Performance investigation of improved box-type solar cooker with sensible thermal energy storage

ABSTRACT

The main aim FIgure 9of this work is to design, develop and experimentally test the performance of an improved box-type solar cooker with thermal energy storage. The improvement features are the ability to concentrate solar rays and store thermal energy. The improved solar cooker became 20% less in inner surface area compared to the conventional solar cooker for the same intercept area of the sun. Experiments are conducted for stagnation test and load test followed by comparison of the thermal performance of improved solar cooker with conventional one. The performance testing parameters are used as per the Indian standard for box type solar cooker. Testing results showed that the averaged first figure of merits (F₁) is 0.115 for conventional and, 0.1349 for improved solar cooker with black stone as a thermal energy storage, 0.1238 for improved solar cooker with concrete as a thermal energy storage and 0.1453 for improved solar cooker without any thermal storage. As per the Indian standard for testing of box type solar cooker, the improved box-type solar cookers in all condition are found to be grade ‘A’ due to the fact that the first figure of merits (F₁) is greater than 0.12. Also the thermal energy storage materials used gives a remarkable storing capacity.

KEYWORDS:

• Solar energy
• box solar cooker
• improved solar cooker
• figures of merits
• thermal energy storage

Introduction

This study is conducted at an area known as Omorate (Daassanech). Daassanech is one of Ethiopian district administrations that named after inhabitant ethnic groups, traditionally they are Nomadic pastoralists. It is a wide remote area located in southern part of Ethiopia, about 780 km far from the capital city, Addis Ababa, near to the boarder of both Kenya and South Sudan.

The geographic coordinates of selected site, Omorate (Dassenech), is:

• Latitude: 4°49′59″ or 4.83333° N

• Longitude: 36°06′00″ or 36.10° E

• Elevation above sea level: 367 m.

Since Daassanech is a very remote location, and all domestic energy needs are achieved by biomass only the people are suffering from so many problems related to health, environment and other social problems.

A solar cooker is a device that utilise the sun’s radiation as an energy source to cook food, boil water and sterilise medical instruments. By using solar cooker it is possible to save time, cost and energy compared to the traditional biomass ovens. Likewise healthy problems resulting from indoor air pollution caused by biomass combustion, deforestation for fire wood and other related traditional biomass cooking problems can be reduced.

The main classifications of solar cookers are: box-, panel- and parabolic-type solar cookers. Often conventional box-type solar cookers are designed for the purpose of warming or heating food. For example, the solar cooker developed by Nandwani (2014) was promoted as Solar Food Warmers for schools in Costa Rica.

To improve its performance box-type solar cookers have been modified in different ways in the different country. Some of those modifications are reviewed as below.

Sethi, Pal, and Sumathy (2014) presented optimally inclined box-type solar cooker with single booster mirror along with design and development of a novel parallelepiped shaped cooking vessel design for efficient cooking. Abu-Malouh, Abdallah, and Muslih (2011) has studied the effect of two axes automatic tracking on a solar cooking system. Achamyeleh et al. (2017) designed and tested two major solar cookers, aluminium plated and black coated boxes. Theoretical and practical comparison was conducted to choose which cooker give the best efficiency with the same working environment. Mohammed, Rumah, and Abdulrahim (2013) developed and tested the performance of a truncated pyramid solar thermal cooker in Nigeria. During testing, the highest plate stagnation temperature achieved to be 145°C, under no-load condition and reflector covered with black cloth. In full-load condition the temperature of 5.2 kg of water inside the cooker raised from 60°C to 90°C in 72 minutes. The First Figure of Merit was calculated to be 0.120 and the Second Figure of Merit was found to be 0.410.

Tekle (2014) designed, prototyped and experimentally evaluated performance of low-cost inverted Pyramid shaped box-type solar cooker in Hawassa University, Ethiopia. Experimental testing has been taken based on standard of thermal test procedures for box-type solar cookers, by Mullick, Kandpal, and Saxena (1987). But the system he designed should track the sun frequently, per 20 minutes.

Tekle (2014) conducted one-year survey under the support of Japanese ODA to investigate the possibility of their newly developed durable and powerful panel-type solar cooker being used in the Federal Democratic Republic of Ethiopia as one of the heat sources for cooking. They conducted two field researches its outcomes revealed that almost all of the local typical food in Ethiopia can be cooked with solar cooker and 80% of the community members give positive feedback on the product.

