experimental investigation of a box type solar cooker...

Experimental investigation of a box type solar cookeremploying a non-tracking concentrator

B.S. Negi a,*, I. Purohit b

a Solar Energy Centre, Ministry of Non-conventional Energy Sources, Government of India, Block-14,CGO Complex, New Delhi 110016, India

Centre for Energy Studies, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India

Received 28 January 2004; accepted 29 April 2004

Abstract

The present work aims at development of a box type solar cooker utilizing non-tracking concentratoroptics to enhance the solar energy availability in the box of the cooker for efficient cooking. A laboratorymodel of a box type solar cooker employing a non-tracking concentrator has been designed and fabricated,and its thermal performance has been investigated experimentally. The concentrator, consisting of twoplanar reflectors suitably positioned in an east-west configuration on an inclined framework, is mounted onthe box of the cooker to reflect incident solar radiation on the base absorber of the cooker. The design angleof inclination of the framework is taken equal to the latitude of the location and it is adjusted seasonally.The thermal performance of the experimental solar cooker has also been compared with that of a con-ventional box type solar cooker whose dimensions and make are identical to the box used with the formerand which was also tested simultaneously under similar solar insolation and ambient conditions. Theexperimental results obtained show that the concentrator solar cooker provides a stagnation temperature15-22 °C higher than that of the conventional box type solar cooker using a booster mirror. It is alsoobserved that the boiling point of water with the concentrator cooker is reached faster, by 50-55 min, thanwith the conventional box type cooker using a booster mirror. Thus, the solar cooker utilizing non-trackingreflectors provides increased heat collection and faster cooking compared to the conventional box typecooker. The results of the tests conducted have been analyzed and discussed.

Keywords: Non-tracking concentrator; Box type solar cooker; Optical design; Stagnation temperature; Load test

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Nomenclature

Tpr

Tpc

HF1F2

Ta« ]

a2

hm

W1

W2

DD0

CF

plate temperature of solar cooker using non-tracking planer reflectorplate temperature of conventional cookertotal solar radiation on cooker levelfirst figure of meritsecond figure of meritambient temperatureangle of first mirror with concentrator baseangle of second mirror with horizontallatitude of placeacceptance half anglewidth of first mirrorwidth of second mirrorwidth of absorber platelength of apertureconcentrator factor

1. Introduction

Solar cooking offers an effective method of utilizing solar energy for meeting a considerabledemand for cooking energy and, hence, protecting the environment. Considerable efforts havegone into the development and performance testing of a variety of solar cookers and their suit-ability for cooking different foods [1-4]. Solar cookers are mainly of two types: box types andconcentrating types. Box type solar cookers are simple and suitable for limited cooking due totheir relatively low heat collection capacity, while concentrating type solar cookers are capable ofgenerating higher temperatures and can efficiently be used for a variety of cooking applications.However, the latter require continued adjustment of the orientation of the concentrator to reflectthe incident solar radiation on the focus where the cooking pot is placed.

Different designs of solar cookers reported in the literature have separate provisions for energycollection and the cooking units. Morrison et al. [4] have utilized an evacuated type solar collectorfor high temperature, while Schwarzer et al. [6] utilized a double glazed solar flat plate collector. Asolar cooker for inside the kitchen has also been developed using a flat plate collector as theenergy collection unit [3]. Mills [5] developed a concentrating type solar cooker using a frequentlyadjusted Fresnel mirror system and a seasonally adjusted mirror with an evacuated tube collector,wherein thermal storage allows the stove to be permanently placed indoors for cooking. Fieldtesting conducted on different designs of solar cookers has demonstrated their ability to cook avariety of foods and acceptability of the various designs by users [7,8]. The box type solar cookeris the most popular one due to its simple design and easy handling requirements. Mullick et al.[9,10] conducted extensive experimental studies and developed a test procedure for performanceevaluation and standardization of box type solar cookers [11]. In India, half a million box type

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solar cookers have been propagated in the country through the popular schemes launched by theMinistry of Non-conventional Energy Sources, Government of India [12].

