Operational Study of a Solar Thermal Installation with Recirculation for Industrial Applications

Abstract

The solar thermal collector network (SCN) and the thermal energy storage system (TES) represent 90% of the solar thermal installation (STI) total costs. STI occupies 30 hectares, and any reduction is significant for the environment. The proposed approach, which includes a solar thermal plant with recirculation, a mixer, and a heat exchanger, reduces investment costs and environmental impact. It facilitates mixing in a simple tank. The developed methodology reduces the number of collectors and the size of the storage system. An industrial-powdered milk process is the case study. Two scenarios and the base case were evaluated. The four seasons and critical meteorological conditions were considered. Scenario one, without a heat exchanger, presents energy surpluses in three seasons. The second scenario, with a heat exchanger, heats the feedwater and guarantees the heat load and target temperature on critical days of the year. In this second scenario, it is possible to reduce the tank filling time from 8 to 7 h. Up to five parallels were reduced in both scenarios, with mass flow of 0.125 kg/s and up to 3.75% of the total tank volume of 52.65 m³ (mass flow 0.075 kg/s). The optimized system is cost-effective, and 10.20% of the total cost was reduced. This methodology can be applied to any low-temperature STI.

1. Introduction

Heat represents three-quarters of industrial energy demand worldwide, with a value of 85 EJ [1]. Solar energy is the most widely accessible, abundant, and cost-free renewable energy source [2]. Solar thermal systems are considered one of the best alternatives for generating energy and contribute to solving the problem of climate change. Solar thermal heat production for industry was 2.0 EJ during 2024 [3]. The design, installation, and operation of solar thermal installations (STIs) constitute the proposal to satisfy the world’s process heat demand. Industrial-scale STIs generally consist of a solar collector network, an energy storage system, and a pumping system [4].

Different industrial sectors use STIs. SHIP plants (solar heat for industrial processes) represented a global total of 1209 facilities in 2023, which supplied 951 MWth of process heat [5]. The food and beverage industries had the largest number of systems (199), and the mining sector had the largest share (47%) of the total operating capacity [6]. According to the IEA Solar Heating & Cooling Program, at the end of 2024, there were 777 Mm² of solar collectors installed worldwide, equivalent to 544 GWth. This meant that 153.5 Mt CO₂ emissions were avoided. That same year, at least 106 new SHIP plants with a capacity of 120 MWth were installed worldwide. Approximately 1315 SHIP plants installed worldwide occupy 1531 Mm² (1071 MWth) [7]. Currently, 73 projects are under construction or planning, and these are expected to generate 277 MW and will be operational in 2027 [8].

The dominant technology to produce solar heat for industrial processes, of the projects developed during 2025–2027, is flat-plate solar collectors (72%) (FPSCs) with respect to concentrating solar collectors (28%). Literature reports solar thermal installations with large areas of FPSC and thermal storage systems (TES). The “Pampa Elvira Solar” solar thermal plant, with 39,300 m² of solar collectors, produces 51,800 MWth of hot water at 50 °C for the copper electrowinning process with a solar fraction of 0.85. The thermal storage system is 4300 m³ of hot water (a tank with a diameter of 17.6 m and a height of 17 m) [9]. France’s “Lactalis Group” whey powder plant has a solar thermal capacity of approximately 13 MWth, the largest of its kind in France. The FPSC field covers an area of almost 15,000 m² and is completed by a 3000 m³ storage tank capable of storing several days’ worth of heat production to ensure continuity of supply at night and on cloudy days during the summer [10]. The textile and leather industry is an emerging sector; in Mexico, the company “Gütermann Polygal Mexicana” reported an installation capacity of 450 m² FPSC and a 20 m³ storage tank, while in Greece, “Tripou-Katsouris Leather Treatment Factory” has a collection area of 300 m² with a 48 m³ thermal storage system [4].

Flat-plate solar collector plants have been the subject of innovations that reduce the large areas they typically occupy, the large volumes required for water storage, and their operating time, resulting in high investment costs [11]. Large-scale solar thermal systems present technical, economic, and environmental challenges for their design, construction, and operation. Martínez-Rodríguez et al. (2023) [12] studied the thermal performance of a heat pump assisted by a solar thermal installation, where the collection area of the solar network is reduced by 85% compared to a conventional collection system. Some studies are looking into how geometry can make flat-plate solar collectors more efficient to increase their absorption area. The use of grooved pipes significantly improves efficiency by up to 12% in transient flow conditions and by 8–20 % at various flow rates compared to smooth pipes [13]. Concentric semicircular riser pipes and the integration of phase change material in the heat sink have energy and exergy efficiencies of 74% and 6%, which are 39.5% and 160.8% higher than those of conventional flat-plate solar water heaters [14]. The implementation of different extended areas increases the efficiency of the solar collector by up to 16.5% [15].

Thermal energy storage (TES) systems allow heat management and storage, compensating for fluctuations between supply and demand, as well as the intermittency of renewable energies [16]. The intermittency of solar energy represents a significant challenge for its large-scale applications, making use of storage systems essential to guarantee a stable energy supply [17]. The impact of these systems extends to mitigating demand peaks, reducing overall energy consumption, cutting CO₂ emissions, and optimizing profitability, thereby improving the overall efficiency of the energy system [18]. TES are widely used in solar applications, including solar water heating [19], space heating [20], cooking [21], drying [22], and water desalination [23]. Solar water heating systems (SWHS) are essential for achieving Sustainable Development Goals (SDGs) 7 and 13 [24]. TES can be classified into latent heat, sensible heat, and thermochemical. TES based on phase transition materials and thermochemical storage are typically more expensive than the value of the storage space they offer, although innovative technologies for high-quality heat storage are being tested, thus expanding the market potential [25,26].

