**1. Introduction**

In the last decades, a strong trend in the industry was shown toward miniaturization and natural resource management, mainly the energy and materials sources (enhancing the energy efficiency of the systems and reducing the equipment sizes are considered important roads to natural resource management reduce the demand for energy sources and minerals). In this, heat transfer systems are widely spread in industry applications, and the development of heat exchangers continues. The latter gave rise to advanced heat exchangers called "compact heat exchangers" involving compact plate heat exchangers (CPHEs) that contain channels with relatively small mean hydraulic diameters, presenting miniature dimensions but with higher heat transfer effectiveness [1,2]. The unique design of plate heat exchangers (PHEs) consists of several plates separating two different cold and hot fluids providing large heat transfer surfaces between them [3]. So far, several configuration types of PHEs were developed for enhancing the heat transfer effectiveness according to the requirements of industrial applications such as aircraft, electronics, chemicals, and other applications that contain cooling and heating equipment. The wavy shape of the plates in the chevron PHEs causes turbulent fluid flow inside the channels even for low Reynolds numbers (*Re*) [4], thus offering better heat transfer effectiveness compared to other normal heat exchangers [5]. However, micro/mini channels/passages that are used in the compact heat exchanger models provide bigger heat transfer surfaces but also higher pressure drops that need higher pumping power in the system [6]. Moreover, high heat loads are presented in those compact heat exchangers which require an innovative method

**Citation:** Ajeeb, W.; Murshed, S.M.S. Comparisons of Numerical and Experimental Investigations of the Thermal Performance of Al2O<sup>3</sup> and TiO<sup>2</sup> Nanofluids in a Compact Plate Heat Exchanger. *Nanomaterials* **2022**, *12*, 3634. https://doi.org/10.3390/ nano12203634

Academic Editors: Henrich Frielinghaus and Rajinder Pal

Received: 18 September 2022 Accepted: 13 October 2022 Published: 17 October 2022

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for intensively absorbing the heat from the surfaces. For this purpose, recent research in the field of thermal management systems, namely in compact heat exchangers, indicates to NFs as superior thermal fluids for enhancing the intensification of the heat transfer method [7]. Various types of nanoparticles have been used to produce NFs by mixing them with conventional heat transfer fluids, presenting various characteristics [8,9]. Besides the developed thermal conduction property of the NFs [10–12], there is an increase in the viscosity levels too, which is not preferable for heat exchangers due to the higher pumping power required [10–12]. Nevertheless, NFs were recommended to be used for compact heat exchangers to improve their thermal characteristics [13]. Moreover, a considerable recommendation was given to Al2O<sup>3</sup> nanoparticles for the preparation of NFs due to achieving good dispersion and improvements in the heat transfer effectiveness [14–16]. An empirical and numerical research by Awais et al. [17] for Al2O<sup>3</sup> NFs flow in a heat sink heat exchanger reported a good improvement of 17% to the thermal performance of the heat sink. Moreover, Choi et al. [18] reported a 6.9% improvement in the thermal performance of the radiator by using Al2O<sup>3</sup> NFs as a coolant instead of the BF for a high-level power system. Another study by Huang et al. [19] studied the performance of PHE with Al2O<sup>3</sup> and MWCNT NFs and an inconsiderable heat transfer improvement for both NFs was reported in comparison with BF, i.e., water. Furthermore, an empirical study by Mare et al. [20] presented a better cooling performance for the used CNTs NF than Al2O<sup>3</sup> NF for the fluid flow through PHE.

So far, numerical examination methods such as computational fluid dynamic (CFD) tools showed good flexibility and a big advantage to be used for studying the heat transfer characteristics of heat exchangers by different numerical modelling methods [21,22]. Yet, numerical modelling has been used to simulate the performance of NFs for heat transfer of NFs flow through uniform mini-channels [23] and micro-channels [24], and it showed respectable agreement with experimental measurements for several conditions such as non-Newtonian rheology behavior for the NFs [25]. In addition, different computational methods were presented in the literature to investigate the behavior of NF flows for different applications such as solar energy systems, electronics, and automotive [26,27]. Ahmed et al. [28] numerically tested the thermal performance of Cu NFs in the isothermally corrugated channel and a considerable heat transfer upgrading was reported by using NF instead of water for *Re* between 100 and 1000. Other researchers have numerically tested the performance of other types of NFs. For example, Shirzad et al. [29] investigated Al2O3, CuO and TiO<sup>2</sup> NFs in PHE for *Re* between 1000 and 8000. In their investigation, while Al2O<sup>3</sup> NF had the best heat transfer values for low *Re*, TiO<sup>2</sup> NF had the better performance in heat transfer for high *Re*. Bahiraei et al. [30] numerically tested the flow of Al2O<sup>3</sup> NFs in micro PHE and different shapes of particles were used at 1.0 vol.%. concentration and *Re* of 500. Platelet-shaped Al2O<sup>3</sup> particles presented the best heat transfer rates. There is a numerical research study conducted by Tiwari et al. [31] on PHE works with CeO<sup>2</sup> and Al2O<sup>3</sup> NFs as homogeneous fluids using the CFD tools (ANSYS-FLUENT). The numerical predictions were well matched with the experimental measurements and better performance was found for CeO<sup>2</sup> NFs as coolants. Generally, preparation and stability influence the thermal performance in any heat transfer systems, such as PHE [7] and heat pipes [32].

In addition, the literature shows a single-phase numerical technique as a common method to simulate the NF's behavior in heat exchangers and a good agreement is usually presented when numerical predictions are compared with experimental measurements [7]. Nevertheless, reported numerical investigations on NFs for compact heat exchangers were not supported by enough validation and comparison with experimental measurements [33,34], and the thermophysical properties of the used NFs are mostly obtained theoretically by using mixture laws and without studying the stability of NFs. Furthermore, the real mechanism behind the deviation between the numerical and experimental measurements was not identified, and the thermal behavior of the NFs in the flows was not explained. Therefore, the current study intended to perform firstly a thorough experimental determination of the thermophysical properties of Al3O<sup>2</sup> and TiO<sup>2</sup> NFs with low particle concentrations

(0.01–0.2 vol.%) to be suitably tailored in the numerical simulations through the corrugated channel of compact chevron PHE. Furthermore, a careful experimental investigation was carried out for the heat transfer of the NFs flows in the hot loop of a compact PHE system. The details of the numerical methodology (geometry dimensions, boundary conditions, flow rates, etc.) were determined based on the experimental investigation and the equivalent working conditions were applied for an accurate comparison between the numerical and experimental measurements.
