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Energy Procedia 57 (2014) 1613 – 1622

2013 ISES Solar World Congress

Theoretical and Experimental Comparison of Box Solar

Cookers with and without Internal Reflector
Mulu Bayray Kahsaya*, John Paintinb, Anwar Mustefaa, Asfafaw Haileselassiea,
Meseret Tesfaya, Biniam Gebraya
a
Department of Mechanical Engineering, EiT – M, Mekelle University, P.O.Box 231, Mekelle, Ethiopia
b
Department of Electrical Engineering, EiT – M, Mekelle University, P.O.Box 231, Mekelle, Ethiopia

Abstract

Box solar cookers are commonly built with internal sheet metal painted black as an absorber. In order to
increase the performance, a design which incorporates internal reflection is proposed in this paper. The
aim of this paper is to report comparisons made between box solar cookers with and without internal
reflector. Theoretical modelling of the two types of cookers has been made by considering the radiation,
convection and conduction heat transfer employing the thermal network method. The theoretical analysis
made was based on steady state heat transfer analysis of the cookers. Experimental comparisons were also
made on two cookers having the same aperture area and made from the same type of materials except the
internal absorber. The tests were made as per the American Society of Agricultural Engineers (ASAE)
procedure.

The result of the theoretical analysis predicts that the performance will be higher in the cooker with
internal reflector than the same cooker without reflector. The steady state analysis shows that for the
cooker with reflection the temperature of the bottom absorber plate is higher than the cooker without
reflector. Similarly, results of dry test and water boiling test show better performance by the cooker with
reflector. The standard stagnation temperature and the cooking power were higher in the cooker with
reflector as compared to the cooker without reflector. In conclusion, the performance of box solar cookers
can be enhanced by making appropriate angle side walls of the absorber and providing internal reflection.

© 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
© 2013 The Authors. Published by Elsevier Ltd.
(http://creativecommons.org/licenses/by-nc-nd/3.0/).
Selection
Selection and/or
and/or peer-review
peer-review under responsibility
under responsibility of ISES. of ISES

Keywords: Box solar cooker, thermal network method, steady state analysis, dry test, water boiling test

* Corresponding author. Tel.: +251 914 301683; fax: +251 344409304.

E-mail address: mul_at@yahoo.com

1876-6102 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/3.0/).
Selection and/or peer-review under responsibility of ISES.
doi:10.1016/j.egypro.2014.10.153
1614 Mulu Bayray Kahsay et al. / Energy Procedia 57 (2014) 1613 – 1622

1. Introduction

Solar cooking is one of the cheapest alternatives in countries where there is plenty of sunshine. There
are various kinds of solar cooker technologies. One of the simplest technologies is the box solar cooker.
Box solar cookers can be used to cook variety of food items. However, box solar cookers have their own
limitation. It is not possible to cook food items which need high temperature. Hence, the cookers cannot
completely replace other energy sources. It can reduce the dependence on unsustainable use of biomass or
any other non-renewable sources. The other limitation is that box solar cookers need sometime which may
range 2-3 hours to cook food. Compared to electric or biomass stoves, the cooking time is long. This
limitation is probably the most influencing factor for users to accept solar cooking.

Improvements in the performance of box solar cookers will have positive influence in reducing
cooking time and hence increase the acceptance by users. In order to make improvements on performance,
it is essential to look at theoretical models. Such models can be used to study the effect of changing some
parameters on the performance and optimize the geometry, size and materials to be employed. Once such
models are developed experimental tests are necessary to validate the models. The modeling discussed in
this paper is to look at inner reflectors in enhancing performance.

Reflectors on the sides and in the rear of the box are used to increase solar radiation entering into the
cooker. Such reflectors which are commonly made on the outside edges of the box have the advantage of
reflecting solar radiation in to the box. On the other hand, the disadvantages are that the reflector materials
add weight and cost to the cooker and require more frequent tracking to avoid shading. The back reflector
can be kept since it has the additional function of a cover and protection for the cooker glazing when not
in use. The outer side reflectors have to be replaced to avoid the above disadvantages. The design which is
discussed in this paper is to use all the sides of the box cooker as reflector and the bottom as an absorber.