Sensible heat storage is the most developed and used option, thanks to the simplicity of its operating principle and its low cost [27]. From a market perspective, sensible heat storage systems are expected to be the dominant technology due to their residential and industrial applications [28,29]. In these systems, heat is stored to raise the temperature of a liquid (water, oil, organic solvents, etc.) or a solid (concrete, metal, rocks, bricks, sand, etc.) without a phase change occurring. The installation of these technologies in the industrial sector represents 5% of the final energy consumption [30]. To store thermal energy as sensible heat, the technology has evolved considerably in recent years and is expected to reach approximately 10.1 BUSD by 2027 [31].

Hot water tanks are a widely used system for sensible heat storage [32]. Vallese et al. (2026) [33] conducted a comprehensive review of thermal energy storage technologies and their applications in the industrial sector. Solar water heating systems (SWHS) represent the technology located at the highest levels of technological maturity (TRL between 8 and 9). Al-Mamum et al. (2023) [34] reviewed the state of the art of existing SWHS and the design of their main components (the solar collector, storage tank, heat exchanger, thermal fluid, and absorber layer, among others), concluding that the efficiencies of flat-plate solar collectors can be increased up to 35% by introducing thermal nanofluids such as multi-walled carbon nanotubes (MWCNTs). Ortiz-Rodríguez et al. (2020) [35] studied indirect air heating using a network of 48 solar water collectors (92.4 m²), coupled to a 6.15 m³ horizontal thermal storage tank. During the first eight hours of day 1 (7:35 to 16:05 h), the air collectors dehydrate the fruit; subsequently, indirect air heating is used to complete the energy demand of drying. During those eight hours, the pumps of the water heating system operate continuously. After two days, the temperature of the thermal tank rises by 42.71 °C, that is, 50% of the total incident solar energy was stored in the tank during both days. During the waiting period to operate the following day (mainly during the night), the tank lost 1.99 °C. Kalogirou (2003) [36] evaluated a solar thermal system for heating 2000 kg/h of water over a temperature range of 60 °C to 240 °C, corresponding to the average hot water consumption in medium-sized food industries. The solar thermal system, composed of five FPSCs, a circulation pump, and a storage tank, is single-pass (there is no return of hot water to the storage tank). In this scheme, the hot water used is directly replaced by water from the network. It is observed that as the operating temperature increases, a larger collector area is required, until reaching 90 °C, when it is no longer possible to collect more energy. The results also showed that at low operating temperatures, the size of the storage tank remained the same.

Storage systems using recirculation could be understood as the practice of storing materials in tanks continuously. Recirculation causes significant heat losses, but when integrated into a solar heating system, these losses are compensated for; moreover, feeding the solar system with cooler liquid prevents overheating [37]. With recirculation, tanks with such low degrees of stratification can be achieved, whereby the tank contents are completely mixed (totally mixed storage), i.e., thermal stratification degradation occurs; temperature differences of up to ±20 °C at the tank inlet cause stratification losses up to 3.12 times more pronounced [38].

TES costs vary depending on the requirements, size, and technology used. The price of storage systems represents approximately 30% to 40% of the total system cost [39]. TES solutions are expected to become more competitive as research in energy storage technology continues to reduce the initial capital requirement. Çomakli et al. found a relationship between the storage tank volume and the area of the solar collector field. As the tank volume increases, the collector efficiency increases, but the average tank temperature decreases [40]; this has a direct impact not only on the results obtained but also on the costs. Solar thermal energy is considered a profitable long-term investment, with payback periods ranging from 5 to 15 years for the industrial sector according to various reports. The average payback time for any industrial solar thermal installation is 6–7 years, and with 30% subsidies, this time is reduced to 4–5 years [41]. At low temperatures (80/60 °C), the payback period remains below 5 years, even reaching 3.2 years [42]. Reducing payback times for solar thermal installations is key to their widespread use worldwide.

This paper proposes a new approximation to reduce the inversion cost, energy cost, and environmental impact, proposing a way to operate a solar thermal installation with recirculation, a mixer, and a heat exchanger. The cost of the collector network and solar energy storage system decreased by 11.4% and 7.82%. A deterministic sensitivity analysis of the total cost was performed using four variables. The maximum variation in the total cost was 0.25%. The period in which the collector network outlet temperature reaches or exceeds 85 °C increases by 38%.

2. Methodology

The proposed approach uses experimentally validated models using the efficiency curve of the commercial collector selected for the design of the solar collector network, as established in the methodology of Martínez-Rodríguez et al. (2019) [43]. Regarding the meteorological data obtained at the meteorological station of the University of Guanajuato, these were validated with NREL data, as shown in the 22-year percentile analysis performed by Martínez-Rodríguez et al. (2024) [44]. To validate the homogeneous temperature in the tank, a polynomial was introduced that models the way in which the solar collector network heats. The results show that mixing and a homogeneous temperature in the tank are favored. The polynomial was used as a feed condition to the tank in the design and numerical simulation in COMSOL Multiphysics, v. 5.3. The polynomial is a function of the solar collector array operating time (8 h) and is entered into the interface definitions as a piecewise function over the operating time interval in minutes from 0 to 480 min. The temperature profile is used as a temperature input to the tank at the fluid heat transfer interface. The 2D simulation validates the thermal and hydraulic behavior of the tank. It is assumed that there are no stagnation zones and that the temperature is the same at all points based on the simulation results and the heat loss assessment performed. The insulated tank loses 1.08 °C, over a 16 h period. The proposed device solar collector network–storage system with water recirculation (SCN-TES with recirculation), achieves objectives such as mixing, looking for a homogeneous temperature in the water storage tank through recirculation, and thereby increasing the feedwater temperature of a solar collector network. In order to thermally characterize the behavior of a solar thermal installation with recirculation, different mixing ratios between the hot water in the storage tank and the cold water at ambient temperature are analyzed. The temperature of the water mixture at the outlet of the mixer and its effect on the outlet temperature of the solar collector network are analyzed to ensure the heat load and target temperature required by the process. The water temperature levels at the network outlet are directly related to the water temperature at the collector network inlet and to the flat-plate solar collector technology used in the collector network design. The cold water feed flow guarantees the volume required to supply the heat load. The proposal is compared with a nearly identical system, called the base case, which lacks water recirculation. For days with critical weather conditions, low ambient and irradiation temperatures, and high wind speeds (>2.5 m/s), a heat exchanger is used to heat the feed water to ambient temperature to mix it with the recirculation stream from the storage tank.