The present work aims at developing a solar cooker design that can enhance the heat capacityof a box type solar cooker by augmentation of the solar energy in the box for efficient cooking byutilizing non-tracking concentrator optics [13,14]. A laboratory model of a box type solar cookeremploying a non-tracking concentrator has been designed and fabricated, and its thermal per-formance has been evaluated experimentally. The solar cooker design employs two mirrors in aneast-west configuration, suitably fixed on a framework tilted at a certain angle with respect to theupper surface of the cooker such that all incident solar rays impinging on the mirrors within acertain specified range hm (acceptance half angle) with respect to the normal to the concentratoraperture plane are reflected onto the base absorber of the box of the cooker The cooker isdesigned with the framework of the concentrator tilted at an angle equal to the latitude of the sitewith a provision for seasonal tilt adjustment to keep the concentrator aligned with the direction ofthe sun. The absorber, i.e. the box of the cooker is kept stationary in a horizontal position.Performance testing of the laboratory model of the solar cooker was conducted without load andwith load, at the Solar Thermal Test Facility in the Solar Energy Centre of the Ministry of Non-conventional Energy Sources. A number of tests were conducted under varying operating con-ditions to determine the stagnation temperature and to study the heat capacity of the cooker.Further, in order to quantify the increase in the temperature achieved with the laboratory modelof the solar cooker, a box type solar cooker with dimensions and make identical to the box used

(2ot2-0-em-9O)(204+0 - 6m- 90)

Fig. 1. Schematic diagram of non-tracking concentrator with box type solar cooker.

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4 B. S. Negi, I. Purohit / Energy Conversion and Management xxx (2004) xxx-xxx

with the former was also tested simultaneously under similar solar radiation and ambient con-ditions. A comparison of the performances of the two cookers indicates that the cooker utilizingthe non-tracking concentrator provides higher stagnation temperature and faster boiling of waterthan the conventional box type solar cooker using a booster mirror. The experimental results havebeen analysed and discussed in detail.

2. Design methodology

Fig. 1 illustrates the optical geometry used for the design of a solar cooker employing two non-tracking plane mirrors in an E-W configuration with the lateral sides of the box of the cooker.The lateral side walls of the solar cooker may offer the advantage of intercepting increased solarradiation compared to vertical sides. PQRS is the cross-section of the solar cooker absorbersurface; PQ and RS are the sides and QR (= D) is the width of the base absorber plate of thecooker. The solar concentration is accomplished in such a way that the reflectors positioned on aplane making an angle equal to the latitude of the site with the plane of the solar cooker reflect theincident solar energy on the absorber plate of the box of the cooker. The width of the reflectors isdetermined in such a way that any incident ray making an angle hm with the normal to the baseplane of the concentrator and striking the extreme upper edge of the mirror, after reflection, meetsthe extreme edge of the absorber plate on the opposite side of the mirror. The ray reflected fromthe mirror placed on the left side will meet the edge R and that reflected from the mirror placed onthe right side will meet the edge Q of the absorber. Thus, all the incident rays within hm, afterreflection, will be intercepted within the QR portion of the absorber plate. The design is generatedfrom the given size of the cooker, i.e. for a given depth of the cooker and width of the base andsides of the absorber tray of the cooker, and the angle of inclination of the reflectors with theconcentrator base and the angle of inclination of the concentrator are determined.

The width of the mirror, W1, placed on the right hand side towards the southern wall ofthe cooker and making an angle a1 with the horizontal plane, or making an angle a1 þ U with theconcentrator base plane is determined using simple geometrical optics as,

= D0 ~ aÞ Sinð2a1 þ / ~ hm - 90Þ1 Cosða2 þ (/>-em) ð

where

D0 =D þ 2dCos60 ð2Þ

and

= 5Sin(120-(2«1+ (/>-gm-90))a Sinð2a1 þ / - hm - 90Þ U

s being the width of the sides of the cooker. The angle of the walls of the cooker tray with thehorizontal is taken as 60° for the purpose of the present study.

The width of the mirror, W2, placed on the left hand side towards the northern wall of the solarcooker and making an angle a2 with the horizontal plane, or making an angle a2 — U with theconcentrator base plane is calculated as,

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W 2 = •

where

B.S. Negi, I. Purohit / Energy Conversion and Management xxx (2004) xxx-xxx

-b')Sin(2a2-2^-em-90))

Cosða2 -4>-6{ '

and

b = Sin(2a2 -2</>-Om- 90) ^

The concentration factor (CF) of the cooker, defined as the ratio of the sum of the projections ofthe two mirrors on the plane of the concentrator and the width of the aperture of the cooker to thewidth of the absorber is calculated as,

D0 þ W1 Cosða1 þ/Þþ W 2Cosða2 — /ÞC = (7)

where D0 is the width of the aperture of the cooker.