Solar cookers with thermal storage

All solar cookers, like any other solar powered systems, can use thermal energy storage material to increase system performance. Specially, an indirect-type solar cooker uses thermal storage as a common unit of the system. TES is also used in box type and other concentrator-type solar cookers. The main purpose of thermal storage for solar cooker is to hold extra amount of heat and to balance the heat usage over the day in daily variation or over the year for seasonally varying incident.

Several works are carried out by researchers on phase change materials (PCM) integrated solar box cookers. Buddhi and Sahoo (1997) has designed and fabricated box-type solar cooker with latent heat storage for the composite climatic conditions of India. The experimental results demonstrate that it is possible to cook the food and provide a nearly constant plate temperature even in the evening with a solar cooker having latent heat storage. They also compared experimental results with those of a conventional solar cooker.

Many research works have been conducted with experiment by using different sensible thermal heat storage materials. Shrestha and Byanjankar (2007) investigated the effect of using stone pebbles as thermal energy storage. A thermal performance of box-type solar cooker with stone pebbles inside the cooker was tested with methodology described in ASAE international test standard. For the comparison, the cooker was put to test without stone pebbles, with uncoated stone pebbles and with black coated stone pebbles.

Saxena and Karakilcik (2017) have developed box-type solar cooker with low cost thermal energy storage for the thermal performance evaluation. A mixture of sand and granular carbon with an optimum ratio was used as sensible thermal energy storage in solar box cooker (SBC). The experimentation procedure was conducted under climatic conditions of Moradabad, India. The results indicated that the first Figure of merit (F₁) was 0.13, second Figure of merit (F₂) was 0.44, thermal efficiency was estimated to be 37.1%, and cooking power was estimated as 44.81 W. Then the system was found feasible for cooking during the off sunshine conditions.

Cuce (2018) experimentally analysed box-type solar cookers with and without thermal energy storage under Bayburt climatic conditions, Turkey. He used Bayburt stone, a special natural stone with low density and notably high specific heat capacity, to utilise as a sensible thermal energy storage medium in a cylindrical box-type solar cooker and compared thermal performance assessment of Bayburt stone cooker with a conventional cooker without thermal energy storage through a comprehensive experimental research and thermodynamic analysis. Energy efficiency of Bayburt stone cooker is found to be in the range of 35.3–21.7% while it is 27.6–16.9% for conventional solar cooker. Finally, he concluded from the results that Bayburt stone as a TES medium remarkably improved the thermal performance figures of box solar cookers.

Even though so many research works have been done in this area, still there is a wide research gap to fulfill societies need and to design socially acceptable solar cooker for the specific site. So in this work partially concentrating box-type solar cooker with locally available thermal energy storage material is designed, fabricated and tested in remote area of Ethiopia.

Thermal modelling of box-type solar cookers

Description of the solar cookers

As shown in Figure 1below both inner wall and outer reflectors direct sunrays in addition to beam and diffuse solar energy to black painted absorber with TES. Because black makes sure, the incoming sunlight is absorbed and metal easily conducts the heat to the food inside the pan or TES under plate.

Solar intercept area of this solar cooker is 50 × 50 cm² with inclined glazing glass and 4 cm thickness of plywood and inset fibre natural insulation has been used. Detail dimensions has been presented in Figure 2.

Figure 1. Schematic description of IBSC

Figure 2. Improved and conventional solar cookers with equal aperture area

Box-type solar cooker model

Losses through bottom and side (wall) can easily calculate from the following equation:

$U_b=\frac{K\ast A_b}{\mathrm{\Delta }x}$

$U_s=U_{p-e}=\frac{K\ast A_e}{\mathrm{\Delta }x}$

The top loss coefficient U_t can be calculated from the empirical equation by following the basic procedures of klein (1979) as given in Duffie and Beckman (2006):

$U_t={\left(\frac{N}{\frac{C}{T_{pm}}{\left(\frac{T_{pm}-T_a}{N+f}\right)}^e}+\frac{1}{h_w}\right)}^{-1}+\frac{\sigma \left(T_{pm}+T_a\right)\left({T_{pm}}^2+{T_a}^2\right)}{{\left({\epsilon }_p+0.005591\ast N\ast h_w\right)}^{-1}+\frac{2N+f-1+0.133{\epsilon }_p}{{\epsilon }_g}-N}$