Nomenclature
Aap Aperture area of the cooker [m2]
Cp Heat capacity of water [J/kg oC ]
G Global solar radiation [W/m2]
I Solar power through aperture of the cooker [W]
Pbab, Psp Heat input at bottom absorber plate and side plate, respectively [W]
qij Heat flow between nodes i and j [W]
Re,ij Equivalent thermal resistance between nodes i and j [oC/W]
SST Standard stagnation temperature [oC]
Tamb,Ti,Ts Temperature at ambient, node i and at stagnation, respectively [oC]
η Efficiency of cooker
 Mulu Bayray Kahsay et al. / Energy Procedia 57 (2014) 1613 – 1622 1615

2. Literature Review

The time needed for cooking food items using box solar cookers is an important factor in acceptance
of the cookers by users. The time needed to cook for different food items are indicated in many reports
and user manuals of cookers, for example [1]. Any improvements in the performance of the box cookers
will have influence in the cooking time. Theoretical analysis coupled with experiments can provide an
optimized option. By making comparison between theoretical and experimental results real situation
thermal behavior can be found. For this reason mathematical structured modeling is useful for designing
solar cookers.

Theoretical modeling of the box solar cookers can be done using different methods. Numerical
methods such as finite difference, finite element and computational fluid dynamics (CFD) are the
alternative techniques. However, the complexity and computational time are high for the methods such as
CFD [2]. The analogy between the equations of heat transfer and electrical circuit can be used quite easily
for the steady state modeling of the cookers. The method is based on the similarities between the
diffusion equation for thermal analysis and electrical circuit analysis. The method is called thermal
resistance network modeling [3, 4]. In this method voltage is analogous to temperature while current is
analogous to heat flow. Hence the nodal analysis method used in solving electrical circuit problems can
be implemented in a spreadsheet to solve for nodal temperatures.

Experimental procedures for performance testing are recommended in international standards. The two
widely reported in literature are the American Society of Agricultural Engineers (ASAE) [5] and
European Committee on Solar Cooking Research (ECSCR) [6]. The standards describe the conditions
during testing, controlled variables, instrumentations and performance parameters.

3. Methodology

3.1 Description of the cookers

The cookers are made from the same types of materials. The outer box is made of wood, the inner box
is made of metal sheet and the upper cover is made of double glazing. The only difference is in the
geometry of the inner metal box. For the cooker without reflector the metal box is painted black all
around the inner surfaces. For the cooker with reflector the sides and front are shaped at 60 degree slope
and the surfaces are covered with reflecting film. Figure 1 shows the schematic diagram of the cookers.
For the cooker without reflector inner metal box is shown in solid lines and for the cooker with reflector
inner metal box shown in dashed lines. The aperture area remains the same for both designs. Table 1
shows dimensions and materials used for the fabrication of the cookers.
1616 Mulu Bayray Kahsay et al. / Energy Procedia 57 (2014) 1613 – 1622

Double glazing

Wooden
outer box

Dashed lines show

Wooden Edge of inner
Air gap all around inside reflector
spacers metal box
metal box

Figure 1 Schematic drawing of the cookers showing the difference between the two designs.

Table 1 Dimensions and materials of the cookers

Overall Width 0.43 m

size Length 0.48 m
Height at front 0.15 m
Height at back 0.35 m
Aperture area 0.142 m2
Outer box Wood Thickness 50 mm
Inner box Steel sheet Thickness 1.5 mm
Glazing Glass Thickness 4 mm
Spacing between 10 mm
upper and lower
glazing
 Mulu Bayray Kahsay et al. / Energy Procedia 57 (2014) 1613 – 1622 1617

3.2 Theoretical modeling

In order to simplify the modeling the following assumptions are made.

x The surfaces of the cookers to be modeled are considered as nodal points and hence isothermal.
x The surfaces except the reflector are assumed to be diffuse emitters for thermal radiation.
x The input solar energy is assumed to last indefinitely so that steady state temperatures will be
reached.
x Proper tracking is assumed hence the solar radiation strikes the absorber plate at zero angle of
incidence.
The cooker is modeled into eight nodal points and the ambient condition is considered as the ninth
nodal point. The node numbering and definition is shown below in Table 2. The bottom absorber plate
and side plate are separately included to consider the difference in the two designs. In the case of the
cooker without reflector the side plate will be an absorber while in the case of the cooker with reflector
the side plate will have no absorption and will radiate the incoming solar radiation.

