a review on test procedures, performance parameters and...

A Review On Test Procedures, Performance Parameters And

Models Of a Solar Cooker: Part IV

Aman Shrivas*,

P.G. Student, Energy management system, Chandrapur, India.

Email:- [email protected]

Abstract

Since from 1950’s, many designs of solar cookers have been developed. With the

development in the designs, performance evaluation techniques have also been evolved.

Prior to 1980’s, a climate dependent parameter was used to evaluate the performance of

solar cooker, but then after that, Mullick proposed figure of merits, which are more or less

independent of climatic conditions and are accepted all over the world by different

authors for evaluation of their SBC’s performance. Many more or less climate

independent parameters have been evolved after Mullick’s figure of merits. In this paper,

a review is made on all the different test procedures, performance parameters and models,

which has been used for evaluating and comparing the performance of solar cooker’s.

Keywords: Models, Performance parameters, SBC test methods, test procedures.

1. Introduction

Umpteen methods have been evolved to harness the sunshine in tropical regions of the

world for different uses. But, solar cooking has proved to be one of the most viable and

attractive options for solar energy utilization. Its emphasis is even more in the developing

regions of India, where the drudgery is involved in cooking food and where, the sunshine

is available in plenty. Presently, a major portion of total available energy resource is

utilized for cooking in these regions. This cooking energy is supplied by non-commercial

fuels like firewood, agricultural waste, cow dung and kerosene in rural areas. Women’s of

urban areas are involved in several activities in daytime in addition to their cooking work.

Use of solar cooker for cooking will keep them away from other activities as cooking is

slow in a solar cooker [1]. So urban people mostly use LPG, Natural Gas and electrical

energy for cooking purposes [2]. As solar energy is free and clean, & many advantages

like no running cost, high nutritional value of the food are furnished by solar cooking,

more people will attract towards the solar cooker, if its performance will be meliorated. It

can be either meliorate by using a rugged performance parameter, which is needed by

prominent designs or by using a computer or mathematical models. The availability of a

thermal performance parameter for comparing the performance of solar cookers is still an

issue which is open and unsolved. There has been an appreciable interest in the design,

development and testing of solar cookers like box type, concentrator type and advanced

type around the world. The need to appraise a cooker and compare its various designs,

entails testing procedures, modelling and thermal performance parameters (TPPs) which

represent their respective thermal performance. The work aimed at addressing these

concerns have resulted in many useful test procedures, models and TPPs. These

parameters must be independent of geographical, climatic, operational and other social

variables such as food habit of a society and judgment of a person. Many of the TPPs are

largely independent of aforementioned variables [3]. The present paper aims at reviewing

all the test procedures, TPPs and models used for evaluating and comparing the

performance of solar cookers.

2. Solar Cooker – Box Type – Test Methods (IS: 13429 Part 3:2000)

2.1. Leakage Test

International Journal of Research

Volume VIII, Issue III, March/2019

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(a) Cooking Tray Leakage Test - In this test, the cooking tray is dismantled from the main body and fill with water. After an hour, the joints of the tray are examined for any signs of

leakage.

(b) Rubber Gasket Leakage Test - In this test, a piece of paper is inserted in between the

gasket and the cover plate in at least four positions along each side of the cooker. The

paper used shall be approximately 50 mm wide and maximum 0.05 mm thick. It should be

ensured that the cover plate is properly tightened and the paper shall exhibit a firm

resistance to withdrawal by hand at all points tested.

(c) Cover Plate Leakage Test - In this test, leakage from cover plate is tested from upper

and lower sides. In first test, i.e. in leakage test for upper side of cover plate, it is first

ensured that the cover plate is properly tightened. Then a thin film of water is poured on

the cover plate. After an hour, the cover plate is examined for any signs of water entry

between the two glass sheets. This test shall be done in the shade. While in second test,

i.e. in leakage test for lower side of cover plate, the cooking pots are filled with water and

keep them in the cooking tray. Then, the cover plate is tighten and the cooker is placed in

an open around 1000 h for exposure to sun rays for 4-5 h. After that, the cooker is placed

in shade for 15 minutes to allow any vapour to condense & the cover plate is examined

for any signs of water vapour entry between the gap of inner and outer of cover plate.

(d) Rain Penetration Test - 5 mm spray nozzle is a basic apparatus used in a rain

penetration test. In this test, the closed cooker is sprayed water on all sides using a spray

nozzle at a pressure of 0.1 MPa. Spray from the nozzle is directed downwards from the

cooker top and also towards the four corners of the cooker. The water is sprayed on the

cooker top and corner for 10 min. After the completion of test, external surface of the

cooker is wiped dry and the cooker is inspected visually for any entry of water vapour.

2.2. Slam Tests

This test is to ensure that the mirror or cover plate shall not be damaged when allowed to

fall from the fully opened position as given below:

(a) Cover Plate Slam Test - In this test, the lid is kept open and the cover plate is lifted as high as possible. Then, let it fall to a closed position. This shall be repeated five times.

There shall be no damage to the glass sheets.

(b) Mirror Slam Test- In this test, the mirror is hold at near vertical and let it fall to a closed position. This shall be repeated five times. There shall be no damage to the

mirror, the cover plate, or any other part of the cooker.

