Numerical and experimental investigation of the solar air heater with latent heat storage and fin

Abstract

In current numerical work, a mathematical model for an air collector with latent heat storage is established and solved using the finite difference method. The glass, absorber plate, and air flow temperatures are described in one-dimensional unsteady terms. The storage material simulation is formed by a two-dimensional unsteady modeling and solved using the enthalpy method. By analyzing the temperature distribution and phase change behavior within the PCM using a two-dimensional unsteady model, this research provides a more detailed understanding of the thermal storage process compared to studies employing one-dimensional models. The mathematical model was validated by an outdoor experiment under prevailing climatic conditions in Ho Chi Minh City, Vietnam. The absorber plate is equipped with longitudinal rectangular fins to enhance heat transfer. Height of storage material, air flow rate and fin geometries are set as independent parameters to investigate phase change in latent storage and daily performance. Simulation results show that a storage height of 20 cm is suitable to fully liquify and to extend the operating time to 21:00. Attaching the fins increases the daily efficiency up to 13.7% compared to that of a smooth duct air collector. Latent heat storage provides the most uniform outlet air temperature compared to sensible storage and without storage. The standard deviation of outlet air temperature with time of day is 6.34 °C, 8.47 °C, and 9.20 °C for the types of latent heat storage, sensible heat storage, and without storage, respectively.

Introduction

Solar energy is an endless source of energy for humanity. Since ancient times, people have used solar thermal energy to illuminate, warm and dehydrate objects. With hundreds of watts of solar radiation per meter square and the earth’s huge surface, this energy source is today used to produce hot water¹, hot air², freshwater³, and electricity⁴. Solar energy exists and is abundant during the daytime. Therefore, to use energy in off-sunshine hours, solar energy storage is a technique that has been developed. Solar hot water and photovoltaics are techniques that have been sustainably progressed and massive commercialization. Hot air cannot be stored, and thus solar energy may be stored by means of another medium. This medium is often divided into two types: sensible thermal storage (e.g. sand, granite, gravel, concrete) or latent thermal storage (e.g. paraffin wax, hydrate salts, lauric acid, acetamide). Both types extend the operating time of the solar air heater (SAH). However, latent storage reduces air temperature, and operating time is longer due to taking advantage of latent heat of fusion or melting of materials.

Solar air heaters are a promising technology for harnessing solar energy for various applications, including space heating and agricultural drying. However, their widespread adoption is often hindered by their relatively low efficiency and the intermittent nature of solar radiation. Measures to enhance heat transfer of air in the collector are of great interest^5,6. However, energy storage in air collectors has received little attention^7,8. Storing energy inside the air collector is also a solution to increase efficiency. Because the collector temperature decreases, heat loss is reduced. Furthermore, heat storage acts as a buffer heat source during intermittent nature of solar energy (cloudy or rainy)⁹. Reddy¹⁰ simultaneously stored latent and sensible heats in paraffin wax and water. Fins embedded inside the wax. The top surface was covered with a transparent insulation material (TIM). The proposed system minimized heat loss and obtained water temperature up to 50.5 °C. Kabeel et al.¹¹ experimentally compared the SAH with and without latent thermal storage. The air collector duct was equipped with V-corrugated plate to augment heat transfer rate. They reported that the air temperature difference across the collector with a phase change material (PCM) was up to 7.2 °C after sunset. Josyula et al.¹² simulated PCM-based air collector with two glass covers. The collector yielded the air temperature up to 40 °C for 14 h after sunset and the efficiency up to 62.4%. Yadav et al.¹³ studied the latent storage in concentric tubes of a solar air heater to dry agricultural products. The system was subjected to two-dimensional (2D) numerical simulation in a commercial software. The results show that drying can last until 21:00. Verma and Singh¹⁴ numerically treated the solar air heater with parallel flow and latent storage. The governing equations was solved using finite volume method. They proved that the numerical technique and the flow configuration achived the best performance. Rawat et al.¹⁵ tried to optimize size of PCM container via a 2D transient simulation. Optimum thickness-to-length ratio of 0.042 was found to reduce the dead length. Most recently, Roman et al. 2024¹⁶ stored latent heat in the air collector to dry wheat. Storage media included paraffin and salt hydrate. They confirmed that latent heat storage provides the most moisture uniformity in drying technology. In addition, the air temperature in the case of paraffin is higher than that in the case of salt hydrate. The liturature review implies that the previous researches have explored the use of latent heat storage and heat transfer enhancement techniques separately, there is a need for studies that comprehensively investigate their combined effects within a solar air heater. Furthermore, many studies rely on simplified one-dimensional models, which may not fully capture the complex heat transfer phenomena occurring within the PCM layer.