Table 2 Description of nodes.

Node Description Temp. Remark

1 Bottom absorber T1 Solar energy input
plate to the node Pbab
2 Side plate T2 Solar energy input 5
4
to the node Psp
3 Cooker inside air T3
4 Inner glazing T4
5 Outer glazing T5 3
6 Side inner T6
wooden wall
1 2 6 7
7 Side outer T7 9
wooden wall
8 Bottom wooden T8
wall 8
9 Ambient Tamb
environment
Figure 2 Thermal network model of the cooker.
The thermal network has been developed by considering the heat flow between each combination of
nodes. The thermal network model of the cooker is shown in Figure 2. The node numbers and the
equivalent thermal resistance between nodes are shown in the Figure. At steady state condition the heat
flowing into a node and out of a node are balanced. The following eight simultaneous equations represent
the heat balance at nodes 1-8. The eight equations are sufficient to find the unknown temperatures. Node
9 is with known condition of ambient temperature.

Node 1: Pbab + q18 + q13+q14 = 0 Node 2: Psp + q21 + q23 + q26 = 0 Node 3: q31 + q32 + q34 = 0
Node 4: q41 + q43 + q45 = 0 Node 5: q54 + q5amb = 0 Node 6: q62 + q67 = 0
Node 7: q76 + q7amb = 0 Node 8: q81 + q8amb = 0
1618 Mulu Bayray Kahsay et al. / Energy Procedia 57 (2014) 1613 – 1622

Where qij represents the heat flow from node i to node j and P bab and Psp are the heat absorbed at bottom
absorber and side plate respectively. The heat flow between nodes can be written in terms of the
temperature difference (Ti – Tj) and the equivalent resistance between the nodes Re,ij , i.e:

qij = (Ti – Tj)/ Re,ij

The heat flow between nodes can be a combination of the three modes of heat transfer: conduction,
convection and radiation. Therefore, the equivalent thermal resistance is determined by considering the
three heat transfer modes for the specific nodes. The eight simultaneous equations above can be solved
for the eight unknown temperatures. This can be done using an iterative procedure since the convective
and radiation heat transfer coefficients and hence the equivalent thermal resistances are function of
temperature. The iteration was made on an Excel worksheet. The solution method that was used in this
work was the “optimize” add-in program with Newton-Raphson algorithm. The details of the procedure
may be referred in [7].

3.3 Experimental tests

Two box cookers made from similar materials described in previous section, were fabricated in the
same workshop. The difference was the inner metal box as indicated in section 3.1. The cookers were
tested simultaneously following a standard procedure as recommended by ASAE. The test was conducted
with measurements of temperature using k-type thermocouple and National Instruments (NI) data logger.
The main procedures during testing were:
x Tests were started at around 10:00 AM and were stopped before 2:00 PM.
x The cookers were kept under shading before the start of the tests and brought to receive solar
radiation simultaneously.
x Tracking of the cookers was done every ten minutes.
x Thermocouples were attached to the center of the bottom absorber plate during the stagnation
test and were immersed into water during the boiling test.
x Half liter of cold water was used at each start of the boiling test.
x Solar radiation measurement was taken from a pyranometer in the nearby campus metrological
station.
x Wind speed measurement was not taken. Any influence of wind speed is assumed to affect both
cookers equally.