2.3. Mirror Reflectivity Test

The apparatus required for this test are two pyranometers and a stand with two axis

tracking arrangement for holding the mirror and a pyranometer parallel to the mirror at a

distance of about 30 cm. The stand should have a pointer (10-15 cm long pin) fixed

normal to its plane. The stand is placed in an open space free from shadow and reflected

radiations from the surroundings. The mirror is fixed on the stand parallel to its plane.

Also one of the pyranometers (P1) fix in such a way that its sensor faces towards the

mirror. Then the other pyranometer (P2) is placed horizontally near the stand for using it

as a reference pyranometer. The stand is adjusted for normal incidence in such a way that

shadow of the pointer is not there. The stand is tilted about 10° from the normal position

and the position of pyranometer (P1) is adjusted on it in such a way, that radiation

reflected from the mirror, falls on the pyranometer sensor. After that, the readings R1 and

R2 of the pyranometers P1 and P2 are recorded and without changing the tilt of the stand,

the pyranometer P1 is reverse, so that its sensor faces the Sun and is parallel to the mirror.



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Then the readings R3 and R4 of both the pyranometers P1 and P2, are recorded. It should

be noted that the two readings of the reference pyranometer P2 (R2 and R4) should not

change by more than 5%. The experiments should be performed in clear weather and the

global radiation recorded should be more than 600 W/m2. The reflectivity of the mirror is

calculated from the relation R =R1/R3. The test have to be repeated six times. The average

of the six values of the R will give the reflectivity of the mirror.

2.4. Exposure Test

In this test, solar pyranometer, along with a recording device are used as a basic

apparatus. The solar cooker is left to stagnate which may lead to the following possible

degradation:

Breakdown of rubber or plastic material.

Outgassing from the insulating material,

Discoloration or peeling of black paint on the cooking pots and cooking tray;

Depositions of water vapour, dust or any other material inside the double glass lid; and

Cracking of glazings and/or mirror and/or body.

The solar cooker is left open in an un-shaded area for at least 30 days having daily

irradiation level of at least 4 kWh/m2 on a horizontal surface. These days need not to be

consecutive. The cooking pots inside the cooker are empty. The mirror is placed vertically

and the cooker is oriented to face south. The cooker may be kept inside during rains. [4]

3. Test Procedures For Calculation Of Thermal Performance Parameters

(a) Standard Stagnation Temperature test

The stagnation temperature gives an understandable figure for the maximum possible

temperature achievable by a cooker under a specific set of conditions. This test was

conducted using a dry, empty cooking vessel with two thermocouple leads fixed such that

they measured the air temperature roughly in the centre of the cooking pot. The standard

stagnation temperature is simply given by:

SST = (

) ₓ 700 … (1)

Where, Ts = Highest air temperature reached, Tair = Ambient air temperature, averaged

over testing period, Imeasured = Horizontal insolation, averaged over testing period.

(b) Standard Sensible Heating Time test

In this type of test, we record the time taken by the cooker to heat a known quantity of

water to 50℃ above ambient temperature under a horizontal insolation of 700 W/m2. The

basic equation describing an energy balance on the thermal mass within the cooking

vessel is given by:

to = (

) t … (2)

Thus, for any set of measured values; T, t, and I it is possible to calculate the Standard

Sensible Heating Time. It should be noted, however, that for T values that are very high

or approaching boiling, the accuracy of this equation quickly breaks down. It only applies

in the sensible heating region and if T includes any phase change or otherwise non-

linear temperature transient regions, the equation will produce inaccurate results. It is

suggested that values for a T of approximately 50C be used, to ensure that the phase



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change region is not approached. Data for this test can be taken concurrently with that for

the Standard Cooking Power.

(c) Unattended Cooking Time test

This test is conducted after the measurement of Standard Cooking Power and Standard

Sensible Heating Time and is intended to measure how long the cooker can maintain a

high temperature without being actively tracked to follow the sun. The cooker is left

stationary and the temperature of the pot contents (water) measured, as with prior tests.

This continues until the pot contents have decreased in temperature by 20C from starting

temperatures (i.e. the final temperature at the end of the Standard Cooking Power test).

Once again this time measurement is normalized to 700 W/m2.

tc,s = tc (

) …(3)

Where, tc,s = Cooling time, standardized, tc = Cooling time, measured, I = Horizontal

insolation, averaged over test period.

(d) Water boiling test

In this test, first initial temperature of water kept in the cooking pot is measured. The

ambient temperature, water temperature in the cooking pot, absorber surface temperature

and cooking pot temperature after every five minutes is measured along with solar

radiation incident in the box cooker. Time required to boil the water (or reached to

100℃) in the cooking pot is evaluated by this method.

τboil =

˟ ln *

(

)+ …(4)

By using these tests, thermal performance parameters of any solar cooker are calculated. [5]

4. Test Procedures For Determination Of Optical Efficiency Factor TPP (F’ηₒ)

Subodh kumar et al. (1996) [6] employed three different experimental test procedures for

determination of optical efficiency factor F’ηₒ of a paraboloid concentrator solar cooker.

