Heat-Transfer Mechanisms in a Solar Cooking Pot with Thermal Energy Storage

Abstract

This paper presents a detailed analysis of the heat-transfer mechanisms in a solar cooking pot with thermal energy storage using computational fluid dynamics (CFD). The vast majority of studies on solar cookers have been experimentally performed using local temperature measurements with thermocouples. Therefore, the heat-transfer mechanisms can only be studied using lumped capacitance models as the detailed profiles of temperature and heat fluxes inside the cooker are missing. CFD is an alternative modelling technique to obtain this detailed information. In this study, sunflower oil is used as both cooking fluid and energy storage medium. Comparison of the model with the available experimental data shows that the deviation is within the measurement accuracy of the latter. Hence, despite some assumptions, such as axisymmetry and an estimation of the heat transfer parameters to the ambient, the model is able to describe the involved physical processes accurately. It is shown that, initially, the main heat-transfer mechanism is conduction from the cooker’s bottom towards the thermal energy storage (TES). This heats up the oil near the bottom of the TES, creating convective plumes, which significantly enhance the heat transfer. In equilibrium, about 79% of the incoming solar flux goes towards heating up the TES. The heat is further transferred to the pot, where convective plumes also appear much later in time. However, the heat transfer to the pot is much smaller, with an average heat-transfer coefficient of 1.6 Wm${}^{-2}$K${}^{-1}$ compared to 7.5 Wm${}^{-2}$K${}^{-1}$ for the TES. After two hours of charging, the oil reaches a temperature of 397 K in the TES and 396 K in the cooking pot. Moreover, the temperature distribution in the cooker is quasi-uniform. During the charging period, the storage efficiency of the TES is about 29%. With the results in this study, solar cooking pots with TES can be further optimized towards efficiently transmitting the heat form the solar radiation to the food to be cooked.

1. Introduction

The use of solar cookers enables the reduction of greenhouse gas emissions generated by fossil-fuel-based cookers. These greenhouse emissions are detrimental to both human health and the environment. Recent comprehensive reviews have highlighted the different types of solar cookers as well as their advantages and disadvantages [1,2,3,4,5]. The most efficient type of solar cooker in terms of the shortest cooking time and the highest cooking temperature is the parabolic dish cooker, which enables the frying, roasting and boiling of food. Cheap and efficient designs of the parabolic dish solar cooker for developing countries have recently been investigated [6,7]. The results obtained showed that the parabolic dish solar cooker can be used to effectively cook food for refugee camps.

The major drawback of most types of solar cookers, including the parabolic dish cooker, is that they cannot be used when the sun is not available, for instance at night and during cloudy periods. To cater for this drawback, thermal energy storage (TES) systems can be integrated with solar cookers so that off-sunshine cooking can be possible as highlighted by in the recent reviews on solar cookers with TES [8,9].

The two main options for TES for solar cookers are indirectly storing the thermal energy in a storage tank using a heat transfer fluid (HTF), for instance nanofluids [10,11] or storing the thermal energy directly in the cooking pot. The latter seems to be more economically viable since the use of fluid circulating pumps and pipes is reduced. Added to this, the piping heat losses for indirect solar cookers with storage are reduced when using direct storage cooking pots.

Recent work on solar cooking storage pots is rather limited, and some of the available studies are presented in this section. A portable parabolic dish solar cooker with a phase change material (PCM) storage pot was investigated by Lecuona et al. [12]. The storage pot was fabricated from two conventional coaxial cylindrical cooking pots consisting of an internal one and a larger external one. PCM was poured between the space of the two pots. The results of storage cooking experiments inside an insulated box showed that both evening and early morning breakfast cooking was possible using the stored heat.

A parabolic solar cooker with an acetanilide storage receiver/pot was investigated experimentally by Chaudhary et al. [13]. Acetanilide (PCM) stored heat during the day, and during the evening, the stored heat was used to cook food when the receiver was placed in an insulated box. Three cases were considered to enhance the thermal performance, which were: an ordinary solar cooker with a normal storage pot, a solar cooker with the outer surface of the pot painted black, and a solar cooker with the outer surface of the pot painted black and with glazing. The solar cooker with the glazed black pot showed better performance compared to the other cases, and it stored around 32% more heat compared to the ordinary storage pot.