2.1. Base Case. Operation of the Solar Collector Network–Storage System Without Water Recirculation (SCN-TES Without Recirculation)

The design strategy for base solar thermal installation was proposed by Martínez-Rodríguez et al. (2019) [43]. It considers a continuous feed of water at ambient temperature to the solar collector network arranged in a parallel-series configuration. The hot water leaving the solar collector network is accumulated in a vertical storage tank without recirculation, as illustrated in Figure 1. The sizing of the collector network guarantees the target temperature and the supply of the heat duty required in the process under low-irradiance conditions present in the winter period of the northern hemisphere. For the operation of the solar thermal installation, the period of time necessary for the network to meet the energy objectives of the process is determined, and this begins when the temperature of the water at the outlet of the solar collector network is equal to or greater than the target temperature. Under this operating condition, the temperature of the hot water stored in the tank is, on average, greater than or equal to the target temperature. As a result, the hot water supply time to the process is short, and a large solar collector network is required to meet the heat load. Another way to operate the solar thermal installation is to assume that the average temperature of the stored hot water reaches the target temperature. Under this operating condition, the operating time is longer, and a smaller solar collector network is required. The operating period to achieve the energy targets is during the highest available irradiance.

2.2. Proposed Case: Solar Collector Network–Hot Water Recirculation Storage System (SCN-TES with Recirculation)

The proposal of this study is that a recirculation system has now been added to the base case. The base solar thermal plant now operates with a vertical thermal storage system with hot water recirculation to the solar collector network, as shown in Figure 2. The recirculated hot water stream leaving the storage tank is at the temperature of the stored water. To obtain hot water at an average temperature to feed the solar collector network, the recirculated hot water is mixed with ambient water. Initially, the system operates without recirculating hot water to the collector network until a stored water temperature of 25 °C or higher is reached. Recirculation of the water from the storage tank then begins and continues until the target temperature of 85 °C is reached, also ensuring the heat load required by the process.

The main components of the proposed system are a solar thermal system with recirculation, a mixer, and a heat exchanger. Two scenarios are proposed to assess the contribution of each of the additional components: recirculation (to promote mixing and maintain a homogeneous temperature in the tank) and the heat exchanger (to increase the temperature of the cold water and subsequent mixing under critical conditions). The evaluated operating scenarios are described below.

Scenario 1: The SCN-TES system with recirculation and mixer. This is evaluated during all four seasons of the year. Under these conditions, there will be a greater amount of hot water with temperatures above the target and below 100 °C.

Scenario 2: The SCN-TES system with recirculation, a mixer, and a heat exchanger. The so-called critical meteorological conditions of the year are evaluated [44]. The critical conditions present numerical values below those reported for February 18. The first objective is to ensure the heat load at the target temperature. The goal is also to reduce the time required to maintain the volume required to meet the process’s thermal requirements. In this scenario, part of the water from the heat recovery network is used to heat the mixing feedwater using a shell-and-tube heat exchanger.

In the methodology proposed by [43], the temperature of the stored hot water is the average obtained during the network’s operating period, and it is assumed that there is a homogeneous mixing of the hot water inside the tank. In this study, it is considered that the water stored in the tank has a homogeneous temperature; that is, there is no stratification in layers with different temperatures, due to the difference in density. In the article, the ratio between the mass flow of hot and cold water to feed the solar collector network was varied. Ratios equal to or greater than 2 do not achieve the target temperature required by the process. The optimal ratio after evaluating several ratios was 1.82. This ratio was used on the five days that represent typical irradiation values.

A COMSOL Multiphysics simulation was performed on how recirculation increases turbulence and, therefore, mixing in the tank. The simulation has an equation governed by the heating model being used [43]. Both mixing and heating are modeled. Based on the profiles observed in the simulation, it can be concluded that the temperature in the tank is homogeneous due to recirculation, turbulence, and mixing. To validate the effect of hot water recirculation in the storage tank, a 54 m³ capacity tank was simulated in COMSOL Multiphysics. A 2D simulation of the tank was performed to observe the mixing effect due to the recirculation of water and the homogenization of the water temperature in the tank. The geometric model of the tank was built with dimensions of a commercially available tank. The physics modules selected were heat transfer in fluids and laminar flow to simulate the thermo-hydraulic behavior of the tank. The water inlet flow rate was 4.25 kg/s, and the hot water feed temperature profile was y = −0.0007x² + 0.4447x + 20.029.

The irradiance data is not punctual. They are based on a parabolic irradiance curve constructed with 481 data points for each measured meteorological variable. The outlet temperature of the collector network depends on the number of collectors connected in series, the technology used, and environmental conditions such as irradiance, ambient temperature, and wind speed. Ambient conditions were registered every minute, and the outlet temperature of the network is also determined every minute. An analysis was performed in which it was found that the points corresponding to each minute did not show significant variation with respect to every 15 min. Therefore, fixed irradiance is not being used. Instead, it was found that it was possible to use the 15 min averages to determine changes in the outlet temperature of the network.

2.3. Determination of the Optimal Mass Flow Rate of Feed to the Solar Collector Network

Two important variables define the optimal flow rate selection. The ambient water supply controls the fill time to reach the hot water volume and heat load. The other variable is the recirculation temperature of the storage tank, which controls the storage temperature in the tank, which must be greater than or equal to the target temperature. Therefore, the ratio of the hot water mass flow rate to the cold water mass flow rate defines the heat load, the maximum storage temperature, and the fill time.