Standard stagnation temperature is found from:

SST = (Ts – Tamb) (850 W/m2)/G

Solar power input I into the cooker was calculated from:

I = G Aap
Cooking power Pc during boiling of mass of water ‘m’ from initial temperature T i to final temperature Tf
during time ‘t’ is calculated from:

Pc = mCp(Tf – Ti)/t
The cumulative efficiency of the cooker after ‘n’ time intervals is found from:

ηn = ∑Pci/∑Ii
 Mulu Bayray Kahsay et al. / Energy Procedia 57 (2014) 1613 – 1622 1619

4. Results and Discussion

4.1 Results of theoretical modeling

The set of simultaneous nodal equations were modeled in an Excel worksheet. The constant input data
as well as data which vary with temperature were entered using lookup tables. The steady state solutions
were then determined using the solver discussed in the methodology section. The results are discussed for
each type of cooker as shown in Table 3 (Cooker 1 is without and Cooker 2 is with reflector).

Table 3 shows the temperature at each node for the modeled cookers. The temperature at the bottom
absorber is T1 which is expected to be the maximum. For cooker 1 the result shows T1 = 153.8 oC while
for cooker 2, T1 = 177.6 oC. This temperature is the maximum stagnation temperature assuming solar
radiation of 800 W/m2 and ambient temperature of 24oC. The standard stagnation temperature predicted
by the theoretical modeling is therefore 137.9 oC and 163.2 oC for cooker 1 and cooker 2 respectively.
This shows that there is significant difference between the two designs in terms of the stagnation
temperature. The theoretical modeling predicts that the cooker with reflector can perform much better
than the cooker without reflector.

Table 3 Temperature predictions of the nodes

Node 1 2 3 4 5 6 7 8
Temperature
(oC) Cooker 1 153.8 134.0 131.0 104.5 52.5 40.5 24.3 27.3
Temperature
(oC) Cooker 2 177.6 159.2 150.1 121.0 59.8 44.4 24.6 26.2

4.2 Results of experimental tests

Stagnation test
Tests were conducted as per the procedure discussed in the methodology section. Temperature was
measured using thermocouples every ten minutes. The plot of temperature and solar radiation for three
days of testing are shown in Figure 3. The standard stagnation temperature for each day and cooker
design has been calculated and the results are shown in Table 5. The experimental result also indicates
that the standard stagnation temperature of the cooker with reflector is higher than the cooker without
reflector. The difference is on average about 22oC. In comparison the stagnation temperature of the
cookers found from experiment is much less than the theoretical prediction. This is due to an unaccounted
heat loss factors in the theoretical prediction such as leakages around the cooker doors and around the
edge of the outer wooden box. However, the stagnation test also indicates that the cooker with reflector
performed better.

Table 5 Results of stagnation test.

Cooker Day 1 Day 2 Day 3
Maximum Average SST Maximum Average SST Maximum Average SST
temperature radiation temperature radiation temperature radiation
(oC) (W/m2) (oC) (oC) (W/m2) (oC) (oC) (W/m2) (oC)
Without 106.2 785.6 86.8 103.9 719.3 92.1 86.7 868.6 59.4
reflector
With 129.3 785.6 111.8 117.8 719.3 108.5 111.3 868.6 83.5
reflector
1620 Mulu Bayray Kahsay et al. / Energy Procedia 57 (2014) 1613 – 1622

200 1000 200 1000

Solar Radiation W/m2

Solar Radiation W/m2

Temperature 0C
800 800

Temperature 0C
150 150
600 600
100 100
400 400
50 200 50 200
0 0 0 0
10:00

10:20

10:40

11:00

11:20

11:40

12:00

10:00

10:20

10:40

11:00

11:20

11:40

12:00
Time Time
200 1000

Solar Radiation W/m2

800
150
Temperature 0C

600
100
400
Day 3 Cooker 1
50 Day 3 Cooker 2
200
Solar radiation
0 0
10:00

10:20

10:40

11:00

11:20

11:40

12:00
Time

Figure 3 Stagnation tests, top to bottom, Day 1, 2, and 3.