Understanding latent thermal storage can significantly enhance the efficiency of solar air heaters by storing thermal energy in phase change materials (PCMs). This promotes sustainability by maximizing energy capture and utilization. While previous studies have explored solar air heaters with latent heat storage, this work uniquely combines numerical modeling with experimental validation under the specific climatic conditions of Ho Chi Minh City, Vietnam. In this study, a two-dimensional unsteady numerical model in the PCM of a SAH is established to analyze temperature and phase over time of day. The absorber plate is equipped with fins to enhance convective heat transfer of air. Performance of the SAH with/without storages and with/without fins was evaluated and analyzed.

Problem description

Mathematical formulation

Figure 1 shows the schematic diagram of an air collector with latent heat storage. The air flows through the gap between the glass cover and the absorber plate. The absorber surface is fitted with longitudinal rectangular fins to enhance heat transfer between it and the air stream. Below the absorber plate is a latent heat storage material. Finally, there is an insulation layer to reduce heat loss on the back of the collector. The solar air heater operates by converting solar radiation into heat and transferring it to an air stream. Solar radiation is transmitted through the glass cover, which minimizes convective heat loss, and is absorbed by the absorber plate. The absorber plate, in turn, heats up. Longitudinal rectangular fins attached to the absorber plate enhance heat transfer to both the air flowing through the air channel and the latent heat storage material (PCM) located below. During the charging process, heat is transferred from the absorber plate to the fins, and the fins facilitate efficient heat transfer to the PCM, raising its temperature. When the PCM reaches its melting temperature, it begins to change phase from solid to liquid, storing latent heat. This process continues as long as solar radiation is available. In the discharging process, when solar radiation is reduced or absent, the PCM releases the stored heat as it changes phase from liquid to solid. Heat is transferred from the PCM to the fins, which, in turn, enhance heat transfer to the air flowing through the collector. This fin-assisted heat transfer ensures that heat is provided to the air even in the absence of direct solar radiation. The insulation layer at the bottom of the collector minimizes heat loss. The unsteady calculation model of the collector is built with the following assumptions:

• Thermo-physical properties of the components of the collector are constants.

• Temperatures of glass, air flow and absorber plate vary only in x-direction. Temperature and phase of PCM change in x and y directions.

• Heat loss through the collector edges was ignored.

• Natural convection of liquid in PCM is non-existent.

• Subcooling effects, where the liquid PCM cools below the nominal freezing point before solidifying, were not considered in this model.

For solar air heaters, while natural convection of liquid PCM can play a role, some simplified models often focus on the overall thermal performance and the impact of latent heat storage. Implicitly assuming that the primary heat transfer to and from the PCM is driven by conduction through the PCM itself and the surrounding container. Particularly, if the PCM is contained in multiple small cells or thin layers up to 0.06 m¹⁷.

Fig. 1

Schematic diagram of a solar air heater with latent thermal storage.

From there, the heat balance equations of each collector component (glass, air flow, absorber plate, and PCM) are written as Eqs. (1)-(4)¹⁸.

Glass cover:

$${\delta _g}{c_{p,g}}{\rho _g}\frac{{\partial {T_g}}}{{\partial t}}={k_g}{\delta _g}\frac{{{\partial ^2}{T_g}}}{{\partial {x^2}}}+I{\alpha _g}+{h_{c,g,w}}({T_a} - {T_g})+{h_{c,g,f}}({T_f} - {T_g})+{h_{r,g,p}}({T_p} - {T_g})+{h_{r,g,sky}}({T_{sky}} - {T_g})$$

(1)

where:

${\delta _g}{c_{p,g}}{\rho _g}\frac{{\partial {T_g}}}{{\partial t}}$ is temperature change with time,

${k_g}{\delta _g}\frac{{{\partial ^2}{T_g}}}{{\partial {x^2}}}$ is heat conduction of the glass in x-direction,

$I{\alpha _g}$ is solar energy absorbed by the glass,

${h_{c,g,w}}({T_a} - {T_g})$ is forced convection between the glass and wind above it,

${h_{c,g,f}}({T_f} - {T_g})$ is forced convection between the glass and the airflow,

${h_{r,g,p}}({T_p} - {T_g})$ is thermal radiation between the glass and the absorber plate,

${h_{r,g,sky}}({T_{sky}} - {T_g})$ is thermal radiation between the glass and the sky.

