The heat exchange between the glass and the external environment ( Q p , a v 1 ) is mainly due to the transfer of heat by convection and by radiation.

Q p , a v 1 = ( h c , v - a m + h r , v - s k y ) ( T v – T a m ) (1)

where h c , v - a m is the coefficient of exchange by convection between the glass and the ambient,

h r , v - s k y radiation exchange coefficient between the glass and the sky,

T v is the temperature of the window (K),

and T a m : Ambient temperature (K),

h c , v - a m is given by:

h c , v - a m = 5.67 + 3.86 V W i n d V W i n d ( Wind   speed ) < 5   m / s (2)

and h r , v - s k y = σ ε v ( T v 4 − T s k y 4 ) T v − T a m (3)

where σ ε v is the Boltzman constant (m²kg/s⁻²∙K⁻¹), ε v : glass emissivity and T s k y the sky temperature is determined by T s k y = 0.0552 T a m 1.5 ;

Equation (1) becomes:

Q p , a v 1 = h c , v − a ( T v − T a m ) + σ ε v ( T v 4 − T s k y 4 ) (4)

The heat exchange ( Q p , a v 2 ) between the glass and the absorber is by convection and by radiation.

Q p , a v 2 = ( h c , p - v + h r , p - v ) ( T p + T v ) (5)

h c , p - v : Coefficient of heat transfer by convection between the glass and the absorber and

h r , p - v : coefficient of heat transfer by radiation between the glass and the absorber given by:

h r , p - v = σ ( T p + T v ) ( T p 2 + T v 2 ) 1 ε p + 1 ε v − 1 (6)

where:

T p : Absorber temperature (K);

T v : Glass temperature (K);

ε v :Emissivity of the glass;

ε p : Emissivity of the absorber;

To determine the convection coefficient h c , p - v , the following correlations are used:

N u = 1 + 1.44 [ 1 − 1708 ( sin 1.8 β ) 1.6 R a ] [ 1 − 1708 R a cos β ] + [ ( R a cos β 5830 ) 1 / 3 − 1 ] [9] (7)

β : angle of incidence of the cooker and

R a : Rayleight’s number

R a = g ( T p − T v ) L c 3 T m a V a α a (8)

L c : characteristic length (space between the absorber and the glass);

g: intensity of gravity (m∙s⁻²);

α a : thermal diffusivity of air (m²∙s⁻¹);

V a : the kinematic viscosity of air (m²∙s⁻¹);

T m a : the average temperature of the air between the absorber and the glass, given by:

T m a = ( T p + T v ) / 2 (9)

And V a = μ a / ρ a (10)

μ a : dynamic viscosity of air (kg∙m⁻¹∙s⁻¹);

ρ a : density of air (kg∙m⁻³);

α : thermal diffusivity of air:

α = λ a / ρ a C p a (11)

C p a : heat mass of air at constant pressure (J∙kg⁻¹∙K⁻¹);

λ a : thermal conductivity of air (W∙m⁻¹∙K⁻¹);

N u = h c , p - v L c / λ a (12)

From which we get the convection coefficient:

h c , p - v = N u ( λ a / L c ) (13)

Duffie and Beckman have given an empirical relationship due to Kelvin for the calculation of the overall exchange coefficient before U a v , with an error of less than ±0.3 W/m² [9].

U a v = ( N C T p m [ T p m + T a m N + f ] e + 1 h c , v - a ) − 1     + σ ( T p m + T a m ) ( T p m 2 + T a m 2 ) 1 ε p + 0.00591 N h c , v - a + 2 N + f − 1 + 0.133 ε p ε v − N (14)

U a v : Loss coefficient of the front panel (W/m²∙K),

N: Number of glass

f = ( 1 + 0.089 h c , v - a − 0.1166 × h c , v - a × ε p ) ( 1 + 0.07866 N ) , (15)

h c , v - a = 5.67 + 3.86 × V w i n d (16)

C = 520 ( 1 − 0.000051 β 2 ) for 0 ∘ < β < 70 ∘ , and for 70 ∘ < β < 90 ∘ We take β = 70 ∘ ,

e = 0.43 ( 1 − 100 T p m ) , (17)

ε g : Glass emissivity,

T p m : Average plate temperature (K).

