mathrm{conv}}$). These coefficients are then used to refine $T_{\mathrm{avg}}$, enabling the calculation of the outlet oil temperature ($T_{\mathrm{outlet}}$) [84].

The oil enters at the top with an inlet temperature ($T_{\mathrm{inlet}}$, z = 0) and flows downward, gradually cooling as it reaches the bottom, exiting with an outlet temperature ($T_{\mathrm{outlet}}$, z = L). The function T(z) represents the temperature variation along the height (z) of the radiator.

Heat dissipation calculations generally follow a consistent methodology across the reviewed studies, utilizing a standard equation as shown in [84,90]. However, Kim et al. [78] proposes a unique approach that calculates each fin’s heat dissipation and then sums up these contributions to determine the total dissipation.

The accuracy of analytical results for radiator systems strongly depends on the equations and assumptions applied. For instance, one study reported an average deviation of 3.4% between analytical and numerical results, considered highly accurate due to the inclusion of radiative effects and coefficient equations outlined in Table 11 [84]. Conversely, another study observed significant discrepancies, with deviations of 13.4% from CFD results and 31.6% from experimental data, highlighting the potential for incorrect conclusions if solely relying on analytical methods [78].

5.2. Numerical Simulation Approaches

CFD is a widely used and reliable tool for analysing and improving heat transfer mechanisms. It has been extensively validated and is frequently applied to radiator cooling system studies, particularly in power transformers. CFD remains indispensable despite ongoing efforts to develop mathematical models that offer faster results and provide design guidelines for transformer cooling systems [79]. Its high precision and reliability make it a crucial tool for simulating and optimising radiator performance. CFD not only evaluates conventional designs but also facilitates the exploration of innovative cooling strategies. These include passive enhancements, such as optimising radiator dimensions, and active methods, like advanced fan placement. Achieving accurate and validated results requires defining an appropriate computational domain with sufficient detail to meet study objectives without imposing excessive computational demands. Many reviewed studies lack detailed information about the computational domain’s dimensions relative to the size of the analysed object. In [101], the independence of computational domain dimensions was addressed; however, further clarity is needed, especially regarding the ratio between the computational domain and the object of study. This gap was highlighted by COST 732 [110] in case studies of buildings, but its principle was also applied to radiator case studies [1,83]. Additionally, it has been observed that the dimensions of computational domains in AF systems remain consistent across horizontal and vertical ventilation configurations, with no significant variations in length or height. Beyond computational domain dimensions, boundary conditions are equally critical in CFD simulations. These typically include parameters such as inlet oil temperature, radiator mass flow rate, and ambient air temperature, all of which can be experimentally measured. Properly defining these conditions is fundamental to creating a reliable simulation environment. To the best of our knowledge, among the reviewed studies, only Ansys Fluent and Ansys CFX have been used to investigate power transformer cooling systems, except [79,91], which utilised open-access software.

Table 14. Simulation considerations from the evaluated studies summary.

Article	Simulation Considerations	Av. Error Compared with Experimental: Cooling Power (%)	Goal
[71]	Turbulence model: standard $k-ϵ$; Velocity-pressure coupling (SIMPLE); Natural convection: Boussinesq approximation; Conjugation of heat transfer and fluid flow in the geometry of radiators: PMA (Porous Media Approach); Software: ANSYS FLUENT 13.0	5.15%	Compare Horizontal and Vertical ventilation
[102]	Turbulence model: Shear Stress Transport (SST); Eddy viscosity; Radiation: Calculated by DTM - Discrete Transfer Model; Software: Ansys CFXV. 12.1	No experimentally validated	Compare four different cooling fan configurations
[2]	Turbulence model: standard $k-ϵ$; Velocity-pressure coupling (SIMPLE); Natural convection: Boussinesq approximation; Conjugation of heat transfer and fluid flow in the geometry of radiators: PMA (Porous Media Approach); Software: ANSYS FLUENT 13.0	5.15%	Compare nine different cooling fan configurations
[80]	Turbulence model: Shear Stress Transport (SST); Software: Commercial flow solver (not specified)	6.05%	Compare Horizontal and Vertical ventilation and uncentered fans
[90]	Radiation: Not considered; Software: ANSYS product (not specified)	No experimentally validated	Investigating temperature rise characteristics of radiators
[18]	Turbulence model: Shear Stress Transport (SST); Radiation: Calculated by DTM; Software: Ansys Fluent 18.0	No experimentally validated	Study new radiator design options
[101]	Turbulence model: Shear Stress Transport (SST); Radiation: Calculated by DTM; Software: Ansys CFX 12.1	17.35%	Compare Horizontal and Vertical ventilation
[79]	Turbulence model: Germano’s model [111] (LES); Velocity-pressure coupling (SIMPLEC); Software: HPC CFD Code Saturne	Validated but do not compare the values with experimental data	Reduced model validation
[1]	Turbulence model: k-w SST; Pressure discretisation (PRESTO); Software: Ansys Fluent 2023 R1©; Radiation: Surface to Surface (S2S)—Ray Tracing	7.90%	Parametric study and optimization design of radiators (Oil and air simulation)
[83]	Turbulence model: k-w SST; Pressure discretisation (PRESTO); Software: Ansys Fluent 2023 R1©; Radiation: Surface to Surface (S2S)—Ray Tracing	9.80%	Parametric study and optimization design of radiators to train artificial neural networks to cooling power estimation
[91]	Turbulence model: LES; Velocity-pressure coupling (SIMPLEC);	30.00 %	Analyse the cooling capacity, validate the numerical simulation and calculation procedures for further design on a radiator with ONAN mode