The first procedure, primarily uses the sensible heating curve of the water in the cooking

pot placed at the focus of the paraboloid concentrator solar cooker. If in a time interval τ,

the water temperature rises from Tw1 to Tw2, then the optical efficiency factor of the

paraboloid concentrator solar cooker can be expressed as:

F’ηₒ =

[(

) (

)

]

…(5)

Where, τₒ = is the time constant obtained from the cooling curve and C is the ratio of the

aperture area of the paraboloid reflector (Ap) to the area of the pot (Apot). Once the value

of the time constant τₒ is known experimentally, F’ can be determined from:

F’UL =

…(6)

With representing the heat capacity of water as well as that of pot.



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It is worth mentioning that while deriving equation (5) both & are assumed to be constant during the given time interval τ. The value of F’ηₒ can therefore be obtained from

the sensible heating curve of water by applying equation (5) over small time intervals and

its time variation can also be studied.

In second procedure, an arrangement allowing a steady flow of water through the focal

zone of the paraboloid concentrator cooker (where the pot is placed during cooking) is

made. The flow rate of water is so adjusted that the average of the inlet (Twi) & outlet

(Two) water temperatures is equal to the ambient temperature, thus reducing the overall

heat losses to zero. In such a case, the heat balance equation may be simplified to give:

F’ηₒ = ̇

…(7)

Where, ̇& are the mass flow rate and specific heat of water.

The third procedure is the combination of two methods discussed above. It involves the

sensible heating of water for a certain time interval in a cooking pot placed at the focus of

a parabolloid concentrator cooker. However, the initial (Tw1) and final (Tw2) temperatures

of the water in the cooking pot are so adjusted that the average water temperature during

the time interval τ is equal to the ambient air temperature, as in the case of the second

procedure. The optical efficiency may then be calculated as:

F’ηₒ =

…(8)

5. Thermal Performance Parameters Of Solar Cooker

These performances can be determined by an elaborate analysis of the optical and thermal

characteristics of the cooker materials & the cooker design or by

experimental performance testing under different operating conditions [7]. Performance parameters for different solar cookers are described below in detail:

5.1. Performance Parameters Of Box Type Solar Cooker

In 1985, Khalifa et al. [8] discussed some of the performance parameters like utilizable

efficiency (ηu), characteristic boiling time (tc) and specific boiling time (ts) etc. They

determined utilizable efficiency to grade the cookers TPPs in terms of two figures of merit

(F1 and F2) which was proposed by Mullick et al. [9] in 1987 and was adopted by Bureau

of Indian Standards [10]. It enables prediction of sensible heating time of the water in the

cooking pot. Funk [11] discussed about international standard procedure for testing of

solar cookers in 2000 and in that context calculated standard cooking power (Ps) which is

helpful in comparison of performance of different other types of solar cookers as well.

While, in 2005 Kumar used the linear regression analysis of experimental F2 data for

different loads of water for calculation of optical efficiency factor (F’ηₒ) and heat capacity

(MC)’. Thus, to predict the thermal performance of solar cooker, F’ηₒ and (MC)’ may be

considered as essential design parameters. Nahar [12] used efficiency as a TPP for box

type solar cooker. Some of these parameters used by different researchers are discussed

below:

Vaishya et al. (1985) [13] suggested a new test method which is based on the

measurement of stagnation temperature and insolation. They characterized cooker box by

equation:

K=

= U/(τα)e … (9)



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Where, Iin = solar intensity on cooker box, W/m2, α = solar absorptance, dimensionless, τ

= glass cover transmittance, dimensionless, Ta = ambient temperature, °C, Ts =

stagnation temperature in cooker box, °C, U = overall heat loss coefficient, W/m2°C, K =

ratio of overall heat loss coefficient and transmittance absorptance product, W/m2°C.

Overall utilizable efficiency was discussed by Khalifa et al. (1985) [14] for box type solar

cooker is calculated by using the following expression:

ηu =

...(10)

where, QF is the useful heat stored in the food for a temperature rise of T. For relatively constant direct normal radiation GNR, collector area Ac, and cooking time , solar input Qin, can be expressed as:

Qin = GNRAc t … (11)

The specific boiling time (ts) required to heat mass of water M, to boiling is expressed as:

ts =

… (12)

Alternatively,

tc = ̅

... (13)

Where, tc is the characteristic boiling time and GNR is reference direct normal radiation

and is taken to be 900 W/m2 and ̅ is average solar radiation.

Mullick et al. (1987) [15] Provided some guidelines for thermal performance evaluation

of box type solar cooker. They proposed experimental tests & identified appropriate

parameters, which were related to the cookers and independent of the climatic variables as

well as the products cooked. The tests were conducted under two conditions for obtaining

Table 5.1: Various parameters for evaluating solar box cookers performance

Sr.

