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With today’s article, we try to offer you an introduction on the functioning of solar cookers and ovens, which can be applied both to solar box ovens and to solar panel cookers and parabolic solar cookers.

In particular, with this article you will be able to understand how much time does it take for a solar cooker or oven for reaching its maximum temperature and what is the maximum tempererature that can be reached.

The information reported hereunder are mostly derived from  “The Technology of Solar Cooking” wtitten by Professor Ed Pejack.

We hope you enjoy reading it!

##### From the Sun to the solar cooker or oven

The solar radiation which hits the surface of the Earth in a given place has an intensity that varies during the day, as well as from month to month.

This solar radiation can be divided into three components: direct, diffuse and reflected radiation, which are represented in the picture below. Solar cookers mainly cook thanks to the direct component of the solar radiation. Nonetheless, the diffuse and the reflected components partly determine the temperature of our solar cooker or oven.

It is important to note that when we cook, not only the energy that we provide to the food matters, but also the velocity with which we provide it, that is to say the power of the solar radiation. The unit of measurement of the power of solar radiation is W/m2, where W=J/s (Watt = Joule per second). During the day, the power of the Sun starts from 0 to reach up to 800 W/m2 during midday.

The variation of the power of solar radiation throughout all the day has a “bell curve” shape. According to this, in a dedicated page of our website (in Italian), we have reported some graphs relative to the direct, diffuse and reflected components of the radiation of the Sun for the  different months of the year. These graphs indicate the monthly average of the solar radiation, so that it is possibile to have some days in which the intensity of the solar radiation is higher than in other days.

Right above we have indicated a power of 800 W/m2 for the solar radiation. We might note that this power has not a high spatial concentration (our pot or dishes do not occupy a surface of 1 m2!), so we need something that allows us to concentrate the solar radiation. That’s the reason why we use solar cookers and solar ovens!

If we want to compare the power of the solar radiation with the cooking power that is available at home, we can consider that the cooking power of gas stoves is tipically comprised between 800 W (small stoves) and 3 kW (bigger and newer stoves), but their efficiency goes from 50% to 65%, as indicated in the following picture. It is important to note that more than simply concentrating the solar radiation, solar box ovens and solar panel cookers are also able to trap the heat inside their cooking chamber, thanks to the greenhouse effect that is created from the combination of the transparent closure and the dark pot. This effect is not necessarily present in the parabolic solar cookers, where the pot can be put in the focal point of the cooker without necessarily adding a transparent cover, thanks to  the higher concentrating ratio and the higher power (more than 1 kW) that these cookers are able to reach.

##### Power balance and heat balance in solar cookers and ovens

Solar cooking uses the power of the Sun to cook. Part of this power reaches the pot and the food, part is dissipated to the surrounding environment in the form of heat.

So we have a power balance and also a heat balance.

Here we will try to describe the heat balance through a mathematical equation, regarding all the heat components that are involved in solar cooking. In particular, we can say that the heat that is provided by the Sun thanks to its irradiation (Qi) is partly utilized for heating the oven and cook the food (Qf) and partly is dissipated to the environment (Qdiss).

Therefore, the equation for the heat balance is the following: Ar regards the equation, let’s hypothesize that Qi is constant during the cooking period. Indeed, Qi varies during the day as the relative position of the Earth and the Sun varies. Nonetheless, we can choose the average value of the solar radiation for the time of a cooking test with a solar cooker or solar oven and thus we can have Qi as constant.

Under this hypothesis then, we will have that the sum of Qf and Qdiss is constant and equals Qi. Even if their sum is constant, Qf ad Qdiss will vary throughout the time of the coooking test, as shown in the graph reported hereunder. As we can see, at the beginning there is no dissipation of heat to the surrounding environment. This is because the dissipation of heat depends on the difference of temperature between the temperature of the oven and the temperature of the environment and at the beginning this difference is zero. So all the heat that comes from the Sun is transferred to the solar oven or cooker and from here to the pot and the food.

Subsequently, the temperature of the solar oven or cooker will rise progressively and so does also the difference between the temperature of the solar oven or cooker and the temperature of the environment. After some time the solar oven or cooker will reach its maximum temperature and almost all the heat will be dissipated to the surrounding environment. There will still be only a small contribution of heat that will continue to go to the solar cooker or oven. This represents the heat that needs to be provided to the solar cooker or oven in order to mantain the food at a constant temperature.

##### More detailed description of the heat balance

The single components of the heat in the heat balance equation can be calculated as follows: where

Pirr = thermal power that is provided from the radiation of the Sun [W/m2]

η = overall efficiency (optical and thermal) of the solar cooker or oven [-]

Ai = aperture area of the solar cooker or solar oven, that is the area that receives the solar radiation [m2]

Qfmin = heat that need to be provided to the solar cooker or oven in order to mantain  it at a constant temperature when the maximum temperature is reached [J]

τ = time constant for the heat equations for Qf and Qdiss [s]

Value of Qi. Recalling the graph relative to the heat balance that has been already provided right above in the previous box, we can add more information regarding the value that we have chosen for Qi. This value equals 100, because we have hypothesized that Pirr = 800 W/m2 = constant. Indeed, as we have already said, even if the solar radiation varies throughout the day, we have hypothesized that its value can be considered constant for the 25 minutes of the cooking test, taking 800 W/m2 as the average value of the solar radiation during this period of time. Moreover, we have hypothesized to work with a solar panel oven having η = 0,5, Ai = 0,25 m2.