3. Laboratory model of non-tracking concentrator box solar cooker

The experimental laboratory model of the solar cooker essentially consists of the box of aconventional box type solar cooker and a non-tracking concentrator. The box is made of

Fig. 2. Photograph of the laboratory model of box type solar cooker employing non-tracking concentrator.

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aluminum sheet in a tray shape with the inner surface painted black as an absorbing surface. Thetray is enclosed in a box made of aluminum with the gap between the tray and the box filled withfiber glass wool as an insulator. The tray is covered with an aluminum framed double glazed lid.As a matter of fact, two box type solar cookers of identical shape and dimensions were taken forthe purpose of the present study and tested for their performance without load and with load inorder to quantify accurately the increase in temperature in the box of the cooker when operatedwith a non-tracking concentrator. The concentrator, comprising two commercially availablemirrors in an east-west configuration, was designed and fabricated for operation with one of theboxes of solar cookers indicated above. The concentrator was designed for a given size of tray ofthe box of the solar cooker based on the design considerations described above. The mirrors aresuitably fixed on an aluminum angle section framework mounted on the cooker and tilted with

Table 1Design parameters of the laboratory model and conventional model of box type solar cookers

S. No.

1

IN)

3

4

5

Design/parameters

Glass covers(i) Number(ii) Thickness(iii) Spacing(iv) Transmittance(v) Type (outer)(vi) Type (inner)

Absorber plate(i) Material(ii) Coating(iii) Absorptivity(iv) Angle of lateral sides

Reflector mirror(i) Number(ii) Thickness(iii) Type(iv) Dimensions

(v) Angles

Cover plate(i) Dimensions(ii) Aperture area

Cooking pots(i) Number(ii) Material(iii) Coating(iv) Dia of big pot(v) Dia of small pot(vi) Height of big/small pots

Conventional box typesolar cooker with reflector

23.5 mm2 cm83%ToughenedPlane

AluminumBlack paint0.9065°

13.5 mmToughened458 mm x 458 mm

-

43.3 cm x 43.3 cm0.188 m2

3 (one big and two small)AluminumBlack paint202 mm150 mm57 mm, 50 mm57m

Box type solar cooker withnon-tracking concentrator

23.5 mm2 cm83%ToughenedPlane

AluminumBlack paint0.9065°

24 mmToughenedW1 — 460 mm x 460 mmW2 — 440 mm x 440 mma1 =51° , a2 = 97°

43.3 cmx43.3 cm0.188 m2

3 (one big and two small)AluminumBlack paint202 mm150 mm57 mm, 50 mm57m

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B.S. Negi, I. Purohit / Energy Conversion and Management xxx (2004) xxx-xxx 7

respect to the cooker upper surface. The concentrator was designed with the tilt angle of theframework of 28° (i.e. the latitude of New Delhi). The framework is supported by hinges fixed onthe southern wall of the cooker and is also provided with another hinge having an elevationtracking arrangement to set the concentrator for its seasonal tilt adjustment. The box of thecooker receives the solar radiation both directly and by reflection from the two mirrors used. Thephotograph of the laboratory model of the solar cooker is shown in Fig. 2. The concentrationfactor of the solar cooker is calculated as 1.68. The detailed design parameters of the laboratorymodel of the solar cooker and the conventional solar cooker tested for the present studies arepresented in Table 1.

4. Thermal performance testing

Thermal performance testing of the laboratory model of the solar cooker and the other boxtype solar cooker using a booster mirror was conducted extensively, without load and with load toquantify the improvement in the performance of the box type solar cooker by using a non-tracking solar concentrator. The tests were conducted under similar insolation and ambientconditions for comparative analysis.

The thermal performance of a box type solar cooker is evaluated by conducting two tests,namely, a stagnation test and a load test [9,11]. The results of these tests provide the figures ofmerit of the cooker. The first test, i.e. the stagnation test (or no load test) provides the first figureof merit denoted by F1. The second test provides the second figure of merit denoted by F2. The testprocedures of the thermal performance tests for determining the values of F1 and F2 of the boxtype solar cooker have been discussed in Appendix A.