2.4. Case Study: Pasteurization Process for the Production of Powdered Milk

The operation of a solar thermal installation was analyzed to supply the heat requirement of the raw milk pasteurization stage for the production of 6.8 t/h of powdered milk in a process that operates 7200 h/y for 360 days a year [45]. In total, 42.84 t/h of raw milk are processed and stored at 7 °C in a process that operates 20 h a day. The first stage is the preheating of the raw milk to a temperature of 50 °C, which corresponds to the separation temperature of milk into cream and skim milk. In the second stage, the preheated milk is centrifuged to separate its components, which are cream, with a higher fat content, and skim milk, in a ratio of 1:8.92. In the third stage, the skimmed milk and cream are pasteurized at 75 °C and 85 °C, respectively. In the following stages, the skimmed milk is treated to produce powdered milk, while the cream is cooled and stored for further processing or as a secondary product for sale. Pasteurization of the skimmed milk is carried out at 85 °C with a heat load of 212 kW provided by a natural gas boiler. A simplified diagram of the main stages of the powdered milk production process is shown in Figure 3. The pasteurization process streams are also identified in Figure 3, and the data for these stages are presented in

Table 1. Data on the milk pasteurization process streams.

Stream	Temperature (°C)	Mass Flow Rate (kg/s)	${\mathit{C}}_{\mathit{p}}$ (kJ/kg·K)
M1	7	11.9	3.87
M2	50	11.9	3.89
M3	50	10.7	3.96
M4	70	10.7	3.97
M5	75	10.7	3.97
M6	40	1.75	- 1

¹ The original source of the case study [45] does not report the ${\mathit{C}}_{\mathit{p}}$ of the stream.

.

Skimmed and pasteurized milk is concentrated by evaporation, first in a mechanical vapor recompression (MVR) evaporator, and second in a triple-effect thermal recompression (TVR) evaporator. In this stage, the water content in the milk decreases from 15% to 52%. This stream is then taken to a spray dryer, where hot air is used to increase the solids content to 95%. Two streams exit the sprayer: one that passes to a cyclone separator, which recovers the solids contained, and another that passes to a fluidized-bed dryer. The solids recovered in the cyclone are also passed to the fluidized-bed dryer, and in this last equipment, a product with 97.5% solids content is obtained. Table 1 presents the main data of the pasteurization process streams.

2.5. Sizing of the Thermal Storage Tank

The temperature required by the process is controlled by the hot water recirculating from the storage tank, and the volume of hot water, or heat load, is controlled by the cold water supplied to the proposed system. The mixture of streams is fed to the collector network for a period of time that guarantees the target temperature and the heat load of an industrial process. Equations (1) and (2) show the ratio of cold and hot water mixed together, as well as the resulting temperature.

$${\dot{m}}_{wmix}={\dot{m}}_{whot}+{\dot{m}}_{wcold},$$

(1)

$$T_{mix}={\displaystyle \frac{{\dot{m}}_{whot}{C}_{p_{whot}}{T}_{whot}+{\dot{m}}_{wcold}{C}_{p_{wcold}}{T}_{wcold}}{{\dot{m}}_{whot}{C}_{p_{whot}}+{\dot{m}}_{wcold}{C}_{p_{wcold}}}},$$

(2)

where ${\dot{m}}_{wmix}$ is the mass flow rate of the hot and cold water mixture, kg/s; ${\dot{m}}_{whot}$ and ${\dot{m}}_{wcold}$ are the mass flow rates of recirculating hot water and chilled water at room temperature, °C, respectively. $C_{p_{whot}}$ and $C_{p_{wcold}}$ are the heat capacities of the hot and cold water, kJ/kg°C; $T_{mix}$, $T_{whot}$, and $T_{wcold}$, are the temperatures of the mixed water, recirculating hot water, and chilled water taken at room temperature.

To design the solar thermal system, the total heat load supply of 212 kW for 20 h at a target temperature of 85 °C is considered. The total amount of water required by the pasteurization process is determined using Equation (3).

$$Q_{SCN}=m_w{C}_{p_w}\left(T_{obj}-T_{w_{amb}}\right),$$

(3)

where $Q_{SCN}$ is the thermal energy required by the process and supplied by the solar thermal plant, kJ; $m_w$, is the mass of water required by the pasteurization process, kg; $C_{p_w}$ is the heat capacity of water, kJ/kg°C; $T_{obj}$ is the temperature of the stored water (85 °C); and $T_{w_{amb}}$ is the water temperature at ambient conditions (19.5 °C). The volume of the storage tank was obtained using Equation (4) [46].

$$V={\displaystyle \frac{Q_{SCN}}{{\rho }_w{C}_{p_w}(T_{obj}-T_{w_{amb}})}},$$

(4)

where ${\rho }_w$ is water density (965 kg/m³).

The mass flow of water circulating through the solar collector network, ${\dot{m}}_{w_{SCN}}$, is determined from Equation (5).

$${\dot{m}}_{w_{SCN}}={\displaystyle \frac{m_w}{{t_{op}}_{SCN}}},$$

(5)

where ${t_{op}}_{SCN}$ represents the hours of operation of the solar thermal collector network, h; and ${\dot{m}}_{w_{STN}}$ is the mass flow rate, kg/s.

To meet the process requirements, heat load, and target temperature, a parallel-series arrangement is used. The number of parallel branches, $N_{SSCN}$, is determined by Equation (6).

$$N_{SSCN}={\displaystyle \frac{{\dot{m}}_{w_{SCN}}}{{\rho }_w{\dot{V}}_{SSCN}}},$$

(6)

where ${\dot{V}}_{SSTC}$ is the flow of water that passes through a series of solar collectors.

2.6. Assessment of the Four Seasons of the Year 2023

Four days representing the four seasons of 2023 were analyzed (one day from the winter period and one more for each of the three seasons of the year). The data were obtained from the meteorological station located on site (21°01′37.0″ N, 101°16′09.7″ W).

Table 2. Four-day meteorological variables for the year 2023 represent each of the seasons of the year.