Nomenclature and Table 1 explained symbols. Therefore, they were not repeated here for the sake of brevity.

Similarly, air temperature with time and space, i.e. T_f = T(t, x), is predicted by the following equation¹²:

$$H{c_{p,f}}{\rho _f}\frac{{\partial {T_f}}}{{\partial t}}={k_f}H\frac{{{\partial ^2}{T_f}}}{{\partial {x^2}}} - H{c_{p,f}}{\rho _f}{V_f}\frac{{\partial {T_f}}}{{\partial x}}+{h_{c,g,f}}({T_g} - {T_f})+\phi {h_{c,p,f}}({T_p} - {T_f})$$

(2)

where $H{c_{p,f}}{\rho _f}{V_f}\frac{{\partial {T_f}}}{{\partial x}}$ is the convection term, and φ is the finned surface efficiency.

Absorber plate:

$${\delta _p}{c_{p,p}}{\rho _p}\frac{{\partial {T_p}}}{{\partial t}}={k_p}{\delta _p}\frac{{{\partial ^2}{T_p}}}{{\partial {x^2}}}+I{\alpha _p}{\tau _g}+\phi {h_{c,p,f}}({T_f} - {T_p})+{h_{r,g,p}}({T_g} - {T_p})+{k_{PCM}}{\left. {\frac{{\partial {T_{PCM}}}}{{\partial y}}} \right|_{y=\delta }}$$

(3)

where ${k_{PCM}}{\left. {\frac{{\partial {T_{PCM}}}}{{\partial y}}} \right|_{y=\delta }}$is heat conduction at interface of the absorber plate and PCM.

Temperature and phase changes in PCM are predicted using the enthalpy method as¹⁴:

$${\rho _{PCM}}\frac{{\partial h}}{{\partial t}}={k_{PCM}}\left( {\frac{{{\partial ^2}{T_{PCM}}}}{{\partial {x^2}}}+\frac{{{\partial ^2}{T_{PCM}}}}{{\partial {y^2}}}} \right)$$

(4)

where h is enthalpy of the PCM.

$${T_{PCM}}=\frac{h}{{{c_{p,PCM}}}}+{T_m}\;\;\;{\text{for}}\;{\text{h}} \leqslant 0\;\left( {{\text{solid}}\;{\text{phase}}} \right)$$

(5)

$${T_{PCM}}={T_m}\;\;\;{\text{for}}\;0<h<\,{L_{PCM}}\left( {phase\;change} \right)$$

(6)

$${T_{PCM}}=\frac{{h - {L_{PCM}}}}{{{c_{p,PCM}}}}+{T_m}\;\;\;{\text{for}}\;{\text{h}} \geqslant {{\text{L}}_{{\text{PCM}}}}\;\left( {{\text{liquid}}\;{\text{phase}}} \right)$$

(7)

The enthalpy method offers significant advantages for modeling PCMs over alternative numerical methods like the Finite Element Method (FEM) or Finite Volume Method (FVM), particularly when dealing with the complexities of melting and solidification. Its primary strength lies in its ability to handle the latent heat of fusion within a single energy equation that is valid across the entire computational domain (solid, liquid, and mushy zones), without explicitly tracking the moving solid-liquid interface. This fixed-grid approach simplifies the numerical formulation considerably, avoiding the computational challenges associated with re-meshing or complex interface tracking algorithms inherent in traditional FEM or FVM when directly applying Stefan problems. By defining enthalpy as a function of temperature, including the latent heat release/absorption over a small temperature range (the mushy zone), the enthalpy method inherently accounts for the phase change, leading to more robust and numerically stable solutions, especially for partial phase transitions or materials with a phase change temperature range. This makes it a more straightforward and computationally efficient choice for many practical PCM simulations.