A PCM-based system for indoor and outdoor cooking was designed by Rekha and Sukchai [14]. The receiver was constructed as two hollow concentric cylinders, and heat transfer oil filled the gap between the cylinders. The outer layer of the receiver was surrounded by vertical cylindrical PCM tubes. The PCM receiver showed an optical efficiency factor that was double that of the receiver without PCM. PCM solar cooking was found to be a good alternative to fossil-fuel-based cooking. An experimental study was performed using magnesium chloride hexahydrate as the thermal storage material in a boiling type of cooking pot [15]. The obtained results showed that 50 g of rice was cooked in around 30 min using 100 mL of water. The heat utilisation efficiency was around 33% for temperatures above 100 ${}^{°}$C.

Yadav et al. [16] investigated a parabolic dish solar cooker with a combined latent and sensible heat TES unit for evening cooking. Sensible heat-storage materials were combined with a PCM in the storage unit. During the solar cooking period, the cooking pot was placed on the focal point of the dish. During the storage cooking period, the cooking pot was placed inside an insulated box loaded with food, and stored heat from the combined system was used to cook the food. The results showed that the PCM-Sand and PCM-Stone pebble cases stored 3- to 3.5-times more heat compared to the PCM-Iron grits and PCM-Iron ball cases. The PCM assisted in cooking, while the outer sensible heat material assisted the PCM to maintain its performance.

A solar storage cooking pot with acetanilide as the PCM was investigated by Choudhari and Shende [17]. A one-dimensional model was developed and compared to the experimental results. The PCM was able to cook during non-sunshine hours. An evacuated tube solar collector was used to charge up a solar cooking storage pot using acetanilide and stearic acid as the PCMs. Acetanilide showed a superior heat utilisation efficiency of 31% compared to 25% for stearic acid. Mixed sugar alcohols were utilised by Senthil and Cheralathan [18] as PCMs in a solar receiver for off-sunshine usage. The average energy and exergy efficiencies of the receiver with the PCMs were 66.7% and 13.8%, respectively, while using an HTF flow-rate of 80 kg/h.

A feasibility study on a collapsible parabolic cooker with a PCM storage cooking pot was recently investigated by Keith et al. [19]. The PCM storage cooker was able to cook during the evening. A parabolic dish solar cooker with a PCM storage cooking receiver was designed in [20]. A solar salt, which melted at 220 ${}^{°}$C was used in the receiver, and the stored heat was used for frying 0.25 kg of potato chips with cooking oil temperatures between 170 and 180 ${}^{°}$C.

Coccia et al. [21] presented a study on a portable solar cooker coupled with a 2.5 kg erythritol TES unit. Using the storage unit, the average load-cooling time in the range of 125–100 ${}^{°}$C was extended by around 351.16%. The study by Mawire et al. [22] compared two solar cooking storage pots during solar cooking and storage cooking periods. One pot contained erythritol as the PCM, and the other pot contained sunflower oil as the sensible heat-storage material. Cooking during both solar and storage cooking periods was feasible with both storage cooking pots. The sunflower oil pot cooked much faster during solar cooking periods but its heat utilisation performance was lower than that of the erythritol pot during storage cooking periods. The authors also suggested the development of a numerical model for TES system enhancement and optimisation.

Wollele and Hassen [23] investigated the heating of a storage cooking pot using two small parabolic dish solar concentrators. Used engine oil and granite were used as the two storage materials. Used engine oil showed higher cooking temperatures when compared to granite. The performance of a solar box cooker assisted with a latent heat storage cooking pot was presented in [24]. Oxalic acid dihydrate was used as the PCM due to its high specific enthalpy and its melting point close to the boiling point of water. They found that the solar box cooker with PCM could be used effectively to cook food during off-peak hours of solar radiation.