No. Author name Performance parameters Expression Recommended values

1 Vaishya et al.

(1985)[13]

Performance characteristic,

K K= U/(τα)e ≤ 10.0 W/m

2 ℃

2. Mullick et al. (1987)[15]

First figure of merit, F1

Second figure of merit, F2

F1 =

,

F2 =

[

(

)

(

)]

0.12-0.16 m2℃/W

0.254-0.490 m2℃/W

3. Kameen (1990) [16] Parameter index, P.I. P.I. = ∫ [ ]

∫ [ ]

1.86 (good)

4. Funk (2000) [11]

Cooking power, P

Standard cooking power, Ps

P =

Ps =

̅

Details not available

45 W at = 50℃

5. Nahar (2003) [12] Efficiency of cooker, η

∫

27.5%

6. El Sebaii (2005) [40] Utilizable efficiency,ηu ηu =

26.7% at

7. Ozturk (2007) [18] Energy and exergy, η & ψ

ηE =

,

Ψ = [( )

*

+



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two figure of merits: In first test, they kept their solar cooker in sunlight without vessels

and obtained the first figure of merit by using the expression:

F1 =

… (14)

They manifested that it ensures that the glass covers have a good optical transmission & a

cooker has a low overall heat loss factor and the minimum value of F1 varies between

0.12 to 0.16 m2 ℃/W.

While, they obtained the second figure of merit by operating the solar cooker with a full

load of vessels with 1 kg water by using the expression:

F2 =

[

(

)

(

)] … (15)

They manifested that it checks whether F’ is high i.e. whether there is a good heat transfer

to the contents in the vessel and whether CR is high i.e. effective heat capacity of cookers

interiors & vessels is small and the minimum value of F2 is 0.254 m2 ℃/W.

A time constant (τₒ) could also be obtained by them from the second figure of merit

equation:

τₒ =

{

(

)

(

)]

... (16)

where, Tao & Ho are some arbitrary standard climatic conditions. The time constant

obtained from eqn (16) has the units of time (in hours) and is a measure of the sensible

heating time or preheating time for the cooker with full load under some standard

conditions. This factor is necessarily empirical since preheating time varies according to

the climate. They manifested that it provides a combined single measure to the lay user of

solar cookers who may otherwise find it difficult to compare cookers with different sets of

values of F1 and F2.

To estimate the first figure of merit (F1) and second figure of merit (F2), they required to

measure the intensity of solar radiation falling at the surface of the cooker, ambient

temperature, wind speed, initial water temperature, final water temperature etc. They

recommended that experiment should be done within 1:30 h of the solar noon with the

intensity of solar radiation above or equal to 600 W/m2. Initial temperature of water

should be higher than the ambient temperature and the final temperature of water should

be lower than the boiling point. It may be 90 or 95℃ to avoid error in reading from the

experimental curve as the curve flattens at higher temperature i.e. around 100.8℃. The

sensible heating test is to be conducted at full load as suggested by the supplier.

Kammen and Lankford (1990) [16] adopted the parameter free index and use this index to

compare the heating times, thermal stability, and thermal capacity while cooking foods of

the two constructed oven types. They also manifested that their index is useful in rating

the efficiency of the oven at a given moment or as a running index of oven performance.

The index can be expressed as:

P.I. = ∫ [ ]

∫ [ ]

… (17)



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Mullick et al. (1996) [17] found that, F2 increases, with increase in number of pots, if load

is kept constant and equally distributed. This is attributed to an improvement in the heat

exchange efficiency factor (F’) with number of pots. They also determined that F2

increases with increase in load, if number of pot is kept constant and the load is equally

distributed. This is because of an improvement in heat capacity ratio CR, as mass of water

in the pots increases. They suggested that F2 should be determined at full load and with all

the four standard pots since the value is lower with lower load and lesser number of pots.

To study the effect of increasing number of pots on F2 it is suggested that load should be

kept constant irrespective of number of pots and should be 1 kg of water. Test should be

conducted for one, two, and four pots. To study the effect of load on F2, recommended

test load is1.0, 1.5, 2.0, 2.5 kg of water which should be divided equally in the four pots.

Funk (2000) [11] discussed two types of test variables. They are mainly uncontrolled

(weather) variables and controlled (cooker) variables. Wind, ambient temperature, pot

contents temperature, insolation and solar altitude and azimuth are the uncontrolled

variables while loading, tracking, temperature sensing are the controlled variables. From

Funk’s definition, cooking power maybe expressed as:

P =

… (18)

Where, P is the cooking power, M is the mass of water, Cw is specific heat of water, dTw

is temperature difference of water and dt is time interval.

He also introduced the term standard cooking power which can be expressed as:

Ps =

̅ … (19)

Where, Ps is standard cooking power, T is temperature difference and ̅ is average solar radiation. To find the cooking power and standard cooking power the parameters to be

measured are wind speed, ambient temperature, water temperature, solar radiation,

intercept area of the cooker etc. Wind speed should be less than 1 m/s. If wind speed is

2.5 m/s for more than 10 min then test should be stopped. Ambient temperature should be

in the range of 20–35℃. Water temperature of the pot should be recorded in between 40

and 90℃. Solar radiation during the experimentation should be in the range of 450–1100

W/m2. The suggested load is 7 kg of water/m

2 intercept area of cooker and should be

distributed in the pots equally. For box type solar cooker zenith angle tracking is not

required if the duration of test is less than 2 h. To calculate standard cooking power the

reference solar radiation should be 700 W/m2.