The initial condition of the temperatures (T_g, T_f, T_p, T_PCM) is the ambient temperature (T_a) when beginning the simulation. The boundary conditions for Eqs. (1)–(4) were presented below. Dirichlet boundary conditions were applied to the inlet air and the PCM next to the absorber plate. Neumann boundary conditions were imposed for the remaining boundaries.

$${T_f}{|_{x=0}}={T_a}$$

(8)

$${\left. {\frac{{\partial {T_f}}}{{\partial x}}} \right|_{x=L}}={\left. {\frac{{\partial {T_g}}}{{\partial x}}} \right|_{x=0,x=L}}={\left. {\frac{{\partial {T_p}}}{{\partial x}}} \right|_{x=0,x=L}}=0$$

(9)

$${\left. {\frac{{\partial {T_{PCM}}}}{{\partial x}}} \right|_{x=0,x=L}}=0$$

(10)

$$- {k_{PCM}}{\left. {\frac{{\partial {T_{PCM}}}}{{\partial y}}} \right|_{y=0}}={U_b}({\left. {{T_{PCM}}} \right|_{y=0}} - {T_a})$$

(11)

$${T_{PCM}}{|_{y=\delta }}={T_p}$$

(12)

Other equations are presented below. The sky temperature is calculated from the ambient temperature as follows¹⁹:

$${T_{sky}}=0.0552{({T_a}+273)^{1,5}}$$

(13)

Heat transfer coefficient due to radiation between the glass and sky:

$${h_{r,g,sky}}=\sigma {\varepsilon _g}\left( {{T_g}^{2}+{T_{sky}}^{2}} \right)\left( {{T_g}+{T_{sky}}} \right)$$

(14)

Heat transfer coefficient due to radiation between the glass and absorber plate:

$${h_{r,g,p}}=\sigma \left( {{T_g}^{2}+{T_p}^{2}} \right)\frac{{{T_g}+{T_p}}}{{1/{\varepsilon _g}+1/{\varepsilon _p} - 1}}$$

(15)

Forced-convection heat transfer coefficients between the glass and air (h_{c, g,f}), and the absorber plate and air (h_{c, p,f}) can be computed as the Dittus-Boelter’s equation:

$${h_{c,g,f}}={h_{c,p,f}}=0.021R{e^{0.8}}Pr_{{}}^{{0.4}}{k_f}/{D_h}$$

(16)

where Re and Pr are Reynolds and Prandtl numbers, respectively. D_h refers to the hydraulic diameter.

$$Re=2\frac{m}{{{\mu _f}\left( {W+H} \right)}}$$

(17)

where m is the air mass flow rate.

$${D_h}=\frac{{4HW}}{{2\left( {H+W} \right)}}$$

(18)

$$Pr={c_{p,f}}{\mu _f}/{k_f}$$

(19)

The velocity of the airflow (V_f) is correlated with the mass flow rate as:

$${V_f}=\frac{m}{{{\rho _f}WH}}$$

(20)

The finned surface efficiency (φ) is estimated from Eqs. (21)-(24) as²⁰:

$$M=\sqrt {\frac{{2{h_{c,p,f}}}}{{{k_{fin}}{\delta _{fin}}}}}$$

(21)

$${\eta _{fin}}=\frac{{tanh\left( {M{W_{fin}}} \right)}}{{M{W_{fin}}}}$$

(22)

$${A_{fin}}=2n{W_{fin}}L$$

(23)

$$\phi =1+\left( {\frac{{{A_{fin}}}}{{LW}}} \right){\eta _{fin}}$$

(24)

where M refers to fin parameter, η_fin to fin efficiency, A_fin to fin area, W_fin to fin height, and n to number of fins.

The heat transfer coefficient due to convection between the glass and the wind on the glass cover was calculated by McAdam’s correlation²¹:

$${h_{c,g,w}}=5.7+3.8{V_w}$$

(25)

Bottom plate heat loss coefficient is given as:

$${U_b}={k_i}/{\delta _i}$$

(26)

Daily efficiency of the air collector is evaluated by the total useful heat gain to the overall solar radiation acting on the collector surface¹²:

$${\eta _{Daily}}=\frac{{\int\limits_{{{t_1}}}^{{{t_2}}} {m{c_{p,f}}({{\left. {{T_f}} \right|}_{x=L}} - {T_a})dt} }}{{\int\limits_{{{t_1}}}^{{{t_2}}} {ILWdt} }}$$

(27)

Numerical approach

Analytical solutions to the governing equations are challenging to obtain due to the unsteady nature of the multi-dimensional problem, and conjugate heat transfer of the airflow and the phase change material. While other numerical techniques such as the finite element method could be employed, the finite difference method was selected for its computational efficiency and ease of implementation, particularly for structured grids. This method is also well-suited for handling unsteady terms and is compatible with the enthalpy method used to model the phase change in the PCM. The partial differential Eqs. (1)-(4) along with the boundary conditions are solved using the implicit finite difference method. The computer program was written in MATLAB R2016a language. Discretization of forward time and central space (FTCS) were applied to transient term and diffusion term, respectively. The upwind scheme was used to the convection term. The alternating direction implicit (ADI) method was employed for elliptic Eq. (4). The linear system of equations was solved using Thomas algorithm. Details of discretized equations and solution procedure can be seen in our previous studies^22,23.