Time that is necessary in order to reach the maximum temperature. We have also hypothesized to have a cooking pot which does not contain food, that is to say that contains only air. Under this hypothesis, for a solar panel cooker we have verified experimentally that the maximum temperature is reached after 20 – 25 minutes (the latter corresponding to 1500 seconds). For this reason the graph shows the data for this time interval.

More information about the time constant that appears in the equations for Qf and Qdiss. In an exponential function, the time constant appears as the denominator of the exponent of the Euler’s number (the mathematical constant e).

Seconds are its unit of measurement.

In an exponential function, the time constant has the property that by multiplying its value for a factor of 3, the exponential function will reach 95% of its final value and by multiplying its value for a factor of 5, the exponential function will reach 99,3% of its final value.

For our Copenhagen solar panel cooker, we have experimentally measured that the maximum temperature is reached after 25 minutes and that after 20,5 minutes we have almost reached 95% of the maximum temperature. The value of  τ then will be about 6,8 minutes, which corresponds to 228 seconds.

For a designer or for a researcher, it could be possibile to estimate τ also with a theoretical approach. This could be useful if we have not built yet the solar oven or solar cooker, or if we have not chosen the cooking system. We will try to better describe the theoretical approach in a future article. This approach is quite complex and we have not fully understood it yet.

For now, we will simply say that the time constant can be described as: where

R = thermal resistance of the cooking system [°C /W] = [°C*s/J]

M = mass of the cooking system [kg]

Cp = specific heat of the cooking system [kJ/Kg*°C]

Ac = area of the cooking system [m2]

The calculation of τ is complex due to the parameters R, M and Cp, which depend on the characteristics of the cooking system.

But what is the cooking system? The cooking system is represented by the pot with the lid, by the transparent covering and by the base of the solar oven.

In our case, the transparent covering and the lid of the pot are made of glass, while the base is made of cardboard covered with an aluminum foil, as represented in the image provided hereunder. Moreover, in the cooking system we can also consider the thermometer, that is put outside the pot, but under the transparent covering. ##### Preheating a solar oven or a solar cooker

When we want to cook with our oven at home, we first must turn it on and set the desired temperature. The oven will take some time to reach the maximum temperature, then from that moment we will be able to put the food inside it for cooking.

In a solar oven it is quite the same. The only difference is that we cannot decide what is the maximum temperature, because this depends on the temperature of the environment, on the solar radiation and on the properties of the solar cooker or solar oven. If we put a pot inside the solar oven (for the solar panel, we will need to put the pot under a transparent covering), the air that is contained in it will be heated and will rise with time following the curve of an exponential function. This is similar to what we have seen for the heat equations for Qf and Qdiss.

For the temperature, we have that the equation can be described as follows: The corresponding graph for the temperature will be the following: In this graph we have hypothesized that the temperature of the environment is 20° C and that the maximum temperature that is reached is 160°C.

Theoretically, we can demonstrate that the maximum temperature can be obtained with the following calculation (from  “The Technology of Solar Cooking” wtitten by Professor Ed Pejack): where

Tenvironment = temperature of the environment [°C]

R = thermal resistance of the cooking system [°C/W]

η0 = optical efficiency of the cooking system [-]

Pirr = thermal power that is provided by the solar radiation [W/m2]

Ai = area of the solar oven that intercepts the solar radiation [m2]

Ac = area of the cooking system [m2]

This equation is useful during the design stage, allowing us to choose the dimensions and the materials of the oven, which determine its efficiency and so the maximum temperature that can be reached.

As for the time constant, also for Tmax the calculation is a little bit complex. In this case the reason is that it is difficult to calculate the value of R. Therefore in a next article we will try to calculate theoretically R too.

As regards the maximum temperatures that have been calculated theoretically, you can find them in our page dedicated to solar panel cookers, both for the low-cost version and for the high efficiency version of the Copenhagen solar panel cooker. In particular, you can find them in the section “maximum daily temperatures on different months”. These temperatures are relative to the different months of the year and they have been calculated theoretically starting from the experimental measurements relative to one specific month.

In the page that we have linked right above you can also find the spreadsheet (in Italian) helping you to understand how to calculate the maximum temperatures starting from the available data. Indeed, in the spreadsheet we have used a different equation for the calculation of the maximum temperature with respect to the one that have described above, but the result should be the same (we still need to verify it).

What happens if we add food to the pot? Obviously we could insert the food even if the solar oven or solar cooker has still not reached the maximum temperature, but this will both delay the time in which the maximum temperature is reached and it will also lower the value of the maximum temperature.

For the delay, we can understand it by recalling the equation for the time constant, that is and noticing that adding a mass of food to the cooking system corresponds to an increase in the product of R, M and Cp. Ther reason is that in the cooking system we will substitute some of the air of the pot with food. According to that, we can estimate that the food will have a mass being about 100 times higher than the mass of air and that its specific heat value will be about 3 times higher than that of air, while the thermal resistance will be almost an order of magnitude lower for food relative to air (the thermal resistance is related to the reciprocal of the thermal conductivity and the conductivity is tipically an order of magnitude higher for food relative to air, as can be seen by comparing the data available in this article and in this article).

For the maxium temperature, we can similarly notice that by adding a mass of food the thermal resistance will be lower and so also the maximum temperature will be lower.

For this reason, it is important to do not exceed with the quantity of food, in order to avoid an excessive decrease of the maximum temperature that could prevent us to cook.