From this rather limited literature review, it is clear that more work needs to be conducted on the performance enhancement and optimisation of storage cooking pots before they can be commercially viable. Some of the authors have also suggested the use of a numerical model for performance enhancement and optimisation. The numerical model will save time and costs in experimentation and will also provide an insight of the heat-transfer mechanisms in the storage material, which cannot be provided by purely experimental techniques. In particular, experimentally validated computational fluid dynamics (CFD) tend to provide detailed insights regarding the fluid and heat-transfer mechanisms in thermal systems. There are also only limited studies that have been performed on the CFD of numerical models for cooking processes.

These works often neglect buoyancy effects [25] or use the Boussinesq approximation [26,27] or apply lumped capacitance modelling [28]. Thus, it is essential to develop models that can be used to enhance and optimise the performance of solar cooking storage pots that can be used for off-sunshine cooking hours. The use of solar cooking storage pots is justified since these pots promote a greener environment from the use of solar energy that is renewable and environmentally friendly.

Although PCMs have larger energy storage densities compared to sensible heat-storage materials, most of them are expensive, have low thermal conductivities, undergo phase segregation during multiple heating and cooling cycles and exhibit supercooling. Thus, sensible heat storage seems to be viable solution for TES especially when issues of costs are concerned. The use of vegetable oils as sensible heat-storage materials has been encouraged by recent work by Mawire et al. [22] and Hoffmann et al. [29].

The aim of the paper is to study the heat-transfer mechanisms in a solar cooking storage pot using computational fluid dynamics (CFD) simulations in detail. This detailed analysis can be used for performance prediction, enhancement and optimisation. A detailed CFD analysis of the heat-transfer mechanisms in a solar cooker is currently lacking in the literature as the vast majority of studies are experimental. Due to local temperature measurements using thermocouples in those studies, the heat-transfer mechanisms in the cooker can only by studied using lumped capacitance models as detailed profiles of temperature and heat fluxes in the cooker are missing.

CFD is an alternative to obtain this detailed information and is, hence, used in this work. As a test case, a solar cooking pot using sunflower oil, both as the cooking medium and thermal energy storage (TES), was chosen as sunflower oil is environmentally friendly and cheap. Therefore, the cooking pot can be used in countries with an abundance of sun without any problems or health issues. This makes it particularly interesting for developing countries. However, the model can easily be adapted for other fluids by changing the fluid properties.

First, the model is compared in detail with the experimental results from the study of Mawire et al. [22]. After validation, a detailed analysis of the heat transfer involved was performed for a charging period of 2 h, which revealed the different heat-transfer mechanisms to the TES and the pot itself. With the results in this study, solar cooking pots with TES can be further optimized towards efficiently transmitting the heat from the solar radiation to the food to be cooked.

2. Materials and Methods

2.1. Experimental Setup

The parabolic dish solar cooker used in the experimental tests for validation of the numerical model is shown in Figure 1. The diameter of the parabolic solar concentrator is around 1.2 m (Figure 1, left). It has a manual tracking mechanism to focus the solar radiation onto a cooking pot that is placed on a circular supporting stand in the focal region. The concentrator was purchased from Sunfire Solutions [30] in South Africa and is relatively inexpensive with a cost of about R1500 (∼USD 85).

A photograph of the experimental storage cooking pot with thermocouples attached is shown in Figure 1, right. It was manufactured from stainless steel and has an internal cavity in which the thermal energy storage (TES) material, i.e., sunflower oil, is placed. To improve the absorbance of solar radiation, the pot was painted black. Three air vents on top of the pot allow for thermal expansion of the sunflower oil during heating. Three K-type thermocouples on the sides of the pot in thermal contact with the storage oil measure the oil temperature so that an average storage temperature can be determined. A K-type thermocouple is also placed inside the cooking pot to measure the cooking temperature.