Where: $f=\left(1+0.089h_w-0.1166\ast h_w\ast {\epsilon }_p\right)\ast \left(1+0.07866\ast N\right)$

$C=520\left(1-0.000051\ast {\beta }^2\right)$

$e=0.430\left(1-100/T_{pm}\right)$

${\epsilon }_g=0.88\left(Emmitanceofglass\right)$

$h_w=5.7+\left(3.8\ast V_{wind}\right)$ wind heat transfer coefficient ($W/m^{2}K$)

ε_p is emittance of absorber plate

$V_{wind}$ is wind speed [m/s],

N is number of glazing, $\beta$ is absorber slope

The absorber plate temperature at any time (t+∆t) can be obtained from energy balance of absorbed by and loss from the cooker chamber. The energy balance equation of cooker chamber is:

$q_{stored}=q_{absorbed}-q_{useful\left(absorbedbywater\right)}-q_{loss\left(top,bottom,edge\right)}$

${\left(m{C}_p\right)}_p\frac{d{T}_p}{dt}={\tau }_g{\alpha }_p{A}_c{I}_c-A_c{U}_t\left(T_p-T_a\right)-A_e{U}_{pae}\left(T_p-T_a\right)-A_{pot}{U}_{pw}\left(T_p-T_w\right)-A_b{U}_{pb}\left(T_p-T_a\right)$

Without load the plate temperature will be:

${\mathrm{T}}_p^1=\frac{{\tau }_g{\alpha }_p{A}_c{I}_c\mathrm{\Delta }t}{{\left(m{C}_p\right)}_p}+\left[1-\left(\frac{A_c{U}_t+A_e{U}_{pae}+A_{pot}{U}_{pw}+A_b{U}_{pb}}{{\left(m{C}_p\right)}_p}\right)\mathrm{\Delta }t\right]T_p^0+\left[\frac{A_b{U}_{pb}+A_e{U}_{pae}+A_c{U}_t}{{\left(m{C}_p\right)}_p}\right]T_a\mathrm{\Delta }t$

Where: ${\left(m{C}_p\right)}_p$ is the product of mass and specific heat capacity of the absorber plate.

where$T_p^0$ is absorber plate tmeperature at time, t

${\mathrm{T}}_p^1$ is absorber plate tmeperature at time, t + Δt

${\tau }_g$ is transmitivity of the glass

${\alpha }_p$ is absorpitivity of the absorber plate

Similarly, the water temperature at any time (t+∆t) can be calculated from energy balance of water in the pot as follows.

${\left(m{C}_p\right)}_w\frac{\mathrm{d}{T}_w}{dt}=A_{pot}{U}_{pw}\left(T_{pm}-T_w\right)-A_{pot,t}{U}_{pt}\left(T_w-T_a\right)$

${\mathrm{T}}_w^1=\left[1-\left(\frac{\mathrm{\Delta }t}{{\left(m{C}_p\right)}_w}\left(A_{pot}{U}_{pw}+A_{pot,t}{U}_{pt}\right)\right)\right]T_w^0+\frac{\mathrm{\Delta }t}{{\left(m{C}_p\right)}_w}\left[A_{pot}{U}_{pw}{T}_{pm}+A_{pot,t}{U}_{pt}{T}_a\right]$

where,$T_w^0$ – is the water tmeperature at time, t

${\mathrm{T}}_w^1$ – is the water tmeperature at time, t + Δt

$A_{pot}$ – sum of the bottom and side area of the pot

$A_{pot,t}$ – top area of the pot

$T_{pm}$ – is the mean pot temperature

$U_{pt}$ – is heat loss coefficient from the water to the ambient

$U_{pw}$ – is heat transfer coefficeint from the pot surface to the water

Figures of merits

First figure of merit is based on a stagnation test cooker box without any load, defined as the ratio of optical efficiency to the heat loss coefficient ατ/U_L as follows:

$F_1=\frac{T_p-T_a}{H_s}$

Where:

τ – transimittance of the glass

α – absorptance of the cooking tray

U_L – heat loss coefficient of the cooker, and

H_s – solar radiation on the aperture plane of the box-type solar cooker during steady state

Second figure of merit is computes from a load test that follow water boiling test procedure for the thermal performance evaluation of a solar cooker.