Nahar (2003) [12], proposed the method of calculation of efficiency (η) of the solar

cooker by the following relation:

∫

… (20)

Where, η represents efficiency of the solar cooker; M, mass of water (kg); M1 = mass of

cooking utensil (kg); Cu = specific heat of cooking utensil (J/kg/℃); Tw1 = initial

temperature of water (℃); Tw2 = final temperature of water (℃); C = concentration ratio;

A = absorber area (m2); t = time interval (s) and I = solar irradiance (W/m

2). To estimate

the efficiency of the reported cooker, load should be 1 kg of water and it is to be equally

distributed into four pots of the cooker. The cooker should be placed for cooking 1:00 h of local noon time. Rise in water temperature and time required to reach the water

temperature to boiling point is to be measured.



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Ozturk (2007) [18] Evaluated the quantities of input and output energy and exergy for

performing energy and exergy analyses of the SCs. He manifested that if the terms of

kinetic and potential energy considered negligible, for the steady-state flow process

during a finite time interval, the overall energy balance of the SC can be written as:

Energy input= Energy output+ Energy loss … (21)

He also calculated the energy input of the solar cooker by the equation:

Ei = ItAsc … (22)

The energy output of the solar cooker by the equation:

E0 = mCp(Tf2 – Tf1)/t …(23)

& finally, he took the ratio of energy output to energy input of the SC for finding the

value of energy efficiency. The equation obtained is given below:

ηE =

=

=

… (24)

He also calculated the exergy efficiency which is expressed below, by taking the ratio of

exergy output (which is the exergy gained by fluid in the vessel kept inside the cooker due

to rise in temperature) to the ratio of the exergy input (which is the exergy supplied to

fluid).

Ψ = [( )

*

+

… (25)

He manifested that there was large difference in energy and exergy output and efficiency

because of changes in cooker configuration. He also noticed that exergy analysis is more

convenient than the energy analysis for predicting SC efficiency.

Soteris A. Kalogirou (2009) [19] defined optical efficiency factor as the ratio of the

energy absorbed by the receiver to the energy incident on the collector's aperture. He

manifested that optical efficiency depends on the optical properties of the materials

involved, the geometry of the collector, and the various imperfections arising from the

construction of the collector. The equation can be written as:

ηo= ρ.τ.α.γ[(1-Af.tan(θ)) cos(θ)] ...(26)

where, ρ = reflectance of the mirror, τ = transmittance of the glass cover, α = absorptance

of the receiver, γ = intercept factor, Af = geometric factor, θ = angle of incidence.

5.2. Performance Parameters For Parabolic Type Solar Cooker

Subodh kumar et al. (1994-1997) [20,21] proposed heat loss factor, F’UL & the optical

efficiency factor, F’ηₒ, on which the performance of concentrating type solar cooker is

dependent.

The heat loss factor depends strongly on the pot water temperature & the wind speed,

increasing considerably with both of these parameters. It can be expressed as:

F’UL =

… (27)



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Where, Mw = Mass of Water (kg), Mpot = Mass of Pot (kg), τₒ= Cooling time Constant,

Cpot = Specific heat of Pot, Cpw = Specific heat of water, Apot = Area of pot.

While, the optical efficiency factor defines the theoretical maximum limit of the overall

efficiency of a concentrator solar cooker. It relates to the geometrical perfection of the

reflector’s surface, its reflectance,, the absorptance of the cooking pot, etc. In fact, the

performance of a concentrating solar cooker is more sensitive to its optical characteristics

than its thermal losses. It can be expressed as:

F’ηₒ =

[(

) (

)

]

… (28)

Where, Twf = final temperature of water in ℃, Twi = initial temperature of water in ℃, τ =

time interval, Ib = irradiance in W/m2, Ta = Ambient air temperature in ℃.

5.3. Performance Parameters For Panel Type Solar Cooker

Ibrahim Hassan (2017) [22] Described and calculated some parameters like geometric

concentration ratio and optical concentration ratio for their fabricated funnel panel type

solar cooker. He defined the term "concentration ratio" as the amount of the solar energy

concentration which was

solar energy concentration which was obtained by a certain collector. He had given two

different definitions of concentration that can be used.

The very first is, geometric concentration ratio, CR, which is based on the areas of the

aperture and receiver & is defined as the ratio between the concentrator opening area and

the aperture area that receives all the solar radiation concentrated by the cooker. It is

expressed as:

CRg =

… (29)

While, the other is, optical concentration ratio, which is the ratio of the solar flux, Ir, on

the receiver to the flux, Ia , on the aperture. It is expressed as:

CRo =

∫

… (30)

He demonstrated that the optical concentration ratio gives a ‘true’ concentration ratio

because it accounts for the optical losses from the reflecting and refracting elements,

however, since it has no relationship to the receiver area, it does not give insight into

thermal losses which are proportional to the receiver area. He found that the maximum

concentrator ratio equals 9.

5.4. Other Performance Parameters For Concentrating Type Solar Cookers

Collection efficiency [22] can be expressed as:

η =

… (31)

Where, Ps = Normalizing the cooking capacity to 700 W/m2, Ea = Amount of heat which

collects by aperture area, W [17].

Instantaneous efficiency [41] can be calculated using equation:



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=

… (32)

Where, = difference between initial and final water temperature, t = time interval, Ac = collector area (m

2), Ibrb = irradiance in W/m

2, mw = mass of water, Cpw = specific heat

capacity of water.