All K-type thermocouples are similar and have an accuracy of ±2.2 ${}^{°}$C. The storage cooking pot temperatures and the direct solar radiation were monitored during the experiment, which lasted for about 2 h in Mahikeng, South as previously established by Mawire et al. [31]. An Eppley normal incidence pyroheliometer with a solar tracker was used to measure the direct normal incidence (DNI) radiation. It had a single point measurement uncertainty of less than ±5 Wm${}^{-2}$, and a 95% response time of 5 s. A K-type thermocouple also measured the ambient temperature during the solar heating test with an accuracy of ±2.2 ${}^{°}$C. An Agilent 34970A datalogger collected data to the computer from the measurements of the pyrheliometer and the thermocouples, and a sample was taken every 10 s.

2.2. Numerical Setup

As the solar cooker involves vegetable oil as both the cooking and TES medium, computational fluid dynamics (CFD) are used to model the conjugate heat-transfer mechanisms. The model in this study is based on the one developed by Tegenaw et al. [32], and in this study, the convective flow in the TES and associated instabilities are simulated more in detail. To the authors’ knowledge, no other studies in the current literature can be found describing, in detail, the convective flow in solar cookers using TES. However, CFD gives important physical insights into the heat transfer phenomena involved and is, therefore, crucial to further optimising these cookers. The conservation equations solved are those of continuity, momentum and energy. The continuity equation is given by

$$\frac{\partial \rho }{\partial t}+\nabla ·\left(\rho \mathbf{V}\right)=0,$$

(1)

where $\rho$ is the density of the fluid, (in this case, sunflower oil), and $\mathbf{V}$ is the velocity vector. The momentum equation is given by

$$\rho \left(\frac{\partial \mathbf{V}}{\partial t}+\mathbf{V}·\nabla \mathbf{V}\right)=-\nabla p+\nabla ·\left[\mu \left(\nabla \mathbf{V}+\nabla {\mathbf{V}}^T\right)-\frac{2}{3}\mu \left(\nabla ·\mathbf{V}\right)\mathbf{I}\right]+\rho \mathbf{g},$$

(2)

where $\mu$ is the dynamic viscosity, p is the pressure, $\mathbf{I}$ is the unity tensor, and $\mathbf{g}$ is the gravitational acceleration. The energy equation is given by

$$\frac{\partial \rho h}{\partial t}+\nabla ·\left[\mathbf{V}\left(\rho h+p\right)\right]=\nabla ·\left[k\nabla T\right],$$

(3)

where T is the temperature, k is the thermal conductivity, and h is the enthalpy. To capture the free surface between oil and air, the volume of fluid method is used [33]. This includes solving a transport equation for the volume fraction $\alpha$, where $\alpha$ = 0 corresponds to pure air and $\alpha$ = 1 to pure sunflower oil. The material properties of the sunflower oil, such as the density, heat capacity, viscosity and thermal conductivity, are temperature-dependent and taken from the studies of Mawire et al. [22], Fasina et al. [34] and Hoffman et al. [29]. The equations are solved in a computational domain—schematically shown in Figure 2.

The geometry of the cooking pot is taken from the work of Mawire et al. [22] (Figure 1 right). To reduce the computational load, the cooker is modelled axisymmetric with the x-axis as the symmetry line. Despite the convective flows in the TES system being three-dimensional, the axisymmetric assumption saves an order of magnitude in computational time, and the validation in Section 3.1 shows that this assumption is justified. The radius of the cooker $R_c$ = 0.16 m and the height $H_c$ = 0.11 m. The cooker itself has two compartments: one for the thermal energy storage (TES) with a height H = 0.032 m and one used as the cooking pot with a radius R = 0.125 m.

The walls of the cooker (denoted by the thick black lines in the figure) are made of stainless steel and have a thickness of 3 mm. The walls are part of the computational domain, and the heat conduction equation is solved to model the heat transfer inside the solid part of the cooker. For both compartments, sunflower oil is used as heat transfer fluid. The main motivation is its wide availability and non-toxicity, which makes it ideal for application in rural areas. The volume of oil in the TES system is 3.75 L, and for cooking, a mass of 0.5 kg oil is used.