summarises the key model parameters and conditions, including turbulence models, solvers, approach techniques, and average errors compared to experimental data and study objectives.

The studies presented in Table 14 indicate that in natural convection simulations, the Boussinesq approximation is commonly used to model buoyancy-driven flows [1,79,83], reducing computational costs compared to solving the fully compressible Navier–Stokes equations. A key distinction among these studies lies in their treatment of radiation. For instance, optimisation studies on radiator properties conducted by [1,83] incorporated surface-to-surface ray-tracing models to account for radiative heat transfer, thereby enhancing simulation accuracy. In contrast, the reduced radiator model developed in [91] excluded radiation effects, which can significantly impact results. Supporting this observation, previous research has demonstrated that radiation effects can influence simulation outcomes by up to 22% [19] and 24% [112]. For forced air systems, various approaches are employed to evaluate airflow. Some researchers specify a fixed air velocity for the airflow generated by the fans [90]. In contrast, others use fan modulation, where airflow is determined by operational characteristics such as fan speed (RPM), diameter, and pressure differential [1,83]. One effective technique is the Rotating Frame of Reference (RFR) [113], which uses a frozen rotor interface to simulate interactions between stationary and rotating domains. This approach involves a rotating fluid subdomain around the fan at an angular velocity matching the fan’s speed, significantly reducing computational power and simulation time [80,101,102]. Another widely used strategy is the Porous Media Approach (PMA) [105], simplifying mesh complexity by modelling the radiator as a porous medium. This method reduces computational resource demands, saving time and costs while maintaining accuracy in conjugate heat transfer and fluid flow simulations for complex radiator geometries. When examining deviations between numerical and experimental data, some studies experimentally fail to validate their CFD models, leaving their methodologies’ reliability unconfirmed [18,90,102,103]. In contrast, most studies that undergo experimental validation report deviations below 10%, providing reliable predictions of radiator cooling capacity [1,2,80,83]. However, a few studies report significantly higher deviations, such as 17% [101] and 30% [91], raising concerns about the robustness of their methodologies.

5.3. Experimental Validation and Testing

Developing experimental models for real-world heat exchangers faces challenges such as complex phenomena (e.g., turbulence) and limited data-driven models, which often struggle with generalisation and data quality [114,115]. Calibration issues, like those in molecular dynamics, further complicate predictions [116]. Advances in experimental techniques and analytics offer solutions to improve model accuracy and reliability, such as Particle Image Velocimetry (PIV) for airflow visualisation and infrared thermography for thermal mapping, further enhancing experimental validation’s accuracy and depth [117]. In several studies discussed in this chapter, the primary goal is to measure the performance of radiators using CFD. Various experimental setups have been designed to gather essential data for model validation. Most of these setups utilise an oil tank equipped with an electric heater to simulate the heat losses experienced in a power transformers’ tank [2,71,80,101]. However, using an electric heater directly with the oil can lead to oil degradation. To address this problem, an oil treatment plant with temperature and oil flow control mechanisms was introduced as a better alternative [1,83].