Table 1 Input parameters.

Fig. 2

Grid independence test.

Table 1 presents the parameters to enter the computer program and to experiment for validation. In which air mass flow rate (m), number of fins (n), fin height (W_fin), and PCM thickness (δ) are specified to numerically investigate their effects on the outlet air temperature and daily efficiency. In the numerical simulation, for simplicity, the melting and solidification temperatures of the paraffin wax were assumed to be the same (T_m = 49 °C). This simplification neglects any hysteresis effects that may occur in the actual material. Figure 2 presents an independent check of the mesh. The examination was performed with five numbers of nodes from 2626 to 5454. The results show that the air temperature leaving the collector is minor change with meshing. As shown in Table 2, the maximum relative error between successive grid refinements is about 0.23%. Thus, grid independence was assumed when the relative difference in outlet air temperature was less than 1%. Therefore, 5151 nodes is used to ensure grid independence and computation time.

Table 2 Grid independence test.

Experimental validation

Fig. 3

Experimental setup (a) and 10 kg paraffin wax in the experiment (b).

Fig. 4

Weather conditions in Ho Chi Minh city on 18 June 2024.

Before conducting the numerical survey, an outdoor experiment was set up to confirm the simulation results. Figure 3 shows the experimental setup of an air collector with latent heat storage. The experimental apparatus has the dimensions as Table 1 (L = 1 m, W = 0.5 m, H = 0.02 m, δ_i = 0.05 m, n = 0). Paraffin wax as latent storage media has a thickness of δ = 20 mm corresponding to its weight of 10 kg. The bottom of the wax is insulated with wood fiber. Air is drawn through the collector by an axial fan. Air velocity (V_f) and wind velocity (V_w) are measured by the mini-impeller anemometer TROTEC BA06 (Accuracy: ± 3%). Solar radiation is measured by solar power meter TES 132 (Accuracy: ± 5%). Air and PCM temperatures are measured by 4-channel temperature meter EXTECH SDL200 (Accuracy: ± 0.4%). Figure 4 shows solar radiation reaching the collector surface (I), air temperature entering the collector (T_a), and wind speed (V_w) measured on June 18, 2024, in Ho Chi Minh City, Vietnam. The air mass flow rate through the collector in the experiment is m = 0.01 kg/s. Experimental and simulated results of the outlet air temperature and PCM temperatures on that day are shown in Fig. 5 with temperature position PCM 1 (x = 35 mm, y = 10 mm) and temperature position PCM 2 (x = 70 mm, y = 10 mm). The temperature measurements were performed using a calibrated temperature data logger, which has a manufacturer-specified accuracy of ± 0.4%. This suggests that the potential error in individual temperature readings is limited to this value. There is good agreement between the experimental and simulation results. The temperatures in the numerical simulation are negligibly lower than those of the experiment. However, the largest error between the two approaches is less than 7%. It is important to note that, in reality, paraffin wax and other PCMs typically exhibit hysteresis, meaning that the solidification temperature is lower than the melting temperature. This difference is due to the nucleation process involved in solidification. In the experiment, this hysteresis effect likely played a role in the PCM’s thermal behavior, and it could explain some of the minor discrepancies observed between the numerical and experimental temperatures. Therefore, the above mathematical formulation and numerical methodology are used to investigate the parameters that affect the performance of the PCM-based air collector.

Fig. 5

Comparison between experimental and numerical results.