4.1. Stagnation temperature test

A number of tests were conducted on the laboratory model of the solar cooker and the con-ventional box type solar cooker without load under similar insolation and ambient conditions todetermine their stagnation temperatures and also to check their behavior in terms of their rise intemperature and their heat capacity. The stagnation temperature was monitored for different

Table 2Details of measuring instruments used in present study

S. No. Parameter measured Instrument used Type/make Least count Accuracy

Total solar radiation

Ambient air temperatureCooker tray temperatureWind speed

Water temperatureMass of the water as loadDimensions of cooker

Eppley radiometer

RTDThermocoupleAnemometer

ThermocoupleElectric balanceMeasuring scale

Model PSP 24319 F-3Pt-100(Copper-constantan)

1.0 W/m2 (9.03H,v=1.0 W/m2)0.1 °C0.1 °C

C.P.O. Box 1618, Ja- 0.1 m/span(Copper-constantan) 0.1 °CAVERY -3359 0.001 kgKristeel-Shinwa 0.001 m401E10

±0.5%

±0.2%±0.5%±0.1%

±0.5%±0.2%±0.2%

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starting times of testing and for different modes of operation of the solar cookers. Copper-con-stantan thermocouples were used to monitor the absorber mean plate temperatures of eachcooker, i.e. Tpc and Tpr, respectively, and the ambient air temperature Ta was measured using anRTD. The solar irradiance on a horizontal surface Hs was measured by a pyranometer. Perfor-mance data was recorded immediately after the cookers were exposed to solar radiation for thedesired operating conditions of the tests. The entire monitored data was recorded through a dataacquisition system at intervals of five minutes. The least count, accuracy and other details of theinstrumentation used for the measurements are given in Table 2. Uncertainties in the measure-ments of the different parameters, such as those illustrated in Figs. 4 and 5 for determining thevalues of F1 and F2, respectively, have been calculated from the instrumentation error analysisperformed using the procedures described in Refs. [15,16]. The results obtained from the erroranalysis mentioned above have been summarized in Tables 3 and 4 of Appendix B.

4.2. Thermal load test

The cookers were next tested with four cylindrical vessels with flat base and lids (two small andtwo big) filled with water as per Indian standards [11]. Thus, the exposed surfaces of the vesselsand the plate of the cooker constitute the absorbing surface. The size and dimensions of thevessels are given in Table 1. The quantity of water in the pots was distributed as per Indianstandards, i.e. 8 l/m2 of aperture area. A small hole was made in the side wall of one of the big

1.25

1.00

0.60

075

0.50

0.25

000

45 55 65 75 85 95 105

0.00

. . . . . 0 - — Wi & W2 (m) CF (Wi) & CF (W2)

Fig. 3. Variation of the widths and concentration factors with angles of inclination of the mirrors of non-trackingconcentrator.

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vessel just above the level of the water to insert a thermocouple in such a way that the tip is justdipped in the water contained in the vessel. The hole was made air tight to prevent heat loss fromthe water. The vessels were perfectly closed with their covers to ensure no loss of heat. The coverplate of the box of the cookers was perfectly closed so that there is no loss of heat from theabsorber and pot surfaces. Temperatures are recorded once the cover plate is closed and as soonas the cookers are exposed to solar radiation for the experiments. The cover plate was opened onlyafter the measurements are stopped. The water temperatures Twc and Twr in the vessels placed inboth solar cookers were measured using the instrumentation described above for stagnationtemperature measurements.

5. Results and discussions

To illustrate the design and performance characteristics of a box type solar cooker employing anon-tracking solar concentrator, an analysis has been made for a typical design case. Fig. 3

100

10:30 11:00 11:30 12:00 12:30

Time [hrs]

14:00 14:00 14:00

- Tpr —•— Tpc —a — Ta —*— Hs

Fig. 4. Comparative thermal performance of two identical box type solar cookers under stagnation test condition.