The most commonly measured parameters include the inlet and outlet temperatures of the radiator, which are typically recorded using K-type thermocouples positioned at the upper and lower collectors (or headers) of the radiator [2,71,79,80,101]. In some studies, PT100 resistance temperature detectors (RTDs) are used to measure the same temperatures [1,83,104]. In addition to temperature, the oil flow rate is often measured using an ultrasonic flow meter, typically installed at either the upper or lower collector [80,101,104]. While some studies refer to flow meters without specifying the type [101], others employ a pump to control the oil flow rate [2,71]. Furthermore, thermal imaging cameras are commonly used to evaluate the temperature distribution across the radiator, providing a visual representation of its thermal performance [1,83].

Key parameters such as airflow velocity, air temperature, and fan performance are also measured to enhance the understanding of radiator cooling efficiency. For example, airflow velocity and temperature are commonly measured using a hot-wire anemometer with an 8 mm diameter probe. This probe is typically positioned 200 mm from the centre of the radiator’s collector in a vertical fan configuration, allowing for accurate capture of airflow dynamics [79,91].

Beyond radiator performance, experimental studies often analyse fan behaviour to understand its airflow characteristics under different operating conditions. Airflow measurements are taken across various cross-sectional areas at the fan’s outlet using anemometers, with the measurements summed to calculate the total air mass flow rate generated by the fan [80]. Such data are instrumental in optimizing fan design and placement to enhance radiator performance.

Rogora et al. [104] presented an experimental study evaluating multiple radiator blocks with different radiator types and fan configurations. One of the study’s key objectives was to assess the oil pressure drop across the radiators. For this purpose, FS-type pressure sensors were employed, providing detailed insights into the relationship between radiator design and oil flow dynamics.

5.4. AI/Neural Networks

Artificial intelligence (AI) methods are increasingly used to improve the design and sizing of radiators, delivering accurate results while reducing costs and time compared to traditional approaches. However, to date, only Koca et al. [83] have developed an artificial neural network (ANN) model using a multilayer perceptron (MLP) [118] to evaluate and predict radiator cooling capacity. The dataset comprised 49 data points, with 39 used for training and 10 for testing. Key design parameters, such as N (number of elements) and L (length, in mm), were included in the analysis. The MLP network architecture consists of three main components: an input layer, a hidden layer, and an output layer. The input layer receives the parameters N and L as inputs. These inputs are processed by a hidden layer containing 16 neurons, which use Tan-Sig activation functions to model non-linear relationships. Finally, the output layer, comprising a single neuron with a Purelin (linear) activation function [119], produces the predicted total cooling capacity (QT, in W).

The network operates through a forward pass, where data flows from the input to the output layer. Neurons apply weights and biases to the input data and process it using activation functions. Bayesian regularisation [120] was employed as the training algorithm to minimise overfitting, leveraging a probabilistic framework for improved model generalisation. In comparison, alternative algorithms, such as Levenberg–Marquardt and Scaled Conjugate Gradient, were less effective.

This ANN model demonstrated high accuracy in predicting radiator cooling capacity. It achieved a mean absolute deviation (MoD) close to zero and a coefficient of determination (R2) of 0.99930. Additional performance metrics, including a mean squared error of 1.32E-02, further validated its reliability. The ANN model’s predictions were closely aligned with CFD data, showcasing its effectiveness as a cost- and time-efficient radiator design and sizing alternative. The symbolic configuration of the MLP network, as developed by Koca et al. [83], includes interconnected neurons organised in layers. The input layer receives N and L parameters, while the hidden layer captures complex relationships using the activation functions. The output layer generates the final prediction of cooling capacity. This architecture effectively bridges input parameters to output predictions, ensuring precision in radiator performance modelling.

6. Conclusions

This review presents a comprehensive and systematic analysis of the advancements, challenges, and opportunities in cooling technologies for power transformers. By synthesizing insights into design innovations, monitoring methodologies, and sustainability-focused strategies, it identifies critical gaps in the literature while offering a roadmap for future research and practical applications holding significant practical implications for industry professionals. For instance, the analysis of advanced radiator designs and hybrid cooling systems provides actionable insights for enhancing transformer efficiency while reducing environmental impact. Additionally, the incorporation of artificial intelligence in thermal management can inform predictive maintenance strategies, enabling more reliable and cost-effective transformer operations. These outcomes underscore the potential of integrating innovative technologies and sustainability-focused strategies to address the industry’s evolving challenges.