$F_2=\frac{F_1{\left(m{C}_p\right)}_w}{A_g\ast t}ln\frac{1-\frac{1}{F_1}\left[\frac{T_{w1}-T_a}{H}\right]}{1-\frac{1}{F_1}\left[\frac{T_{w2}-Ta}{H}\right]}\dots$

Where:

F₁ – first figure of merit from stagnation test

${\left(m{C}_p\right)}_w$ – product of the mass of water and specific heat in J/$\text{textdegree}\mathrm{C}$

A_g – aperture area of the cooker cover plate in m²

t – time taken for heating from $T_{w1}$to $T_{w2}$ in seconds

$T_a$ – average air temperature over time period t in $\text{textdegree}\mathrm{C}$

H – average solar radiation over time period ti W/m²

Solar radiation power is calculated by using based on well-known Angström model which was modified latter by Prescott (1940) and Page (1961). An average solar radiation is calculated as maximum in February (6.563 KW/m²/day) and minimum in July Month (5.578 KW/m²/day) and Annual Average daily solar radiation is 6.134 KW/m²/day.

Required thermal energy to raise water from 30°C to 93°C,

$Qw=Mw\ast Cp\ast \mathrm{\nabla }T=2\ast 4200\ast \left(93-30\right)KJ$

$Qw=2\ast 4200\ast \left(93-30\right)J=529.2KJ$

Required energy rate for cooking ($\dot{Q}w$)

$\left(\dot{Q}wr\right)=\frac{529.2\ast {10}^{3}J}{\left(120\ast 60\right)Sec}=73.5W$

Energy loss by evaporation ($\dot{Q}wl$)

$\dot{Q}wl=\frac{m{\hspace{0.17em}}_{l}x\hspace{0.17em}{h}_{fg}}{\mathrm{\Delta }t}=\frac{\left(\frac{10}{100}\ast 2\right)\hspace{0.17em}Kg\ast 2342\ast {10}^3\frac{J}{Kg}}{\left(120\ast 60\right)\hspace{0.17em}sec}=65.06\hspace{0.17em}W$

Energy loss through insulation and glaze (${\dot{Q}}_i$)

$Qi=Ag\left(\frac{7}{100}\ast I_{ac}\right)=Ag\left(0.07\ast 600\frac{W}{m2}\right)=(42\ast Ag)\frac{W}{m2}$

Total power required

$\dot{Q}t=73.5+65.06=138.56\mathrm{W}$

Minimum aperture area of the cooker (A_g),

$\mathrm{A}\mathrm{g}=\frac{\dot{Q}w}{I_{av}-0.07I_{av}}=\frac{138.56}{600-42}=0.25m^2$

Considering the standard for full load testing which is 8 kg/m² of collector area as per IS 13429 (Part 3) 2000, a 2 kg load is selected for the solar intercept area of 0.25 m².

Solar radiation estimation

Global solar radiation based on Angström-prescott model is described as follows (Bekele, Alemu, and Mishra 2013):

$\frac{\bar{H}}{\overline{Ho}}=a+b\frac{\overline{n_s}}{\overline{N_s}}$ … … … … … … … … … … … … … … … … … … … … … … … … (8)

Where: $a=-0.110+0.235cos\phi +0.323\left[\frac{\overline{n_s}}{\overline{N_s}}\right]$

$b=1.449-0.533cos\phi -0.694\left[\frac{\overline{n_s}}{\overline{N_s}}\right]$

$\bar{H}$= monthly average daily radiation on horizontal surface

$\overline{H_o}$ = monthly average daily extraterrestrial solar radiation outside the earth atmosphere

$\overline{n_s}$ = monthly average daily hours of bright sunshine

$\overline{N_s}$ = monthly average of maximum possible daily hours of bright sunshine

$\overline{H_o}=\frac{24\mathrm{x}3600I_{SC}}{365}[1+0.033cos(\frac{360n}{365})](cos\phi cos\delta sin{\omega }_s+\frac{\pi \omega s}{180}sin\phi sin\delta )$

The monthly average daily hours of bright sunshine data for Omorate are obtained from the Ethiopian National Meteorological Agency and tabulated as Table 1.