10

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illustrates the variation of the widths and the concentration factors for the two mirrors withdifferent angles of inclinations a1 and a2 for a typical design case with the width of the absorbersheet D (= 0.5 m), depth of the cooker d (= 0.1 m), angle of walls of cooker tray with horizontal60°, tilt of the concentrator U = 28° (latitude of the site, New Delhi) and hm, equal to 10°. Thewidth of both mirrors increases with the increase in the angles of inclination of the mirrors. Theconcentration factor (CF) of a mirror, defined as the contribution of the mirror to the concen-tration of solar radiation on the absorber surface of width D, is determined by the ratio of thewidth of the projection of the mirror on the plane of the concentrator base to the width of theabsorber (i.e. W1 cosða1 þ UÞ=DÞ or W2 cosða1 — UÞ=DÞ. It may be observed that the CF for mirrorW1 first increases with the increase in a1, reaches a maximum at a1 equal to 54° and, thereafter,decreases with further increase in a1. The CF for W2 also increases with a2, however, the rate ofincrease starts decreasing once a2 reaches 96°. The mirrors are assumed to be specularly reflecting.

800

-Twr —•—Twc —» — Ta —»— Hs

Fig. 5. Comparative thermal performance of two identical box type solar cookers under load test condition.

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Suitable values of a1 and a2, as shown in Table 1, were taken for fabricating a laboratory model ofthe non-tracking solar concentrator for operation with a given box solar cooker.

Figs. 4 and 5 illustrate the comparative thermal performance of the two box type solar cookerstaken for the purpose of the present study and tested under stagnation and load test conditions,respectively, on two different days. The maximum temperature attained by the first cooker, Tpc, is105.86 °C and that attained by the second, Tpr, is 105.99 °C under the stagnation test, and hence,the first figure of merit F1 of the two solar cookers is 0.1250 and 0.1252 oCm2/W, respectively. Thecookers were next tested with load as per Indian standards. The times taken for attaining a boilingtemperature (~90 °C) by the above two cookers were 6320 and 6400 s, respectively. So, the secondfigure of merit F2 has been calculated for both solar cookers as 0.4048 and 0.4051, respectively.Thus, the performances of the two box type solar cookers tested as above are the same.

10:30 11:00 12:30 13:00 13:30 14:00

Time [hrs]

14:00 14:00

Tpr rTpc cTa Hs

Fig. 6. Variation of the plate temperatures with time for laboratory model of solar cooker and conventional box typecooker under stagnation test condition (starting time 10:30 AM), both are in non-tracking mode.

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12 B.S. Negi, I. Purohit / Energy Conversion and Management xxx (2004) xxx-xxx

5.1. Stagnation test under various operating conditions

Figs. 6-9 illustrate the variations of the absorber temperature with time for the laboratorymodel of the concentrator solar cooker and the conventional box type solar cooker using abooster mirror recorded in stagnation tests on different days in the month of March 2002 withvaried starting time and without tracking. The tests were conducted with the concentrator of thelaboratory model of cooker tilted at 28° (the latitude of Delhi). The insolation and ambienttemperature recorded during the tests are also plotted in these figures. The temperature curvesshow that the performance of the laboratory model of solar cooker in terms of increase inabsorber temperature, in each case, is better then that of the conventional box type solar cookerthroughout the period of tests conducted. It is observed that the performance of the laboratorymodel of concentrator solar cooker varies with the starting time of testing; the rate of rise inabsorber temperature increasing when the starting time changes from 10:30 AM to 12 noon.

160

13:00 13:30 14:00

Time [hrs]

Tpr —•—Tpc cTa Hs


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100

11:30 12:00 13:30 14:00

Time [hrs]

14:00 14:00



The rise in temperature increases significantly when the cooker is operated near solar noon. Therate of rise in temperature with the laboratory model of cooker is higher than that of the con-ventional cooker. It may also be noted from the performance curves that the laboratory model ofcooker heats so well that the absorber temperature remains high even when the insolation de-creases.

Fig. 6 shows the performance data recorded for the cookers when testing was started at 10:30AM. The maximum temperature attained by the laboratory model is 139.39 °C and that by theconventional cooker is 132.99 °C. The temperature difference at the stagnation condition is 6.5 °C.The maximum temperature of 132.99 °C that was achieved with the conventional cooker at 12:05PM was achieved with the laboratory model at 11:35 AM (i.e. 30 min earlier). The performancecurve for the case when testing was started at 11:00 AM is shown in Fig. 7. In this case, themaximum temperature achieved with the laboratory model is 144.20 °C and that with the con-ventional cooker is 134.35 °C. The temperature difference at stagnation is 9.85 °C. When the