The boundary conditions for the CFD simulations were estimated from the work of Mawire et al. [22]. The flux measurements are shown in Figure 3. There is some fluctuation on the measurements, and for the simulations, the average flux is taken, which is 965 Wm${}^{-2}$, shown by the dashed red line in the figure. The parabolic dish solar concentrator used in the experiments is not considered in this study and is replaced by a constant heat flux of ${\dot{Q}}_{in}$ = 4950 Wm${}^{-2}$ on the bottom of the cooker (Figure 2).

The heat losses through the top and side walls, ${\dot{Q}}_{loss}$, are modelled as a combination of convective and radiation heat fluxes. The corresponding heat-transfer coefficient h is estimated from the experimental data at equilibrium. At equilibrium, the incoming flux is equal to the outgoing fluxes, which are convection and radiation losses. From this equilibrium, the heat-transfer coefficient can be calculated as

$$h=\frac{{\dot{Q}}_{\mathrm{in}}-\sigma ϵA_p\left(T_{\mathrm{eq}}^4-T_a^4\right)}{A_p\left(T_{\mathrm{eq}}-T_a\right)},$$

(4)

which gives an average heat-transfer coefficient h = 26.5 Wm${}^{-2}$K${}^{-1}$. However, this heat-transfer coefficient can vary largely due to changing ambient conditions, such as wind speed and direction. In the expression, ${\dot{Q}}_{\mathrm{in}}$ is the net incoming heat flux (both from the parabolic dish and the ambient conditions as the cooker is placed in the open sun), $\sigma$ is the Stefan–Boltzmann constant, $A_p$ is the surface area of the cooker without the bottom area, $T_{\mathrm{eq}}$ is the equilibrium temperature of the pot, and $T_a$ is the ambient temperature. The cooking pot itself was modelled as a black body with an emissivity $ϵ$ = 1. At equilibrium, about 27% of the losses are attributed to radiation and 73% to convection.

The conservation equations are solved using the finite volume method implemented in Ansys FluentR2022. As the spatial discretisation scheme, a second-order upwind scheme is used, while for the temporal discretisation, an implicit second-order scheme is chosen. The numerical domain is divided into 216.512 square cells for proper gradient capture, and a grid study in the work of Tegenaw et al. showed that the spatial discretisation error is about 0.3% [32]. In order to accurately capture the dynamics of the flow, the timestep is taken to be $\Delta t$ = 20 ms, giving a maximal Courant number of about one. The coupled solver is used with the PRESTO! scheme for pressure–velocity coupling. A total heating time of 2 h is simulated, giving a total of 360,000 timesteps solved.

3. Results and Discussion

3.1. Temperature Evolution in Time

Figure 4 shows the temperature evolution at the two locations where thermocouples are positioned (the markers in Figure 2). The experimental measurements are depicted by the symbols with their associated error bars, and the numerical simulations are denoted by a solid line. Despite the variable solar flux and wind conditions (which have a large influence on the convective heat-transfer coefficient), the numerical simulations well predict the temperature evolution with an average RMS error, defined as $\sqrt{\sum {(T_{\mathrm{num}}-T_{\exp })}^2}/N$ of 1.8 K, where $T_{\mathrm{num}}$ and $T_{\exp }$ are the simulated and experimentally measured temperatures, respectively, and N = 720 is the number of samples. This value falls within the accuracy of the experiments.

In general, the differences are mostly attributed to the changing environmental conditions of the solar flux and wind speed. In the beginning, the solar flux is below average (Figure 3), and the simulations show a higher temperature increase. Furthermore, between 4000 and 5500 s, the experimental solar flux is higher than average, and the experimental temperature increase is larger than the numerical one. However, overall, the temperature increase can be captured well with the numerical model.

Figure 4 shows that, after one hour, a temperature of 368 K can be reached in the TES and with 364 K in the cooking pot. After two hours, these temperatures rise to 397 and 396 K, respectively. This illustrates that the temperature within the solar cooker becomes more homogeneous over time. Despite that the achieved temperatures using sunflower oil are high, they are still lower compared to the ones obtained using solar salt for the TES, i.e., 493 K [20]. On the other hand, compared to other phase-changing materials, such as paraffin, the maximum temperatures in the TES are in the same range, i.e., 413–433 K [12].