Table 1. Monthly average daily hours of bright sunshine (${\bar{n}}_s$)

Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
Monthly average daily bright sunshine hours (${\bar{n}}_s$)	7.8	7.5	6.9	6.2	7.0	7.4	6.7	7.3	7.2	6.4	6.9	7.8

Based on the above equations the monthly average daily solar radiation for Omorate (Figure 3(a)) is estimated as maximum in February (6.458 KW/m²/day) and minimum in July Month (5.55 KW/m²/day) and annual average daily solar radiation is 6.134 KW/m²/day.

The daily average hourly global radiation on a horizontal surface (Figure 3(b)) can be determined from: (Bekele, Alemu, and Mishra 2013)

$\bar{I}=\frac{H\pi }{24}\left(a+bcos\omega \right)\frac{cos\omega -cos{\omega }_s}{sin{\omega }_s-\frac{\pi }{180}\omega scos{\omega }_s}\dots$

Where: $a=0.409+0.5016sin\left({\omega }_s-60\right)$

$b=0.6609-0.4767\mathrm{s}\mathrm{i}\mathrm{n}\left({\omega }_s-60\right)$

${\omega }_s$ is sunset hour angle

$\omega$ is hour angle

(a) Monthly average daily solar radiation

(b) Monthly average hourly global radiation on horizontal surface for June

Figure 3. Solar radiation data for Daassanech (Omorate)

Experimental setups

In order to construct improved solar cooker, the selected materials are low cost, locally available and able to withstand high temperature (Figure 4). The details materials and their properties are given in Tables 2 and 3 below.

Figure 4. (a) Black stone used as TES and (b) concrete used as TES, (c) ‘Inset’ fibre used as insulation

Table 2. Materials used for construction of IBSC

Part	CSBC	Square glazing with trapezoidal absorber
Absorber	Sheet metal	Sheet metal/black stone
Insulation	Foam	‘Enset’ fibre of thickness 5 cm
Reflectors	Plane mirror and aluminium foil	Plane mirror and Aluminium foil
Box	Wood frame	Wood frame/plywood
Glazing	Glass (k =15 m^−1)	Glass (k =15 m^−1)

Table 3. Physical properties of TES materials

Properties	Concrete	Black stone
Density (kg/m^3)	2350	2660
Thermal conductivity (W/m K)	1.2	1.513
Specific heat (J/kg K)	894	1534

Enset is one of the main indigenous drought resistant crops in Ethiopia. It contributes to food security for more than 20% of Ethiopia’s population [Zerihun 2014]. It is physically like banana plant, thus it is called sometimes ‘false banana’ but unlike banana except seed and leaf all other parts are edible and it has no edible fruits.

As shown in Figure 5 both cookers have the same collector area but improved solar cooker has 5 cm additional height to hold TES material and its absorber area is smaller than the conventional solar cooker.

Figure 5. Experimental setup (left) and sample testing result (right)

Instruments used during experimental testing are k-type thermocouple with four channel digital thermocouple reader and weighting scale. Thermocouples has been calibrated before it is used for testing by using laboratory standard calibrator of ± 0.1% accuracy and obtained a maximum uncertainty of 0.42%.

The total inner surface area including absorber plate, for conventional solar cooker and for improved one is calculated as 0.8 m² and 0.64 m², respectively and this shows the improved solar cooker became 20% less in inner surface area. The experimental data was conducted for stagnation test, load test and cooking test between June 1015, 2019 and the result is explained as below.

Result and discussion

Stagnation test

As it can be seen from Figures 6 to 9 the stagnation (no load) test is carried out from sunrise to sunset and continued up to the midnight for investigating the effect of thermal storage. The plate temperature is observed to increase from sunrise to noon due to the increase of solar insolation and nearly constant till 3:00 PM then after declined up to the sunset following the decrease of solar insolation.

After the sun set the plate temperature continued to decrease due to the heat loss from the cooker to the ambient. Here it is observed that for the case of CBSC (Figure 6) and IBSC without thermal storage (Figure 8) the plate temperature has almost dropped down to the ambient temperature. Whereas for IBSC with thermal energy storages (Figures 7 and 8) even though the plate temperature similarly dropped due to heat loss to the ambient it is still significantly higher than the ambient temperature up to the mid night and this show the capacity of the cooker to warm food even in the absence of sun due to the stored thermal energy.