While, thermal efficiency [42] can be expressed as:

= ηₒ - ˟

… (33)

Where, ηₒ is optical efficiency, UL is overall loss coefficient (W/mºk), Ap = pot area (m2),

Aa = Aperture area (m2), Tw = water final temperature (℃), Ta = ambient air temperature

(℃), Ib = beam radiation (W/m2).

6. Review On Models

In 1991, Jubran et al., Conducted computer simulation studies to predict the unsteady

state thermal behaviour of single and double glazing box type solar cookers with or

without plane reflecting mirrors using a set of important cooker parameters. They utilized

developed mathematical model, which was based on heat balance equations, to study the

effect of some parameters on the hourly and daily performance of the cooker. Their

results indicated that all theoretical models predict higher efficiency, lower specific

boiling time and characteristic boiling time. This was due to the fact that the thermal

analysis of the theoretical models did not take into consideration the effect of the inside

hot air leakage on the performance of the cooker [23].

Habeebullah et al. [82] (1995) Introduced the oven type concept as an alternative

approach for collecting the concentrated solar energy would drastically boost the overall

cooker efficiency. They developed the transient heat balance equations for predicting the

thermal behavior of an oven type concentrating solar cooker. They used this simulation to

show theoretically the great advantage of using a glass-sided oven over the conventional

bare receiver pot. Their analysis showed that the oven type receiving pot has both a higher

fluid temperature and overall receiver efficiency compared to the bare receiver type,

under same working conditions [24].

In 1996, Binark and Turkmen, carried out the thermal analysis of a SBC using the fourth

order Ranga-Kutta method in a Istanbul, Turkey for a model named ITU-2 in 1996. A

theoretical investigation was carried out by them to determine the performance of box

cooker by thermal analysis. Their analysis was independent of number of cooking vessel

placed in a solar cooker. Their results showed that there is a good agreement between the

theoretical and experimental values [25].

After an year, A. A. El-Sebaii and Aboul-Enein, presented a transient mathematical model for a box-type solar cooker with a one- step outer reflector hinged at the top of the cooker.

It is based on analytical solution of the energy-balance equations using Cramer's rule for

different elements of the cooker. They assumed various heat transfer coefficients to be

temperature dependent & for validating the model, they compared the temperature

distribution obtained by computer simulation with experimental results which were

obtained by them in previous work for a typical summer day in Tanta, Egypt. Good

agreement between experimental and theoretical results was observed by them. They

manifested that the proposed theoretical model may be used to investigate the

performance of box-type solar cookers with good accuracy [26].



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A model was presented by P.A. Funk et al. in 1998, for prediction of the cooking power

of a solar cooker based on three controlled parameters, (i.e. solar intercept area, overall

heat loss coefficient, and absorber plate thermal conductivity) and three uncontrolled

variables (insolation, temperature difference, and load distribution). Their model basis is a

fundamental energy balance equation. Coefficients was determined by them for each term

in the model by regression analysis of experimental data and validated the model for

commercially available solar cookers of both the box and concentrating types. They found

that the three-parameter model that was developed was found to be useful for predicting

thermal performance of box type & concentrating type solar cookers & provides a basis

for the systematic understanding of solar cooker thermal performance [27].

After an year, E.L. Mayer et al. developed an energy model, EMAT which is based on

regression analysis of total daily irradiation and maximum daily ambient temperature.

This model is able to predict daily module energy based on these two parameters only.

The data used in their study were collected over a 15-month period at the University of

Port Elizabeth (UPE), South Africa. This model was then compared to two existing

energy models, namely EPTC and ENRA. In this comparison, coefficients were obtained

from data collected over the month of October 1998 & its validity was then evaluated

over the entire 15-month period using seasonal regression coefficients. An application of

the model to predict module energy output is illustrated by using data collected. The

predicted energy is then compared to the energy measured at UPE. Their results showed

that the developed model is valid, easy to use, a good predictor of module energy and

more accurate than the other models [28].

Then in 2007, O.A. Jaramillo et al. developed a simple theoretical model, called

performance factor model, of the oven concentration. In order to analyze the optical

performance of the solar cooker, they conducted an experimental evaluation by using a

scale model of the solar cooker and a heliodon. They manifested that the performance

factor model, is a useful tool to evaluate the gain of solar energy due to the inclination of

the cover and the presence of the reflectors throughout the year. Beside, it can also be

used to evaluate the energy that the solar oven receives if the insolation data over the

horizontal plane is available. Their model results showed that, at noon, the solar cooker

achieves a concentration level greater than 1.95 throughout the year [29].

After an year, Huseiyn Kurt et al. developed a feed-forward neural network model which

was based on the back propagation algorithm for prediction of the thermal performance of

solar cooker with and without reflector. They obtained data set from the box type solar

cooker which was tested under various experimental conditions. The experimental data

set consists of 126 values which were divided into two groups, of which the 96 values

were used for training/learning of the network and the rest of the data (30 values) for

testing/validation of the network performance. They evaluated the performance of the

ANN predictions by comparing the prediction results with the experimental results. Their

results showed a good regression analysis with the correlation coefficients in the range of

0.9950–0.9987 and mean relative errors (MREs) in the range of 3.92516–7.040% for the

test data set. The regression coefficients indicated that the ANN model can successfully

be used for the prediction of the thermal performance parameters of a box type solar

cooker with a high degree of accuracy [30].