Date	Irradiation (kWh)	Maximum Irradiance Level (kW/m2)	Wind Speed (m/s)	Ambient Temperature (°C)	Sun Light (h)
Winter (18 February)	5.58	933	2.31	17.65	11.53
Spring (2 April)	6.63	1086	3.09	22.20	12.30
Summer (2 June)	7.00	1076	2.66	25.22	13.27
Autumn (21 October)	5.97	924	2.85	20.34	11.57

presents the meteorological conditions for the evaluated days: irradiation, maximum irradiance level, wind speed, ambient temperature, and daylight hours. Significant variations in irradiation are observed in each season of the year. The highest irradiation value (7 kWh) occurs in summer. Wind speeds are higher than 2.5 m/s in spring, summer and autumn. According to the Mexican Standard NMX-ES-001-NORMEX-2018 [47], convection losses in solar collectors are significant at speeds greater than 2.5 m/s. The lowest temperatures occur in the winter period with 17.65 °C (18 February).

2.7. Evaluation of Economic and Environmental Indicators

2.7.1. Levelized Cost of Energy (LCOE)

The levelized cost of heat is used as an indicator to assess the profitability of energy systems, given by Equation (7). This indicator relates the investment, operation, and maintenance costs, and the cost of fuels if there is a backup, with respect to the net energy production of the system throughout its useful life (USD/kWh).

$$LCOE={\displaystyle \frac{C·CFR+C_{O\&M}}{E_{NET}}},$$

(7)

where $CFR$ is the capital recovery factor; $C$ is the investment system cost (30% for pumping and pipes), USD; $C_{O\&M}$ represents operation and maintenance costs (1% of the total installation cost per year), USD; $E_{NET}$ is the net energy generated by the system, kWh. The plant’s useful life is 25 years; the project discount rate is considered at 5%, and prices are adjusted for 2024. The analysis does not consider subsidies, incentives, taxes, or special taxes.

The capital costs of the solar collectors and storage tank are given by Equations (8) and (9). These relationships were obtained from updated data on internationally marketed equipment.

$$C_{SC}=278A,$$

(8)

$$C_{TES}=\mathrm{20,000}\left({\displaystyle \frac{V}{10}}\right),$$

(9)

$$C_{HX}=log\left(A_{HX}\right)-0.06395A_{HX}^2+947.2A_{HX}+227.9,$$

(10)

where A is the absorber area of the solar collector network, m²; V is the volume of the storage tank, m³; and $A_{HX}$ is the area of the heat exchanger, m².

2.7.2. Net Present Value (NPV)

The Net Present Value is an economic indicator used to evaluate the profitability of a project. It compares the present value of the future cash flows of an investment with its initial cost, indicating whether the investment will generate profits or losses. NPV can be expressed mathematically as Equation (11):

$$NPV={\sum }_{i=1}^{i=n}{\displaystyle \frac{S_i}{{\left(1+r\right)}^i}}-C,$$

(11)

where $i$ is the actual year, S is the annual savings, $1/{(1+r)}^i$ is the discount factor, $r$ is the discount (interest) rate, and $C$ is the initial investment. NPV considers the long-term effect of the project.

2.7.3. Internal Rate of Return (IRR)

The IRR is defined as the interest rate, $r$, that equates the present discounted value of expected future revenues to the present value of the cash flow disbursements; that is, it solves the equation for the discount (interest) rate that makes the NPV equal to 0. Therefore, the IRR is the solution to $r$ in Equation (12).

$$0={\sum }_{i=1}^{i=n}{\displaystyle \frac{S_i}{{\left(1+r\right)}^i}}-C,$$

(12)

Like the NPV criterion, the IRR also considers the long-term effects of the project.

2.7.4. Payback Period (PBP)

The payback period is the time (usually expressed in years) required to generate sufficient savings to recover the project’s initial capital investment. The shorter the payback period, the more favorable the project. The $PBP$ can be expressed as Equation (13).

$$PBP={\displaystyle \frac{C}{S}},$$

(13)

where S is the annual savings. A simple method that can be used to evaluate alternative projects.

2.7.5. Greenhouse Gases (GHGs)

To estimate the total GHG emissions released into the atmosphere by burning natural gas, $P{E}_{GHG}$, Equation (14) is used.

$$P{E}_{GHG}=\sum {EF}_i·E,$$

(14)

where $E$ is the energy consumed in the process, kWh; and, ${EF}_i$, is the factor or index of emissions of pollutant $i$ generated by the combustion of the fuel. EPA reports the following factors for natural gas: ${CO}_2=53.06$, ${CH}_4=1.0\times {10}^{-3}$, and $N_{2}O=1.0\times {10}^{-4}$, kg/MMBTU [48].

2.7.6. Life Cycle Assessment

Life Cycle Assessment considers all environmental impacts; the LCA of a solar thermal installation would constitute a full paper on its own. However, one of the most important parameters in LCA is the carbon footprint (CFP). For the purposes of this work, the carbon footprints of the base case and the optimized case were evaluated for the manufacturing and operation of the main components of the solar thermal installation. These following factors were used: the carbon footprint for manufacturing a solar collector: 112.5 kgeCO₂/thermal collector [49]; the carbon footprint for manufacturing carbon steel: 1.85 tonneCO₂/ton of steel produced [50]; the carbon footprint for manufacturing mineral wool: 1.25 tonneCO₂/ton of mineral wool produced; and the carbon footprint for manufacturing natural gas: 0.029 kgeCO₂/kWh.

3. Results and Discussion

The proposed approach significantly reduces the area of solar thermal installation, reduces tank filling time, and maximizes the tank’s storage temperature well above the target temperature. Depending on the industrialist’s needs, the new proposal can be adapted to meet this objective.

3.1. Base Case: Operation of the Solar Collector Network–Storage System Without Water Recirculation (SCN-TES Without Recirculation)

The parallel-series arrangement of the flat-plate solar collector network was determined as reported [43]; this guarantees both the heat load (4240 kWh) and the target temperature required by the process (85 °C). In this design (base case), hot water recirculation is not used. The environmental conditions were representative of a day in the winter period, 18 February 2023, at the geographic coordinates: 21°01′37.0″ N, 101°16′09.7″ W.

Table 3. Conditions under which a temperature higher than the target temperature is reached in the base case.