Boiling tests

Boiling tests were also done in a similar manner with 0.5 liters of water in a cooking pot inside the
cookers. Figure 4 shows plots of temperature and solar radiation data for three different test days (Day 4,
5 and 6). The cumulative efficiency plots for boiling tests of the same three days are also shown in Figure
5.
 Temperature 0C

0%
5%
10%
15%
20%
0
20
40
60
80
100

10:10
10:20 10:00
10:30 10:20
10:40
10:50 10:40
11:00 11:00
11:10
11:20 11:20
11:30 Time 11:40

Time
11:40 Temperature 0C

0%
5%
10%
15%
20%
11:50 12:00

0
20
40
60
80
100

12:00 12:20
10:10 12:10
10:20 12:20 12:40
10:30 10:20
12:30
10:40 1:00
12:40 10:40
0

10:50 12:50
200
400
600
800

11:00
1000

11:00 1:00
11:10 Solar radiation W/m2

Figure 4 Boiling tests, top to bottom Day 4, 5 and 6.

11:20
11:20

Time
Temperature 0C

0%
5%
10%
15%
20%
11:30 11:40

Time
0
20
40
60
80
100

11:40 10:10 12:00

Cooker 2
Cooker 1
11:50 10:00
10:20
12:00 12:20
12:10 10:30
12:40 10:20
Solar Radiation
Day 6 Cooker 2
Day 6 Cooker 1

12:20 10:40

Figure 5 Cumulative efficiencies of the cookers during the boiling test.

12:30 10:50 10:40
0

12:40
200
400
600
800

11:00
1000

12:50 11:00

Time
Time

11:10 Solar Radiation W/m2

Mulu Bayray Kahsay et al. / Energy Procedia 57 (2014) 1613 – 1622

11:20 11:20
11:30
11:40 11:40
11:50
12:00
12:00
0
200
400
600
800
1000

Solar Radiation W/m2

1621
1622 Mulu Bayray Kahsay et al. / Energy Procedia 57 (2014) 1613 – 1622

5. Conclusion

The study has clearly shown that in both the theoretical prediction and experimental tests, the
performance of box solar cookers can be enhanced using internal reflectors. The steady state theoretical
analysis predicted difference in standard stagnation temperature of about 25oC. The experiment on
stagnation test also concluded that the standard stagnation temperature was higher by about 22oC.
However, the predicted stagnation temperature for both the cookers was higher than the experimental
value. Similarly the boiling test indicated that the water temperature and the cumulative efficiency were
higher for the cooker with reflector. Therefore, the performance of box cookers can be enhanced by
making appropriate angle side walls of the absorber and providing internal reflection.

Acknowledgements

The authors would like to acknowledge funding for the study from Mekelle University, KTT office and
Tigray Science and Technology Agency. The authors also acknowledge EnPe project for sponsoring a
student for an M.Sc. thesis work during the study.

References

1. Mulu Bayray and John Paintin, “Box Solar Cooker User Manual,” EiT – M, Mekelle University,
2012.
2. Chin, Y.K., Staton, D.A., “Transient thermal analysis using both lumped –circuit approach and
finite element method of a permanent magnet traction motor,”
3. Bruce, Lindberg, “Analogy between thermal and electrical conduction,” www.egr.msu.edu/-
raguin/ame812/Final projects, retrieved on 4/17/2012 .
4. Khas, Hauz “Natural convective heat transfer coefficient in a trapezoidal enclosure of box – type
solar cooker.” Center of Energy Studies Indian Institute of Technology, 2003.
5. Testing and Reporting Solar Cooker Performance, ASAE S580 JAN03,
http://solarcooking.org/asae_test_std.pdf, viewed May 2013.
6. Schwarzer, Klemens, Vieira da Silva, Maria, “Characterization and design methods of solar
cookers,” Solar Energy, 82, 157–163, 2008.
7. Biniam Gebray,” Theoretical Modeling and Experimental Analysis of Box Solar Cooker,” M.Sc.
Thesis, Department of Mechanical Engineering, EiT – M, Mekelle University, 2012.