The choice of transformer type remains fundamental. Core-type transformers are ideal for high-power applications due to their cost-effectiveness and ease of maintenance, while shell-type designs offer superior magnetic and thermal performance for medium- and low-power scenarios. OD designs exhibit the highest cooling capacity and uniform temperature distribution among cooling systems, whereas ON systems prioritise reliability at the expense of lower performance. Despite achieving higher flow rates, OF systems are hindered by oil bypass, highlighting the need for design optimisations.

The study emphasises significant advancements in cooling fluids, such as biodegradable esters and nanofluids, which improve thermal and dielectric properties while supporting sustainability goals. However, the stability of nanoparticles in insulating fluids remains a critical challenge that must be addressed before a comprehensive cost-benefit analysis can be conducted to assess the economic viability of large-scale production and widespread use. Despite its computational intensity, CFD has proven to be an essential tool for optimising fluid formulations and analysing cooling performance.

Radiator design plays a pivotal role in thermal performance, with parameters like fin height, spacing, and density directly influencing efficiency and cost. Innovative configurations, such as top-mounted radiators and chimney caps, offer promising efficiency gains and reduced land use, though their real-world applications require further exploration. Combining passive and active cooling strategies, such as dynamic fan setups and advanced profiling techniques, presents opportunities for synergistic performance improvements.

Monitoring methodologies reveal limitations in conventional analytical models, which often fail to capture the complexities of real-world operations. Advanced instrumentation, such as fibre optic sensors and infrared thermography, provides precise temperature monitoring but is constrained by high costs and scalability issues. Numerical approaches, particularly CFD, are useful for simulating complex thermal behaviours. At the same time, artificial intelligence (AI) models demonstrate significant promise for real-time predictions, bridging the gap between theoretical models and practical applications. Sustainability emerged as a core theme throughout the review. Biodegradable fluids, energy-efficient designs, and innovative cooling solutions form the foundation of environmentally friendly transformer systems. Addressing challenges such as climate change and growing energy demands will require optimising radiator designs, improving fan dynamics, and developing hybrid cooling systems to enhance performance while minimising environmental impact.

Future research with the greatest impact will address critical challenges in efficiency, sustainability, and technological innovation. One pressing area is understanding how rising external temperatures affect the cooling capacity of heat exchangers under natural convection. Optimizing radiator designs, particularly fin parameters and airflow dynamics in radiator blocks, could unlock cost reductions and performance improvements. Integrating passive strategies like advanced radiator profiling with active ventilation offers immense potential for reducing thermal hotspots and enhancing uniformity.

Concerning new ventilation designs, the choice of radiator configurations varies based on the specific characteristics of the power transformer. Due to this variability, the industry often favours simpler, well-established configurations that have demonstrated reliability over the past few decades. While new designs for passive cooling are emerging, they remain in the initial stages of development, with no established standards to guide their design, development, or implementation. This lack of standardization presents challenges for widespread adoption, making it essential for future efforts to focus on developing guidelines that ensure consistent, scalable, and efficient deployment of these innovative cooling solutions.

Dynamic optimisation of fan speeds correlated with ambient conditions is another key area affecting energy efficiency and reliability. By aligning fan operations with thermal loads and environmental changes, systems can achieve consistent cooling while minimising energy consumption and wear. Additionally, incorporating extractor fans into traditional setups could reduce air waste and improve airflow efficiency, though trade-offs such as increased maintenance complexity must be understood.

Advancements in CFD enable detailed simulations of complex systems, such as radiator blocks and hybrid ventilation setups, accounting for multiple variables like airflow interference and thermal interactions. This tool accelerates the development of innovative designs and enhances accuracy. Furthermore, applying neural networks represents a transformative approach to cooling system management. Neural networks are useful in analysing complex, nonlinear datasets and predicting behaviour under varying conditions. Their use in hotspot temperature prediction, dynamic load adaptation, and real-time monitoring offers scalable and adaptable solutions for thermal management, making them a focus for future research.

In summary, impactful future research will prioritise optimising thermal performance, energy efficiency, and adaptability while addressing global challenges such as climate change and sustainability. Integrating passive and active cooling strategies, enhancing ventilation dynamics with technologies like extractor fans, employing advanced neural network models for predictive insights, leveraging computational tools like CFD, and transitioning to environmentally friendly cooling fluids can revolutionise transformer cooling systems. These innovations will improve reliability and efficiency and contribute to a sustainable and technologically advanced future.