Start Hour (h)	Final Hour (h)	Average Irradiance (Wm−2)	Average Hot Water Temperature (°C)	Volume (m3)	Absorber Area (m2)
11:30	14:45	890.86	90.44	47.44	2860 (55 × 26)

shows the average irradiance level recorded during the operating period of the solar collector network–storage system without water recirculation (SCN-TES without recirculation), the average hot water temperature, the tank volume, and the network arrangement. The tank was filled using the criterion of reaching a stored water temperature equal to or greater than the target temperature of 85 °C. The feedwater temperature is also considered to be always at ambient temperature (19.3 °C) with a constant mass flow rate (0.075 kg/s). Under these operating conditions, 47.44 m³ of water was heated to an average temperature of 90.44 °C and an absorber area of 2860 m² to meet the process’s thermal requirements. The operating time was 3.25 h.

When the average temperature of the stored water is around 85 °C, the operating period of the solar collector network–storage system without water recirculation (SCN-TES without recirculation) increases.

Table 4. Operating conditions and network arrangement when the target temperature is reached.

Start Hour (h)	Final Hour (h)	Average Irradiance (Wm−2)	Average Hot Water Temperature (°C)	Volume (m3)	Absorber Area (m2)
10:15	15:15	839.77	86.30	52.65	2028 (39 × 26)

shows the results obtained with this operating criterion, where the operating time was 5 h with an average stored water temperature of 86.30 °C. The hot water volume is 52.65 m³, while the absorber area of the solar collector network is 2028 m².

Both operating criteria ensure the energy requirements of the process. Under the second operating criterion, the operating period of the solar collector array is extended, achieving a 29.09% reduction in the absorption area. However, the storage tank volume has increased by 10%.

Selection of the Optimal Mass Flow Rate Circulating Through the Solar Collector Network

An analysis was performed of the water temperature profile at the outlet of the solar collector network, varying the mass flow rate of water in each series of the collector network. The following water mass flow rates were evaluated: 0.075, 0.125, 0.150, and 0.225 kg/s, with an inlet temperature to the collector network of 19.3 °C. Figure 4 shows the water temperature profile at the outlet of the solar collector network as a function of time and for each mass flow rate. It is observed that as the mass flow rate increases, the water temperature at the outlet of the solar collector network decreases. The maximum temperatures reached for each of the mass flow rates were 97.72 °C (0.075 kg/s), 74.27 °C (0.125 kg/s), 66.93 °C (0.150 kg/s), and 53.15 °C (0.225 kg/s). A maximum temperature difference of 44.57 °C is observed between the lowest and highest mass flow rates evaluated (0.075 and 0.225 kg/s).

The results show that three mass flow rates do not reach the target temperature, and the maximum temperature changes significantly with the increase in the mass flow rate.

3.2. Scenario 1: Solar Collector Network–Storage System with Water Recirculation (SCN-TES with Recirculation)

The proportion of hot recirculating water from the storage tank and cold water (at an ambient temperature of 19.3 °C) that are mixed to feed the solar collector network–storage system with water recirculation (SCN-TES with recirculation, see Figure 5) was determined. Mass flow rates of 0.075, 0.125, 0.150, and 0.225 kg/s were used with an inlet water temperature to the collector network of 40, 50, and 60 °C.

The ratio of the mixture of hot water from the recirculation tank and cold feed water at ambient temperature that meets the thermal requirements of the process is determined. The mixture ratio that guarantees the heat load and target temperature (85 °C) was calculated to be 1.82:1. Figure 5 shows the two scenarios that were evaluated.

Figure 6a–d shows the temperature profiles of the water at the outlet of the solar collector network when the mass flow rate was varied for different inlet water temperatures.

Figure 6a shows the temperature profile for a mass flow rate of 0.075 kg/s with different inlet water temperatures to the solar collector network. An increase in outlet water temperatures was observed as the inlet water temperature increased. For an inlet water temperature to the collector network of 60 °C, the maximum temperature reached is above 100 °C, that is, 1.18 times higher than the base case. Under these operating conditions, the temperature of the water stored in the tank is lower than that required by the process (85 °C), and the tank filling time is 10 h. This is due to the proportion of hot recirculation water and mixed cold water.

Figure 6b,c shows the water temperature profiles at the outlet of the solar collector network for mass flow rates of 0.125 kg/s and 0.150 kg/s. The maximum temperatures obtained at the outlet of the collector network are 99.35 °C and 94.33 °C. In both cases, the temperature exceeds the target temperature (>85 °C), but for the flow rate of 0.125 kg/s, two significant advantages were observed: a higher maximum temperature and a longer storage period above 85 °C. Based on these criteria, an operating flow rate of 0.125 kg/s was selected, as it presents better results compared to the flow rate of 0.150 kg/s.

Figure 6d shows that for a water mass flow rate of 0.225 kg/s and an inlet temperature to the solar collector network of 60 °C, a maximum outlet temperature of 84.76 °C is obtained. However, this water mass flow rate does not meet the target process temperature (85 °C).

3.2.1. Optimal Mass Flow Rate Circulating Through the Solar Collector Network–Storage System with Water Recirculation (SCN-TES with Recirculation)

To determine the optimal ratio between the recirculation mass flow rate (which controls the temperature) and the mass flow rate of cold water at ambient temperature (which controls the volume and heat load required by an industrial process), the mass flow rate of cold water varies from 0.0407 to 0.0445 kg/s. For each evaluation, the proposed system (SCN-TES with recirculation) is designed, and the following parameters are determined: the temperature of the feed water from the solar collector network, the outlet water temperature, and the storage temperature in the tank. A total of 594 evaluations were performed, i.e., for each of the selected flow rates over a full day. In all selected cases, the heat load and target temperature requirements for the process were met.

Table 5. Determination of energy surplus and the parallels that are equivalent to said surpluses of the proposed system (SCN-TES with recirculation).