3.2. Average Temperature Evolution in the TES and Pot

The data plotted in Figure 4 are local temperature measurements from experiments using thermocouple measures in discrete locations. However, CFD simulations can also reveal the temperature distribution inside the solar cooker, while experiments can not. This temperature distribution, together with the heat fluxes are needed to study the heat-transfer mechanisms in detail. To study the thermal behaviour of the TES and cooking pot, a volume averaged temperature is defined as

$$T_{\mathrm{av}}\left(t\right)={\int }_V\alpha T\left(t\right)dV/{\int }_V\alpha dV,$$

(5)

where the temperature is weighted by the volume fraction $\alpha$ to eliminate the contribution of air, and V is the total volume of the TES compartment or the cooking pot. The evolution of these temperature profiles is shown in Figure 5. The TES starts to heat up almost immediately as the heat flux from the bottom of the cooker is transferred rapidly. However, the cooking pot itself only starts to heat up after about 100 s due to the slower transmission of heat coming from the TES (see next section). The temperature evolution of the TES and pot can be predicted by considering both as a lumped model. As the main heat-transfer mechanism involved is convection, the energy equation can be written as

$$mc\frac{d{T}_{\mathrm{av}}}{dt}=hA\left(T_{\mathrm{av}}-T_{\mathrm{eq}}\right),$$

(6)

where m is the mass, c is the specific heat of the oil in the TES or cooking pot, h is the average heat-transfer coefficient, and $A_i$ is the inner surface of the compartment. The general solution of Equation (6) is given by

$$T_{\mathrm{av}}=\left(T_i-T_{\mathrm{eq}}\right)exp\left[-b\left(t-t_{\mathrm{ref}}\right)\right]+T_{\mathrm{eq}},$$

(7)

where $T_i$ is the initial temperature, and the constant b is equal to $hA/\left(mc\right)$. A time delay $t_{\mathrm{ref}}$ is introduced to take into account that both the TES and pot do not heat up immediately. Fitting of Equation (7) to the curves in Figure 5 to determine the parameters $t_{\mathrm{ref}}$, $T_{\mathrm{ref}}$ and b is shown in

Table 1. Fitting parameters of the average temperature profiles of the TES and pot.

	${\mathit{t}}_{\mathbf{ref}}$ [s]	${\mathit{T}}_{\mathbf{eq}}$ [K]	b [s${}^{\mathbf{-}\mathbf{1}}$]
TES	51.5	404.8	3.22 × 10${}^{-4}$
POT	310.8	421.9	2.33 × 10${}^{-4}$

. The delay in heating of the pot is shown by the higher $t_{\mathrm{ref}}$ compared to the TES. The equilibrium temperature of the TES and pot are predicted to be 405 and 420 K, respectively. For the TES, this is very close to the numerical value (409.8 K) [32], while the prediction for the pot is less accurate (405.8 K).

This is attributed to a more dynamic input heat profile of the pot (see the next section). Nevertheless, both models fit with an $R^2$ value of more than 99.6%. From the value of b, the average heat-transfer coefficients can be calculated, which are 7.5 and 1.6 Wm${}^{-2}$K${}^{-1}$ for the TES and pot, respectively. These heat-transfer coefficients are on the order of magnitude for natural convection, which is the main mechanism for both the TES and pot.

In the literature, a storing efficiency is often defined to describe the performance of a solar cooker. This storing efficiency is defined as the ratio of the energy stored in the TES during a certain time period and the total amount of incoming energy during that time period, i.e.,

$$\eta =\frac{Q_s}{Q_{\mathrm{in}}},$$

(8)

where the stored energy in the TES during a time period $\delta t$ can be calculated as $mc\Delta T_{\mathrm{av}}$, and the incoming energy $Q_{\mathrm{in}}={\dot{Q}}_{\mathrm{in}}\delta t$, with $\Delta T_{\mathrm{av}}$ as the temperature rise of the TES during $\delta t$. For the solar cooker in this study, the storage efficiency for a charging period of 2 h was 29%. This value is in the same range as the ones reported by Bhave and Thakare [15], i.e., $\eta$ = 32.38% or by Domanski et al. [35], i.e., 32.4% for TES systems using a PCM.