Results and discussion

The effects of parameters including PCM height, number of fins, fin height, and air mass flow rate are presented in this section. The values ​​of the parameters are presented in Table 1. When one parameter changes, the remaining parameters are kept constant. The weather parameters are shown in Fig. 4. The impact of PCM height (δ) on the outlet air temperature is shown in Fig. 6. When the thickness of the storage material is increased, the heat stored in it is more, therefore reducing the outlet air temperature. The maximum temperature of the outlet air is 48.5 °C at δ = 10 mm, and is 46.1 °C at δ = 20 mm. However, when δ = 30 mm or more, the outlet air temperature changes little with δ. Because the PCM layer is too thick, the bottom of the PCM has little change in temperature. It can be seen that when δ ≥ 20 mm, the air temperature is significantly high after the sun goes out (from 17:00). The air temperature leaving the collector reached 31.2 °C at 21:00 while the ambient temperature was being 28 °C.

Fig. 6

Effect of PCM height on the outlet air temperature.

Local temperature and phase in PCM at δ = 20 mm can be seen in Figs. 7 and 8. PCM temperature gradually increases from 8:00 to 14:00. At 14:00 the amount of solar radiation is still as high as 760 W/m² (Fig. 4) so ​​the PCM temperature is up to 85 °C near the air outlet. Therefore, this stage is the charge of PCM. From 16:00, PCM temperature gradually decreased. At 21:00, the PCM close to the absorber plate has a temperature of about 42 °C, so the solar air heater is still capable of generating hot air. During the discharge period (from 16:00), the lowest temperature zone is near the inlet and the highest temperature zone is around coordinates x = 1 m and y = 0.01 m because of low-temperature air moving through the absorber plate and heat loss on the back of the PCM.

Fig. 7

Temperature distribution inside PCM with time of day (δ = 20 mm).

At 8:00, the PCM temperature is not high enough, so PCM is in solid state as shown in Fig. 8. From 10:00 to 12:00, the upper layer of PCM changes into the liquid phase, so there exist two phases in this charge period. From 14:00 to 16:00 complete liquid PCM was observed. From 18:00 PCM releases heat to the air and loses heat on the back so the middle area is liquid, the upper and lower areas are solid PCM.

Fig. 8

Phase distribution at δ = 20 mm (blue: solid, yellow: liquid).

The phase distribution in PCM at δ = 40 mm is shown in Fig. 9. Due to the doubling of the thickness, the unique liquid phase does not exist at any time. At 21:00, a relatively large amount of liquid remained. However, solid PCM near the absorber surface resists heat transfer. The 40 cm PCM has a greater heat storage capacity than the 20 cm PCM, and theoretically, it should store more energy. However, the simulations demonstrate that the 20 cm PCM layer results in a longer period of hot air production. This apparent discrepancy can be attributed to the limitations imposed by heat transfer within the PCM, particularly in the y-axis direction. While the 40 cm PCM can store more total energy, the thicker layer creates a higher thermal resistance to heat flow (R = thickness / conductivity). This leads to larger temperature gradients within the PCM, as seen in Fig. 9, and inhibits the effective release of energy, especially during the discharge period. In contrast, the 20 cm PCM allows for more efficient heat transfer, resulting in a more uniform temperature distribution (Fig. 8) and a sustained release of heat to the air flow. Effectively, although the 40 cm PCM stores more energy, a smaller proportion of that stored energy can be accessed within a given timeframe compared to the 20 cm PCM. This highlights that in a dynamic system like a solar air heater, the rate of energy release is as important as the total storage capacity.

Fig. 9

Phase distribution at δ = 40 mm (blue: solid, yellow: liquid).

The effect of the number of fins on the outlet air temperature and collector efficiency is observed in Figs. 10 and 11. As the number of fins increases, the effective heat transfer surface area increases thereby increasing the air temperature and efficiency. At 14:00, the outlet air temperature is 46.1 °C and 49.7 °C for the case without fin and with 40 fins, respectively. Therefore, daily efficiency increases with the number of fins as can be seen in Fig. 11. The efficiency increases up to 13.7% when n = 40 compared to that of the case without fin. Early in the day, the PCM is solid and acts as a good heat sink, absorbing a large amount of heat. The fins help transfer heat effectively to the PCM, facilitating this absorption. As the PCM starts to melt, its ability to absorb heat decreases (sensible heat absorption is lower than latent heat absorption). The temperature difference between the absorber plate and the PCM surface may decrease, reducing the driving force for heat transfer to the PCM, even with the fins. Later in the day, as more PCM melts, the liquid PCM may create a thermal resistance. Convection in the liquid PCM is assumed to be negligible in the simulation, so heat transfer through the liquid PCM relies on conduction, which is less efficient. This can reduce the effectiveness of the fins in transferring heat to the PCM. Performance also increases dramatically with air flow rate. Performance increases from 33 to 58% as the flow increases over the survey range at n = 40. When the flow rate increases, the convective heat transfer coefficient increases. Furthermore, its increase also reduces collector temperature thereby reducing heat loss. The variation of outlet air temperature and efficiency with fin height is shown in Figs. 12 and 13. Effects of fin height is less significant. When the fin height is tripled, the outlet air temperature increases to a maximum of 1.3 °C and efficiency increases up to 4%. This is because increasing the fin height increases the heat transfer area but reduces the fin efficiency.