Chaouki Ali et al., developed the models of the different sections of the hybrid solar

cooker like a dark absorber plate, glass cover, parabolic reflector, thermal insulation etc.

in 2010 and numerically simulated to help in predicting the behaviour of the system in

various climatic changes. They manifested that the proposed model had given them better

knowledge of the system of the different components of a solar cooker [31].

After an year, Farid Chejne et al. Developed a mathematical model that describes and

simulates the thermal behaviour of a solar stove based on an electric resistances analogy.



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Their mathematical model includes the three different heat transfer mechanisms between

different surfaces of the solar stove & its environment & it was used to predict the solar

stove entropy generation and its efficiency; also, it was used to evaluate the design

parameters of solar box stove. Making a comparison between the theoretical &

experimental results, they found that the simulation provides a closer & right prediction of

the real thermal behaviour, for that reason, the mathematical structured model is a precise

and reliable tool for designing a solar oven [32].

In 2012, R.C. Punia et al. developed a mathematical model of a heat transfer processes

involved in a box type solar cooker & applied to a light weight low cost solar cooker.

They deduced energy balance equation for various components of a solar cooker such as

absorber plate, cooking vessel, cooking fluid, air enclosed and glass covers. These

equations was solved by them using fourth order ranga kutta method to obtained the

thermal profiles of above mentioned components. To validate the model the temperature

distribution obtained by the numerical simulation was compared with the experimental

results obtained for a typical summer day in Jaipur, India. Their results showed that there

was a good agreement between the theoretical and experimental values at low

temperatures. Further, they manifested that, their theoretical model can prove to be highly

useful in studying the performance of any box type solar cooker at different places [33].

After 3 months, Arezki Harmim et al., developed a mathematical model using the heat

balance analysis of the different elements of the solar cooker. They conducted computer

simulation studies to predict thermal behaviour of cooker under transient conditions.

Their results demonstrated competitiveness and promising performance of cooker which

could be easily integrated into building facade [34].

Then in year 2014, Gonzalez Aviles et al. obtained a mathematical thermal model to

explain the behaviour of the solar cooker: ‘Jorhejpataranskua’.They had shown their

model in terms of a coupled system of three non-linear differential equations. They

calculated the temperatures for a fluid, the reflectors and the container of the solar cooker,

then compared the numerical results obtained with the model to measurements in field

testing operations & obtained good agreement between numerical and experimental

solutions with a relative error below 4%. Then at last, they use numerical results to

calculate the cooking power and standardized cooking power of the solar cooker for two

different containers. They manifested that their model is useful for predicting some of the

temperatures of interest in thermal analyses of solar cookers & allowed them to calculate

standardized cooking power without making field tests [35].

On same year, Hilario Terres et al. showed the validation for a mathematical model as well as one application to determine the thermal function in a solar cooker box-type with

variables steps. The numerical results were generated by means of a software developed

in C++ & were compared with their own results and experimental data obtained by El–

Sebaii & Domanski. The experimental data obtained by El-Sabaii were selected by them

because these were obtained under controlled operation conditions. For the mathematical

model solution, they used ambient temperature and solar radiation values & for this

purpose, experimental data were obtained. Their main results allowed them to point out,

how the increment in the internal steps, impacts on the temperatures in the solar cooker &

how the mathematical model can be used for different applications as different fluids and

different liquid amounts. It was also pointed out that how the numerical techniques can be

useful to analyze solar devices as solar cookers box-type [36].

D. Tiwardi, conducted mathematical modeling and numerical simulation of phase change

materials (PCMs) used as latent heat thermal energy storage in a solar cooker in 2015.

The PCM to store thermal energy was packed in many small hollow cylinders and placed

in a larger cylinder tank. Heat transfer fluid (HTF) which flows parallel to the PCM

cylinder was used to distribute heat from the solar collector to the PCM storage unit and



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vice versa. He used a mathematical model which was describing the behaviour of

temperature in the PCM and HTF and obtained numerical solutions by transforming heat

conduction equations of the PCM and HTF into enthalpy equation and solving it by using

the Godunov method. Thermal performance during charging and discharging process of

several selected PCMs was investigated by him. His simulation results showed that

magnesium chloride hexahydrate has the highest capacity to store solar thermal energy

whereas erythritol can achieve the highest temperature history during charging time and at

the first 54 minutes of discharging time. While, his results provide an important

information to design a solar cooker prototype equipped with thermal energy storage that

has a good thermal performance [37].

After an year, Sasa Pavlovic et al. presented the process of design, construction and

optical ray tracing analysis of a low cost solar concentrator for medium temperature

applications. To avoid complexity of design of a specific shaped surface, they used a

common offset parabolic antenna to make the reflector. They developed and applied a

new mathematical model for estimating the intercept factor of a new solar concentrator

based on the geometric and optical behaviour of the concentrator in cartesian coordinates.

While performing a ray tracing simulation and analyses of the geometry of solar image in

the receiver, they found that the more suitable geometry for the receiver has an elliptical

form. They manifested that the present mathematical model and optical design of a low-

tech solar concentrator can be used as a potentially low-cost tool for laboratory-scale

research on the medium-temperature thermal processes, hot water systems, heating

systems, cooling systems, poly generation systems etc. [38].