The prototype box-type solar cooker studied is exposed to solar radiation without any charge (empty heating plate). During the test period, the ambient temperature, the temperature of the heating plate also called absorber, the temperature of the indoor air (Tr), as well as the incident solar illumination, are measured.

During the various cooking tests, the following parameters are measured: the ambient temperature, the temperature of the hot plate, the temperature inside the kitchen utensil and the incident global solar illumination. The temperatures are measured using thermocouples, that of the heating plate is fixed in the middle of its surface. The overall solar irradiance is measured using an EPPLEY type pyranometer, with a conversion coefficient k equal to 10.41 mV/W/m² and an error in the measured irradiance ±10 W/m². The kitchen utensil used for these tests is an aluminum pan with a lid, painted black. Its total volume is 2.5 liters and its weight is 0.3 kg.

The preliminary cooking tests focused on the cooking of certain foods: eggs and rice. These tests were carried out to gauge the limits of the prototype in terms of maximum temperatures reached and its capacity to cook certain food products with evaluation of the cooking time (Figure 2).

The measurements carried out without load are intended to study the operation of the solar cooker.

Initially, measurements were taken in the morning in different places of the cooker before the experiment. The temperatures resulting from these different measurements are lower than room temperature. We deduce that during the night, there are heat losses by infrared emission.

The cooker is then exposed to the sun. The absorber temperature (Tp) increases to 92˚C, while the indoor air temperature (Tr) is around 83˚C after one hour. The system therefore has a low thermal inertia. Despite the variations in the illumination due to the numerous cloudy passages, the stagnation temperature of the indoor air is around, 90˚C and that of the absorber, 101˚C, after two hours. The greenhouse effect is not negligible. The double-glazed glass face increases the greenhouse effect and minimizes the heat losses from the absorber to the outside environment. There is also a slight variation in the temperature of the bottom and the side faces during operation. The cooker therefore has good thermal insulation. The ambient air temperature (Ta) varies between 30 and 32˚C. The different fluctuations in the lighting testify to the numerous cloudy periods. These different observations are perceptible in Figure 3.

The egg cooking test took place on 25/10/2019. We cooked two eggs in a saucepan containing 0.5L of water. The average overall illumination was 609.77 w/m². The test started at 10: 25 and ended at 12:55. Intermittent cloudy periods were observed throughout the test. The various measurements taken made it possible to plot the histogram and the curves of Figure 4. The histogram shows the variation of the illumination and the curves show the evolution of the temperatures of the indoor air (Tr), of the absorber (Tp), and cooking (Tw) as a function of time. The absorber temperature curve is permanently below that of the indoor and cooking air. The optimum temperature for the absorber is 115˚C and that for cooking is around 100˚C. This temperature is sufficient for cooking by boiling [10] [11]. During this test we see that the histogram of the illumination presents fluctuations which are due to the numerous cloudy passages. The disturbances are partially observed on the temperature curves of the absorber and the indoor air but less on the cooking temperature.

The test started at 1:00. and ended at 3:20. The cooker was this time previously heated in the sun. We have taken the readings of temperatures and lighting in the different compartments of the cooker. The histogram of the illumination and the curves of evolution of the different temperatures are represented in Figure 5 from the quantities noted during the test. The ambient temperature is around 34˚C and the average global illumination is 533.76 w/m². As indicated by the results in Figure 5, the temperature of the cooking utensil reached 82˚C at 13:35 after 35 min of cooking and 100˚C at 14:30, corresponding to a cooking time of

1:30. The test continued until 15:20 local time, which corresponds to a total cooking time of 2:20. The absorber temperature reached 115˚C.

The cooking of eggs and rice respects the maximum cooking time given by “Solar cookers international” [12] Figure 6 shows the rice and eggs after cooking.