Cold Water Mass Flow Rate (kg/s)	Water Temperature (°C)	Stored Volume of Water (m3)	Heat Load (kJ)	Surplus Heat Load (kJ)	Parallels Number
0.0407	90.48	53.76	16,071.87	1475.88	3.87
0.0415	90.01	53.76	15,965.75	1369.76	3.59
0.0423	89.48	54.72	16,129.05	1533.05	4.02
0.0432	88.95	55.70	16,293.92	1697.92	4.45
0.0440	88.34	56.70	16,441.19	1845.19	4.84
0.0445	88.18	57.20	16,547.73	1951.73	5.11

shows the cold water flow rate (19.3 °C), the temperature of the water stored in the tank, and the volume of water stored. It also indicates the energy surplus in each case and the number of parallels in the solar collector network corresponding to this excess heat load.

The proposed system (SCN-TES with recirculation) shows very sensitive behavior to the mass flow of cold water (19.3 °C). A very small increase in the flow of cold water (0.0038 kg/s) generates an energy surplus corresponding to a parallel arrangement of 26 collectors in series. It is necessary to determine the costs of the network and the storage tank to determine which of them has the greatest impact on the total cost of the solar thermal recirculation installation.

Table 6. Savings in the absorber area and tank volume of the proposed system (SCN-TES with recirculation).

Cold Water Mass Flow Rate (kg/s)	Water Temperature (°C)	Resulting Volume of Water (m3)	% Reduced Volume	% Saved Absorber Area
0.0407	90.55	47.60	7.82	8.16
0.0415	90.02	48.81	5.48	7.42
0.0423	89.48	49.08	4.95	8.55
0.0432	88.95	49.30	4.53	9.67
0.0440	88.34	49.60	3.95	10.69
0.0445	88.18	49.70	3.75	11.40

shows that, for all cold water mass flows, the size of the network is reduced. Furthermore, in all cases, the thermal requirements of the process are met with significant savings, as both the size of the storage tank and the solar collector network are reduced. The percentage reduction in the volume of the storage tank and the absorption area of the solar collector network compared to the base case is indicated.

Figure 7 shows the evolution of the temperature profile inside the storage tank during the 8 h of operation of the filling process. It is observed that the recirculation of hot water to the storage tank favors mixing inside the tank, generating a vortex in the center of the tank, which gradually decreases in size until the tank temperature is homogeneous.

Heat losses in the tank were calculated from when the solar thermal installation stopped operating (16:00 h) until it started again the next day (8:00 h). It was estimated that during the 16 h that the solar thermal installation was not in operation, the temperature of the water stored in the tank decreased by 1.08 °C.

Table 7. Reduction in costs of the proposed system (SCN-TES with recirculation) with respect to the mass flow entering the storage tank.

	Tank Cost (USD)	Solar Network Cost (USD)	Total Cost (USD)	LCOE (USD/kWh)	Payback (y)	% Costs Reduction
Base case	103,276	552,942	853,083	0.0074	5.42	----
Flow 1	95,200	507,839	783,951	0.0068	4.98	8.10
Flow 2	97,620	511,887	792,359	0.0069	5.04	7.12
Flow 3	98,160	505,671	784,980	0.0068	4.99	7.98
Flow 4	98,600	499,455	777,471	0.0067	4.94	8.86
Flow 5	99,200	493,817	770,922	0.0067	4.90	9.63
Flow 6	99,400	489,914	766,108	0.0066	4.87	10.20

summarizes the costs of the thermal storage tank, the cost of the collector network, and the total cost of the solar thermal installation. The LCOE and payback period are also estimated for all designs, and the lowest-cost case (with a flow rate of 0.0445 kg/s) was determined.

It is observed that the size of the solar collector network has a greater impact on the total cost. The most cost-effective case is for a flow rate of 0.0445 kg/s, with a network operating time of 8 h, a total cost of USD 766,108, LCOE = USD 0.0066/kWh, and a payback period of 4.87 years.

A deterministic sensitivity analysis was performed, varying the following variables: solar collector cost, tank cost, plant lifespan, and interest rate. Variables were evaluated within a range of ±25% to determine whether the savings reported in total cost were maintained or affected. The changes in values were not significant, so it was determined that the cost reductions of the optimized proposal were not affected. Likewise, the electrical energy consumption required by the pump (2.80 kWh per day) and the cost associated with electricity consumption (USD 103.88/y) were not significant. The LCOE was USD 0.00725/kWh, which is an additional 6.3% considering pumping.

For the system with the lowest costs, a positive Net Present Value of USD 1,450,925 and an Internal Rate of Return of 9.52% were obtained, which is 5% higher than the selected minimum profitability rate. Overall, this means that the proposed system is profitable.

From an environmental perspective, 269 t/y of CO₂ emissions were avoided. Comparing the carbon footprint of the case that uses natural gas (

Table 8. Carbon footprint (CFP) results in the case using natural gas, the base case, and the optimized case.

Case	Number of Solar Collectors	CFP for Manufacturing toneCO2	CFP for Operating toneCO2	CFP toneCO2
Fossil fuel (natural gas)	0	1106.64	6725	117,389
Base case	1014	140.52	0	140.52
Optimized case	884	124.64	0	124.64

) showed it was 835 times more than the base case. Comparing the optimized case with the base case, there is a 12.74% reduction in CO₂ emissions.

3.2.2. Reduction in the Installation Area of Solar Collectors Due to the Increase in Operating Time of the Solar Thermal System

A solar collector network for industrial processes operates conventionally for short periods of time, during which the highest average temperatures are reached. The design of the solar thermal system, consisting of the solar collector network and the storage system, is carried out using the lowest winter irradiance levels. This design guarantees the heat load at the target temperature of the industrial process; however, this implies that the number of solar collectors in parallel increases [43]. The aim of this study is to consider the start of operation of the solar thermal system when there is sufficient irradiance to raise the temperature of the water inlet to the solar collector network. This occurs at 7:30 h at the site described by the previously indicated coordinates (Section 3.1). On the other hand, the proposal considered that the end of the solar thermal system’s operation will occur when the irradiance tends to decrease and there is no longer an increase in temperature, which occurs at 14:30 h. The proposal implies an increase in the operating time.