14

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- Tpr —•— Tpc

Fig. 9. Variation of the plate temperatures with time for laboratory model of solar cooker and conventional box typecooker under stagnation test condition (starting time 12:00 noon), both are in non-tracking mode.

testing was started at 11:30 AM, the maximum temperature achieved with the laboratory model is148.66 °C and that achieved with the conventional cooker 136.60 °C (which was achieved 25 minearlier with the laboratory model), and the stagnation temperature difference is 12.06 °C (Fig. 8).When the testing was started at 12:00 noon, the concentrator type cooker achieved a maximumtemperature of 154.87 °C at stagnation, while the conventional cooker achieved 136.96 °C, whichwas achieved 40 min earlier with the laboratory model of cooker (Fig. 9). The temperature dif-ference at the stagnation condition in this case is 17.91 °C.

Tests were also conducted to study the effect of tracking/adjustment of both solar cookers toredirect them towards the sun every half an hour on their performance. Fig. 10 illustrates theperformance curves when the testing was started at 12:00 noon with the laboratory model of solarcooker stationary and the conventional cooker with the booster mirror tracked/adjusted everyhalf an hour. The maximum temperature achieved with the laboratory model is 141.27 °C andthat with the conventional cooker is 128.17 °C. The temperature difference at stagnation in this

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160

15

i

I

- Tpr —•— Tpc

Fig. 10. Variation of the plate temperatures with time under stagnation test condition with the laboratory model ofsolar cooker stationary and conventional cooker with the booster mirror adjusted/tracked every half an hour.

test is 13.10 °C. Fig. 11 illustrates the performance curves for the case when the laboratory modelwas tested with horizontal adjustment and the conventional cooker with the booster mirroradjusted/tracked in intervals of every half an hour. The maximum temperature attained by thelaboratory model is 157.40 °C and that by the other cooker is 141.27 °C. The temperaturedifference at stagnation is 15.77 °C. It may be noted that periodic tracking/adjustment of the solarcookers to redirect them towards the sun, particularly the concentrator cooker, provided aslight increase in temperature with flattened temperature curves after the stagnation condition,capturing more solar energy and thereby keeping the cookers hot even with variations in inso-lation. On the other hand, the temperature of the absorber starts decreasing after reaching amaximum near solar noon with insolation and ambient conditions as may be seen from Figs. 9and 11.

Since the concentrator of the laboratory model of cooker is designed with an angle of incli-nation of 28° and the concentrator requires seasonal adjustment to keep it aligned with thedirection of the sun, two tests have also been conducted for two different angles of inclination of

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"Tpr n Tpc-

Fig. 11. Variation of the plate temperatures with time under stagnation test condition with the laboratory model ofsolar cooker tracked horizontally and conventional cooker with the booster mirror adjusted/tracked every half an hour.

the concentrators. Fig. 12 shows the performance curve with the tilt angle of the concentratorframework adjusted at 32° (i.e. U þ 4°) and the conventional cooker with a booster mirrortracked/adjusted every half an hour. The maximum temperature achieved with the laboratorymodel is 140.76 °C and that of the other cooker is 128.17 °C. The temperature difference betweenthe two solar cookers during the test at stagnation is 12.59 °C. Fig. 13 shows the performancecurves with the framework of the laboratory model adjusted at 24° (U — 4°) and the conventionalcooker with a booster mirror tracked/adjusted every half an hour. The maximum temperatureachieved with the laboratory model is 152.24 °C and that with the conventional cooker is 146.89°C. The stagnation temperature difference in this operating condition is 5.35 °C.

5.2. Load test under various operating conditions

Figs. 14-17 illustrate the test results obtained for both types of solar cookers with load for thevarious operating conditions that were tested without load. Both solar cookers were stationary

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Fig. 12. Variation of the plate temperatures with time under stagnation test condition with the concentrator of thelaboratory model of solar cooker tilted at 24° and conventional cooker with the booster mirror adjusted/tracked everyhalf an hour.

during the tests conducted. The concentrator of the laboratory model of cooker was tilted at 28°.The amount of water as load has been taken as per Indian standard, i.e. 8 l/m2. In the load testcondition, the benefits of the laboratory model of cooker can be found in terms of fast cooking.As expected, in this case as well, the thermal energy achieved with the laboratory model in eachtest is higher then that with the conventional cooker. When the testing was started at 10:30 AM,the water heated in the laboratory model of solar cooker achieved the boiling temperature 20-25min faster than the conventional solar cooker (Fig. 14). The boiling of water became faster by 30-35 min when the testing was started at 11:00 AM (Fig. 15). The boiling temperature in the lab-oratory model was attained 40-45 min faster than in the other cooker when the testing was startedat 11:30 AM (Fig. 16). When the testing was started at 12:00 noon, the boiling temperature withthe laboratory model of solar cooker was achieved 50-55 min faster than with the conventionalcooker using a booster mirror (Fig. 17).