Figure 6. Plate temperature of conventional box solar cooker

Figure 7. Plate temperature of improved box solar cooker with concrete

Figure 8. Plate temperature of improved box solar cooker with black stone

Figure 9. Plate temperature of improved box solar cooker without TES

Load test

The load tests have been conducted for both conventional and improved ones starting from 10:00 AM local time. As it can be seen from the graphs of Figure 10–12 the water temperature increase very slowly after 100°C due to the occurrence of a film of water vapours as a result of phase change and covers the inner surface of transparent glass cover increasing the thermal resistance to the radiation absorption.

Figure 10. Load test temperature profile of conventional box solar cooker (CBSC)

Figure 11. Load test temperature profile for IBSC with Blackstone as TES

Figure 12. Load test temperature profile for IBSC with concrete as TES

During the load test for the case of an improved box-type solar cooker without any thermal energy storage (Figure 13) the water temperature has attained a temperature above 100°C within in 2 hours. Initially water was at 37°C and after 2 hours it has become 101.5°C, so averagely it increased 5.375°C per each 10 minutes (0.5375°C/minute).

Figure 13. Water temperature profile for IBSC without any TES

Comparisons of temperature distributions

Comparison is presented for box stagnation and load tests in Figures 14–16. As seen in Figure 14 an improved box-type solar cooker without thermal energy storage has absorbed greater solar radiation and its absorber plate has attained a maximum temperature of 155°C while maximum temperature attained by conventional solar cooker is about 139°C. Also it is observed that the plate temperature of an improved box-type solar cooker without TES is highly fluctuating with solar intensity. During day time the absorber plate temperature of an improved box-type solar cooker with concrete as a TES is seen to be the minimum among all because the solar radiation absorbed by the plate has transferred to the concrete (i.e. high heat loss from the absorber plate to the concrete). During night time (when there is no sun) it is seen that cookers with TES diffuses remarkable heat which can warm food.

Figure 14. Comparing of stagnation plate temperature distributions

As described in Figures 15 and 16 the load tests were started at 10:00 AM with initial water temperature of 38°C and absorber plate temperature above 46°C for all cookers. With increase in time it is observed that the absorber plate and water temperature in the conventional box-type solar cooker is higher than that of an improved box-type solar cooker with TES. This is because in an improved box-type solar cooker with TES there is an additional load due to a black stone and concert in the system which is being used as TES and hence it absorbs heat from the absorber plate and reduces the useful energy to be used for water heating.

Figure 15. Comparing of plate temperature during load test

Figure 16. Comparing of load test temperature profile

Cooking test

Cooking test has been conducted on 15^th of June 2019 for 0.5 kg of potato (Figure 17(left)) with one litre of water added and Shoforo drink (Figure 17(right)) with two litres of water added. The IBSC without TES cooked the potato in 50 minute, IBSC with black stone as TES took 80 minutes to cook and the CBSC has taken 110 minutes to cook the same amount of potato. The Shoforo was cooked using the IBSC without TES and it was cooked enough to drink after 80 minutes.

‘Shoforo’ is a marvellous cultural hot drink in Daassanech; it is a broth of coffee husk, made by infusing coffee husk in boiling water to cook it, and be ready for drink by extracting its broth.

Figure 17. Cooking test for potato using CBSC (left) and ‘Shoforo’ using IBSC without TES (right)

The stored thermal energy can be used for warming a food and this is demonstrated in Table 4 for warming a 2 kg of Shoforo drink as follows:

• Mass of the storage material (Blackstone) = 6.25 kg

• Required warming temperature of Shoforo drink, $T_{warmig}$ = 45 °C.

• The initial temperature of Shoforo drink = ambient temperature

• Energy required for warming a Shoforo drink = ${\left(m{C}_p\right)}_{Shoforo}\left[T_{warmig}-T_{initial}\right]$

• Usable stored energy = ${\left(m{C}_p\right)}_{blackstone}\left[T_p-T_{warmig}\right]$

• Energy stored = ${\left(m{C}_p\right)}_{blackstone}\left[T_p-T_a\right]$

Table 4. Demonstration of stored energy and energy required for warming a Shoforo drink

Time (hr)	Tp of IBSC with black stone (°C)	Ta (°C)	Thermal energy stored [J]	Usable stored energy (J)	Required energy for warming a Shoforo (J)
18:00	119.5	37	790,968.8	714,268.8	67,200
19:00	97.5	35.8	591,548.8	503,343.8	77,280
20:00	90	34.4	533,065	431,437.5	89,040
21:00	83	33.9	470,746.3	364,325	93,240
22:00	70.5	30.5	383,500	244,481.3	121,800
23:00	51	31.5	186,956.3	57,525	113,400
24:00	48.5	30.4	173,533.8	33,556.25	122,640

The result shows that for a time period of 18:00–22:00 hrs, the heat energy required to warm a Shoforo drink from ambient temperature to 45°C is higher than the usable stored thermal energy. Thus, the stored energy can be used for warming a food.