It is observed that, with the new operating strategy of the solar collector network–storage system with water recirculation (SCN-TES with recirculation), the period in which temperatures above 85 °C are reached increases by 38% compared to the base case. This behavior maximizes the efficiency of the thermal process and extends the system’s operability. The operating conditions selected for the design of the solar thermal system with water recirculation are presented in

Table 9. Operating conditions of the proposed design solar collector network–storage system with water recirculation (SCN-TES with recirculation).

Start Hour (h)	Final Hour (h)	Average Irradiance (Wm−2)	Average Hot Water Temperature (°C)	Volume (m3)	Absorber Area (m2)
08:00	16:00	687.33	88.18	49.70	1768 (34 × 26)

.

Compared to the base case, the newly proposed design with water recirculation has an energy surplus. One parallel solar collector in the base case supplies 381.59 kJ, while the energy surplus in the new proposal is 1951.73 kJ, corresponding to five parallel collectors in the base case. Therefore, the solar collector network design proposed in this study has a 34 × 26 solar collector parallel-series arrangement. This represents an 11.4% reduction in network size.

3.2.3. Performance of the SNC-TES System (With Recirculation) During Spring, Summer, and Autumn

On 2 April (Spring), the tank temperature reached 99.37 °C with a volume of 49.7 m³, and the target temperature (85 °C) had been achieved at the network outlet since 10:30 h. On 2 June (Summer), the tank temperature reached 104.78 °C with a volume of 49.7 m³, and the target temperature (85 °C) had been achieved at the network outlet since 9:45 h. For spring, there was a heat load surplus percentage of 10.38%, and for summer, this value was 13.78%. The optimized network is capable of supplying the heat load for these two seasons, while also generating surplus energy. On 21 October (Autumn), the tank temperature reached 85.2 °C with a volume of 53.8 m³, and the target temperature (85 °C) had been achieved at the network outlet since 10:45 h. For autumn, the heat load is supplied with an operating period 45 min longer than the base case. On 18 February (Winter), the tank temperature reached 88.18 °C with a volume of 49.7 m³, and the target temperature (85 °C) had been achieved at the network outlet since 8:00 h.

3.3. Scenario 2: Solar Collector Network–Storage System with Water Recirculation (SCN-TES with Recirculation) and Heat Exchanger

The proposed system with recirculation, a mixer, and a heat exchanger was evaluated under the most critical meteorological conditions for the year 2023 in Guanajuato, Mexico. For 4 January 2023, the average environmental conditions were ambient temperature of 16.37 °C, irradiation of 4.81 kWh, and wind speed of 2.34 m/s. The water at ambient temperature was heated in the heat exchanger with process hot water (70 °C) as shown in Figure 5 (Section 3.2). For an exchanger outlet water temperature of 45 °C, a storage temperature equal to or greater than the target temperature of 85 °C, and the heat load required by the process is reached.

Table 10. Operation of the proposed system under critical meteorological conditions.

Mass Flow Rate (kg/s)	Operating Time (h)	Storage Temperature (°C)	Storage Volume (m3)	Cold Water Mass Flow Rate (kg/s)
0.126	8.0	86.65	49.7	0.0445
0.144	7.0	85.06	50.4	0.0512

shows the results of the proposed system by varying the mass flow rate and maintaining the hot–cold water ratio of 1.82. By increasing the cold water flow by 15%, the operating time is reduced from 8.0 h to 7.0 h.

An additional 30% is added to the solar thermal installation costs, which includes the costs of piping and pumps. For the new proposal, the three pumps and the recirculation and feed piping to the different device components are already included in the additional 30%. For scenario 2, the cost of the heat exchanger to heat the feedwater was added, which is USD 473, and the cost of electricity consumption for the three pumps, which is USD 288. The total cost for scenario 2 is $766,869 with an LCOE of 0.0066 kWh/USD and a simple payback of 4.88 years. The total cost increased by 0.1%, as the payback and energy costs remain constant. Furthermore, the process return temperature is 70 °C, which can be used for days with critical ambient conditions below those reported in this work. For scenario 2, it was necessary to increase the feeding water temperature to 45 °C to ensure the heat load and temperature level.

The literature on the integration of solar energy for industrial applications is limited. For example, approximately 40% of the papers reviewed, not all of which are cited in this article, are not temperature-controlled, nor are the components evaluated jointly as is done with the new proposal. The developed proposal minimizes the solar thermal installation and the relationship between the device components, minimizing the size of the network, the storage system, and the environmental impact, and promoting decarbonization. The above highlights the knowledge gap covered by the developed work and clearly visualizes future research underway. It is demonstrated that this developed work is fundamental for the integration of thermal solar energy into industrial processes. To date, no work has been reported that covers one or all of the results achieved. The novel proposal determines the thermal relationship between the components and the impact of each one, reducing the total cost by up to 10.2%.

4. Conclusions

The new proposal of this paper is to store heated water in a sensible heat storage tank made up of heated water recirculation, a mixer, and a heat exchanger. This new proposal guarantees the supply of the heat load at the target temperature for all evaluated days (representing the four seasons) in 2023. Compared to the base case, the new proposal reduces the area of the solar collector array by up to 12.8% and the storage tank size by 6%.

Under critical weather conditions, the new proposal guarantees the heat load at the target temperature. Even under the same conditions, increasing the cold water flow rate and maintaining the same hot/cold water ratio reduced the tank filling time by 11.5%.

The evaluation of the Net Present Value and Internal Rate of Return indicators is positive, confirming that the proposed system (SCN-TES with recirculation) is profitable. The levelized cost of energy (0.0066 USD/kWh) and payback period (4.87 y) of the new proposal are also competitive compared to fossil fuel technologies (0.06468 USD/kWh), and compared to the base case, there is a reduction in the total cost of 10.20%. Furthermore, the solar thermal installation with storage not only takes up less space but also significantly reduces CO₂ emissions. The carbon footprint is reduced by 12.34% compared to the base case, and zero emissions are achieved due to the elimination of natural gas combustion.