However, much lower values can also be found in the literature, i.e., 11∼14% in the work of Bhave and Kale [20] or 2.5∼7% in the work of Mawire et al. [22]. The difference is attributed to the collector efficiency of the parabolic mirror, which was reported to be on the order of 0.15–0.22 [31]. During this charging period, an amount of about 800 kJ of energy is stored in the TES, which should be sufficient to cook around 0.5 kg of chicken, chips and tomatoes using 0.1 kg of oil during off-sunshine hours [22].

3.3. Transient Heat Transfer Phenomena

In this section, the transient heat-transfer mechanisms are studied in greater detail. Figure 6 shows the heat flux through the bottom of the pot and the TES. The TES starts to heat up almost immediately as the heat from the bottom of the cooker is transmitted very efficiently. The flux increases rapidly and saturates after about 5 min to an average value of 326 W. The flux is highly transient due to unsteady Rayleigh–Bénard convection, which is a time-dependent heat-transfer phenomenon. As the incoming flux from the solar radiation is 413.2 W, about 79% of the incoming heat flux is transmitted directly to the TES.

A more detailed view of the early temperature profiles in the cooker is shown in Figure 7. At the beginning, heat is transferred through conduction to the TES. After 72 s, the bottom of the cooker has heated up to 303.8 K (Figure 7 left), and due to the decreased density of the oil near the bottom, convective plumes begin to appear (Rayleigh–Bénard convection). These plumes increase in size and strength (Figure 7 right) and significantly increase the heat transfer towards the TES (Figure 6 left).

The heat transfer to the pot involves different mechanisms. The heat transfer starts when the first convective plumes originating from the bottom of the TES reach the pot after about 96 s (Figure 7 right). This results in an increase in the heat-transfer rate to about 10 W (Figure 6 right). At about 330 s, as shown in Figure 8 left, the first plumes in the pot begin to appear, and the heat transfer is further augmented.

The heat transfer reaches a peak of around 30 W after 1404 s and starts to decline afterwards due to the reduction in strength of the convective plumes as the temperature difference between the oil in the pot and its wall is decreasing. In general, the heat transfer to the pot is much lower than the one to the TES, and further improvements could be made by, for instance, the introduction of fins. However, this is beyond the scope of this study. The temperature profiles for further timesteps are not shown here as the heat-transfer mechanisms remain similar for a charging period of 2 h.

4. Conclusions

In this paper, we studied the heat-transfer mechanisms in a solar cooking pot with thermal energy storage (TES) using computational fluid dynamics (CFD) simulations. In the solar cooker, sunflower oil was used as both the cooking fluid and TES. First, the numerical model was compared in detail to experimental data from the literature, and the RMS deviation between the simulations and experiments was found to be 1.8 K for a heating period of 2 h. This deviation falls within the experimental accuracy reported. Using the validated numerical model, a heating up cycle of 2 h was simulated, and the heat-transfer mechanisms were studied in detail.

Initially, heat coming from the bottom is transferred to the TES by conduction. This heats up the oil near the bottom, and convective plumes are formed, which significantly increase the heat-transfer rate. This heat is further transferred to the pot by the rising of convective plumes in the TES compartment. A lumped capacitance model of the TES and pot showed that the average heat-transfer coefficients were 7.5 and 1.6 Wm${}^{-2}$K${}^{-1}$, respectively.

Hence, there is much room for improvement to increase the heat transfer from the TES to the cooking pot. Nevertheless, the cooker is well-suited to cook food as temperatures of 397 K in the TES and 396 K in the cooking pot can be achieved. Moreover, the temperature distribution in the cooker is quasi-uniform. When the cooker is charged, about 79% of the incoming flux of the cooker goes to the TES, and the storing efficiency is about 29%.