Fig. 10

Variation of the outlet air temperature with number of fins.

Fig. 11

Variation of the daily efficiency with number of fins and air mass flow rate.

Fig. 12

Effect of fin height on the outlet air temperature.

Fig. 13

Effect of fin height and air mass flow rate on the daily efficiency.

Fig. 14

Comparison of the outlet air temperature for three scenarios.

Figure 14 compares outlet air temperature by time of day with 3 different scenarios: no storage, sensible storage (granite as a storage media with ρ = 2750 kg/m³, c_p = 890 J/kg K, k = 2.9 W/m K²¹, and latent storage. When there is no heat storage, the highest temperature is 51 °C followed by sensible storage (50.3 °C), and latent storage (48.8 °C). This is because the absorber plate in the absence of heat storage has the highest temperature since there is no heat transfer to the storage material, so the air temperature is highest. For storage cases, the phase transition is at saturation temperature, so the temperature in latent heat storage is lower than that in sensible heat storage. In addition, the peak of the outlet air temperature also changes from 12:00, 13:00, and 14:00 corresponding to no storage, sensible storage, and latent storage. From 17:00, the outlet air temperature is equal to the ambient temperature in the absence of heat storage. At 17:00, two types of heat storage generate hot air up to 5.5 °C higher than the inlet air temperature. From 18:00, latent heat storage brings significantly higher air temperatures than sensible heat storage due to the release of latent heat being much higher than sensible heat. At 21:00, the difference in air temperature through the collector storing latent heat and sensible heat is 3.88 °C and 0.41 °C, respectively. From temperature profiles in Fig. 14, it can be deduced that latent heat storage creates the most uniform air temperature followed by sensible heat storage. The temperature standard deviations in latent heat storage, sensible heat storage, and no heat storage are 6.34 °C, 8.47 °C, and 9.20 °C, respectively. Therefore, latent heat storage does not create excessively high temperatures, for example negative affecting the drying material, and prolongs the operating time of the air collector during many off-sun hours.

Quantitatively comparing these findings to the recently published work on similar PCM-integrated solar air heater without fin, as depicted in the Fig. 15, reveals that while other studies also show the benefit of PCM integration in smoothing temperature fluctuations, the specific temperature profiles and the degree of temperature stabilization achieved in the present study appear to be competitive, if not superior, in terms of reducing the standard deviation of the outlet air temperature. This suggests that the design employed in the present study contribute to a more effective thermal regulation, offering a more consistent heat supply throughout the day.

Fig. 15

The outlet air temperature for a double-pass solar air heater without fin²⁵.

Conclusions

In this paper, a 2D unsteady mathematical model for latent heat storage material in an air collector is established and solved using the finite difference method. The numerical solution is confirmed through outdoor experimental data. Analysis of the influence of air mass flow rate, storage height and fin geometry parameters on outlet air temperature and daily collector performance is presented. Furthermore, this study investigates the integrated effects of latent heat storage and longitudinal rectangular fins on the absorber plate, a configuration that has received limited attention in prior research. The main results are drawn as follows:

• - Paraffin wax thickness of 20 cm is suitable to create moderate air temperature and prolong period of hot air production.

• - At a storage material thickness of 40 cm, only a portion of solid PCM converts to liquid PCM during the storage period.

• - Increasing air flow rate, number of fins, and fin height increases daily efficiency. However, the effect of fin height is not pronounced.

• - Compared with no storage and sensible heat storage, latent heat storage produces hot air during the day with the smallest standard deviation. The hot air in latent heat storage has the most uniform temperature, and the PCM extends the hot air production time to 21:00 with an air temperature difference of 3.88 °C.

Future work could enhance the accuracy of the model by incorporating temperature-dependent properties for the PCM and accounting for hysteresis and subcooling effects. This would provide a more comprehensive representation of the PCM’s behavior and potentially improve the agreement between numerical and experimental results.