Figures of merits

The experiments have been conducted following the Indian testing standard procedures which is proposed by Mullick, Kandpal, and Saxena (1987) and approved by Bureau of Indian Standard (BIS). As per this standard (IS 13429 (Part 3) 2000) two figures of merits of (F₁ and F₂) are used as thermal performance parameters. Load and no-load (stagnation) tests have been conducted.

For the conventional solar cooker the theoretical analysis gives the first (F₁) and second (F₂) figures of merits equal to 0.116 and 0.553 respectively, whereas the corresponding experimental result gives F₁ = 0.115 and F₂ = 0.524. This shows there is a good relationship between theoretical and experimental analysis of the solar cooker performance

The average experimental value of the first figure of merits (F₁) is 0.1349 for improved BSC with Blackstone as TES, 0.1238 for improved BSC with concrete as TES and 0.1453 for improved BSC without any thermal storage, respectively. A high value of F₁ indicates good optical efficiency and low heat loss factor from the absorber plate.

The average experimental value of the second figure of merits (F₂) is 0.97 for improved box solar cooker with black stone as TES, 0.865 for improved box solar cooker with Concrete as TES, and 1.0964 for improved box solar cooker without any TES respectively. A high value of F₂ shows cooker has good heat exchange efficiency factor, good optical efficiency, and low heat capacity of the cooker interiors and pans compared to a full load of water.

Both the first figure of merits (F₁) and the second figure of merits (F₂) for improved box-type solar cookers with thermal energy storage are less than that of an improved box-type solar cooker without thermal energy storage. This is due to the fact that a part of thermal energy is transferred from the absorber surface to the storage system for later use when there is no sun.

Comparison of the present work with previous works

The comparisons of the present work with similar previous works done by different researchers are summarised as given in the Table 5.

Table 5. Thermal performance comparison of the present study with the previous researchers work

Solar cookers conditions	Present study 1^st Figure of merits (F1)		Present study 2^nd Figure of merits (F2)		Tekle (2014)		Shrestha and Byanjankar (2007)
	Expt.	Theor.	Expt.	Theor.	F1	F2	F1	F2
Conventional BSC (0.25 m^2)	0.115	0.116	0.524	0.553	0.1250	0.14	0.19	0.55
IBSC with concrete	0.1238	-	0.865	-	-	-	-	-
IBSC with Blackstone	0.1349	-	0.97	-	-	-	0.23	0.27
IBSC w/out TES	0.1453	-	1.0964	-	0.1252	0.28	-	-

The work presented by Shrestha and Byanjankar (2007) is conventional BSC with stone pebbles and Tekle (2014) designed and prototyped modified-type solar cooker with trapezoidal glazing surface. According to the results described in this work, an improved box-type solar cooker with TES is better than the works of Tekle (2014) and Shrestha and Byanjankar (2007). For instance in this work the maximum temperature obtained without stone pebble is about 130°C; in this work also conventional BSC maximum no-load temperature is 145°C. This much difference is revealed due to the difference of volume of cookers. The first and Second figures of merits are 0.19 and 0.55 for Shrestha and Byanjankar (2007) work, in this work it is 0.115 and 0.524 respectively.

The improved box-type solar cooker of the present study shows a higher value for the second figure of merits when compared with Tekle (2014) and Shrestha and Byanjankar (2007) and this shows the cooker has better heating capacity.

Conclusion

From the present experimental study the following conclusions can be drawn:

• The Improved box-type solar cooker with/without thermal energy storage is found to be better than conventional box-type solar cooker.

• It is observed that locally available materials such as black stone and concrete as sensible thermal energy storage and ‘Enset’ fibre as an insulation and wood as a frame can be used for the construction of box-type solar cooker with remarkable thermal performance.

• The experimental test results showed that the maximum no-load absorber plate and full-load water temperatures are 155°C and 110°C respectively. In an improved box-type solar cooker without TES the water boiled in less than two hours whereas in another cookers it take up to three hours.