In 2018, Avala Raji Reddy et al. presented a mathematical model to evaluate temperatures

of all the components of the cooker, including cooking vessel and contents of the vessel

with solar insolation as an input. This model take care of every component of the cooker

like, the presence of air between the lid and vessel contents. From the results of modelling

and simulation they found that the air gap between the vessel cover and the contents of

the vessel acts as a barrier to heat transfer [39].

6. Conclusion

From review, it is concluded that the most of the performance parameters and models are

largely climate independent and can provide the information about the gradable

performance value of the cookers. Mathematical modelling of solar cooker has been tried

by some of the researchers. However, it is found that the results of these studies are not

consistent with the experimental results because of many simplifying assumptions made

for writing heat balance equations.

7. Acknowledgment

I am thankful to my mentors, Dr. R.E. Thombre and D. Subroto, for their valuable

guidance during my research work.



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References

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Nomenclature

Tps = Plate stagnation temperature,

Hs = Insolation on a horizontal surface,

Tas = Ambient temperature at the

time stagnation temperature is reached,

(MC)w = heat capacity of water,

F1 = First figure of merit, F2 = Second figure of merit,

A = Aperture area (m2),

Tw = Water temperature (℃), Ta = Ambient air temperature (℃),

Hs = solar insolation (W/m2),

C = Concentration ratio, m1 = mass of cooking utensils (kg),

m2 = mass of water in cooking

utensils (kg), tv1 = Initial temperature of cooking

utensils (℃),

tv2 = Final temperature of cooking utensils (℃),

tw1 = initial temperature of water

(℃), tw2 = Final temperature of water

(℃), θ = Period of test (h),

η = Efficiency of solar cooker,

Cpw = Specific heat capacity of water (4186 J/Kg-K),

Mw = Mass of water (kg),

t = time in seconds, ηE = Instantaneous energy

efficiency,

Tps = maximum plate surface temperature (℃),

Tw = water temperature (℃),

Twi = Initial water temperature in ℃

U = Overall heat transfer coefficient,

τ = Time difference between readings, seconds,

α = Absorptivity of receiver surface,

ηo = Optical efficiency, C = Cost of the system,

E= Energy saving price for commonly

used fuels, M = Maintainance cost,

a, b = Compound annual interest,

n = no. of years, NPV = Net Present Value,

gi = Thickness (m),

ρi = Density kg/m3,

pum,i = Market price of the ith

component(Rs/kg),

pua,j = Market price of the jth component (Rs/m2),

γ and ϭ = regression coefficient,

Two = Ambient temperature (℃), Ts = Maximum surface temperature

(℃),

Io = Average theoretical insolation, ηo = Optical heat transfer coefficient,

Asc = Aperture area of the solar cooker, m2,

Qleft = Energy left in the system, J,

ID = Solar radiations received at solar dish, W,

tch = Charging time, hr,

ΔTf = Difference between the initial and final temperature of the fluid,

At = Total collector area,

τₒ = Time constant for cooling, Twf = Final temperature of water in℃,

Ibrb = Irradiance in W/m2,

ψ = Instantaneous exergy

efficiency, Ts = Surface temperature of sun,

Δt = Time required to achieve

maximum temperature of the cooking fluid,

Iav = Average solar intensity

(W/m2) during the time interval, τ = Time interval,

G= average solar radiation

(W/m2), GNR = reference direct normal

radiation (W/m2) ,

M1 mass of cooking utensil (kg), N = number of pots,

P = cooking power (W),

Ps = standard cooking power (W), tc = characteristic boiling time

(min m2/kg),

ts = specific boiling time (min m2/kg),

Ta = ambient air temperature (℃),

τₒ = time constant (h), τr= time taken to achieve a

reference cooking temperature (h), τhr = duration of heat retention (h) ,

η= efficiency of the solar cooker,

ηₒ= optical efficiency, ηu = utilizable efficiency,

Ar = Outer surface area of black

cook pot, m2 , CRg = Geometric concentration

ratio, d/l,

CRo = Optical or effective concentration ratio, d/l,

Cpw = Heat capacity of water, J/kg

K,

mw = Mass of water, kg,

̅ = average ambient temperature (℃),

qrefthmax = maximum theoretical energy intercepted by the

reflector,

qrefth = Energy intercepted by the reflector and falling on the

cover,

Cw = specific heat of water (J/kg/℃),

τ = time interval (s),

mp = Mass of black pot, kg, AP = aperture area (m

2),

Ac = collector area (m2),

At = pot surface area (m2),

C = concentration ratio,

CR = heat capacity ratio,

Cu = specific heat of cooking utensil (J/kg/℃),

UL = total heat loss factor

(W/m2 ℃), (MC)’= heat capacity of

cooker’s interiors (J/℃),

(MC)w = product of the mass of water and its specific heat

capacity (J/℃),

Ea = Amount of heat which collects by aperture area, W,

Ia = Insolation average or

Insolation falling on funnelled cooker aperture, W/m2 ,

Tpx = maximum absorber plate

temperature (℃),

Cpp = Heat capacity of black

pot, J/kg K

Arc = Area of the receiver/absorber surface,



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a review on test procedures, performance parameters and...

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