• As it is seen from the experimental results, though an improved box-type solar cooker without TES is better than all other solar cookers to fast cooks in daytime, improved solar cooker with TES is able to store thermal energy to utilise it in evening. Also it makes uniform heat energy supply to the water with naturally fluctuating solar energy.

• Improved solar cooker with square solar intercept area which has 5 cm additional height to hold thermal storage material has 20% less size than the conventional solar cooker inner area for the same intercept area of the sun. Thermal efficiency comparison is done for the same aperture area of conventional and improved box solar cooker but if the same absorber area is used an improved solar cooker can absorb much solar energy and it can have a wide space to hold additional thermal storage materials.

• The thermal energy storage used will help the cooker to warm a food even when there is no sun in the night. Of course the amount of thermal energy stored depends on the storage material type and size.

Nomenclatures

Table

CBSC	Conventional box-type solar cooker
IBSC IS TES	Improved box-type solar cooker Indian Standard Thermal energy storage
STES	Solar thermal energy storage
Cp	Specific heat capacity
Cpw	Specific heat capacity of water (J/kgk)
F1	First figure of merit
F2	Second figure of merit
ASAE	American Society of Agricultural Engineers Standards
I IC ISC H	Hourly solar radiation on horizontal surface (W/m^2) Hourly solar radiation incident on the absorber surface The solar constant = 1367 W/m^2 Daily solar insolation on tilted surface (W/m^2)
Kw	Thermal conductivity of water (W/m^oC)
Mw	Mass of water (kg)
Upb	Bottom loss coefficient (W/m^2K).
Upw	Heat loss coefficient between absorber plate and water
UL	Overall loss coefficient (W/m^2K).
Us, Upae	Side loss coefficient (W/m^2K).
Ut	Top loss coefficient (W/m^2K).
Tp1	Absorber plate temperature of CBSC
TP2	Absorber plate temperature of IBSC
Tw1	Water temperature of CBSC
Tw2	Water temperature of IBSC
Ag	Aperture area
AC	Collector/absorber area
As	Inner wall surface area
${\mathrm{A}}_{\mathrm{e}}$	Heat transfer area through the edge
${\mathrm{A}}_{\mathrm{b}}$	Heat transfer area through the bottom
Greek Symbols
θ	Angle of incidence of beam radiation
β	Angle of inclination of reflectors
βc	Tilt angle of the cover
φ	Latitude angle
εg	Emmittance of glass cover
τ	Transmissivity of glass cover
σ	Stephen Boltzmann constant
δ	Angle of declination of the sun
ω	Hour angle

Additional information

Notes on contributors

Ephrem Milikias

Ephrem Milikias is a lecturer in Dilla University, Dilla - Ethiopia, since Sep. 2016. He received a Bachelor of Science Degree in Mechanical Engineering from Arbaminch University, Arbaminch – Ethiopia in June 2016 and Master of Science Degree in Thermal Engineering from Adama Science and Technology University, Adama - Ethiopia in July 2019. His research area is Renewable Energy.

Addisu Bekele

Dr. Addisu Bekele was born in Ethiopia on 10th May 1985. He Completed B.Sc. Degree in Mechanical Engineering in 2004, from Bahir Dar University, Bahir Dar-Ethiopia, M.Sc. Degree in Mechanical Engineering (Thermal) in 2007 from Addis Ababa University, Addis Ababa-Ethiopia and PhD Degree in Thermal Engineering in 2012 from Indian Institute of Technology Roorkee, Roorkee-India. He has published more than 17 articles on international Referred journals and on international and national conferences. His research areas are solar energy, wind energy, biomass, fluid flow and heat transfer, heat exchanger, numerical and computational analysis, refrigeration and air conditioning.

Chandraprabu Venkatachalam

Dr. Chandraprabu Venkatachalam was born in Tiruchengode, Namakkal (DT), Tamilnadu, India on 25th January 1977, Completed Bachelor of Engineering (Mechanical Engineering) in the year of 1999, completed Master of Engineering (Thermal Engineering) in the year of 2005 and completed PhD (Thermal Engineering) in the year of 2014. He has published 15 articles in international journal, 3 articles in international conference and 7 articles in national conferences. His research area is heat transfer enhancement in the air conditioning system using nano-fluids and solar energy.