18

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160

10012:00 14:00


Fig. 13. Variation of the plate temperatures with time under stagnation test condition with the concentrator of thelaboratory model of solar cooker tilted at 32° and conventional cooker with the booster mirror adjusted/tracked everyhalf an hour.

Tests were also conducted with the laboratory model stationary and the conventional cookerwith a booster mirror adjusted/tracked every half an hour. In this case as well, the laboratorymodel attained the boiling temperature 30-35 min faster then the other cooker when the testingwas started at 12 noon (Fig. 18). In another case, testing was conducted with both cookerstracked, i.e. the conventional cooker with a booster mirror is tracked/adjusted and the laboratorymodel is tracked horizontally every half an hour. It is found that the laboratory model of cookerreached the boiling point about 40-45 min faster than the conventional cooker with reflector (Fig.19).

Similar to the cases of the stagnation tests described above, two tests were also conducted withthe concentrator of the laboratory model tilted at two different angles. Fig. 20 illustrates theperformance curves for the case when the concentrator framework of the laboratory model istilted at 32° (i.e. U þ 4) and the conventional cooker with a booster mirror tracked/adjusted every

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100 I 1 900

19

12:00 12:30

Time [hrs]

Twr rTwc cTa

Fig. 14. Variation of the water temperatures with time for the laboratory model of solar cooker and conventional boxtype cooker under load test condition (starting time 10:30 AM), both are in non-tracking mode.

half an hour. The laboratory model attains the boiling temperature 30-35 min faster then theconventional cooker. When the tilt of the concentrator was fixed at 24° (i.e. U — 4) and theconventional cooker with the booster mirror was tracked/adjusted every half an hour, the boilingtemperature with the laboratory model was reached 20-25 min faster then with the conventionalcooker (Fig. 21).

6. Conclusion

The experimental results obtained from the thermal performance tests performed show that thebox type solar cooker employing a non-tracking solar concentrator can provide improved heatcollection and, hence, more efficient cooking. The cooker offers the advantage of faster cooking

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11:00

- Twr —•— Twc cTa


and, hence, considerably reduced cooking time. The cooker is easy to fabricate and operate. Asregards the cost, the cooker is approximately 10% costlier than the conventional box type solarcooker with a booster mirror. Presently, efforts are being made to improve the design of the solarcooker reported herein for better performance taking into account the spacing between the edgesof the absorber tray and the point where the mirrors can be placed practically, i.e. the spaceoccupied by the double glazed cover of the cooker.

Acknowledgements

The authors gratefully acknowledge the encouragement and fruitful suggestions from Dr. T.C.Tripathi, Adviser and Head, Solar Energy Centre, and Dr. Ashvini Kumar, Director, SolarEnergy Centre, during the process of the experiments performed for the present study.

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100 | 1 900

S so

100

13:30 14:00

Time [hrs]

Twc cTa

21


Appendix A. First and second figures of merit (F1 and F2) of box type solar cooker

The first figure of merit, F1, effectively is the ratio of optical efficiency, go, and overall heat losscoefficient, UL, of the box type solar cooker. It is obtained by keeping the solar cooker in the sunwithout pots in the morning, and allowing the plate temperature to rise gradually. The platetemperature, ambient temperature and solar radiation are measured, periodically. Soon after solarnoon, the plate temperature becomes quasi-steady and the stagnation temperature is achieved. F1is, thus, calculated using the following equation:

F =T — T-* ps -'as (A.1)

where Tps, Tas, and Hs represent the plate temperature, ambient air temperature and total solarradiation on the aperture plane of the box type solar cooker, respectively, at quasi-steady state(stagnation).

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E

300

100

Twr rTwc cTa

Fig. 17. Variation of the water temperatures with time for the laboratory model of solar cooker and conventional boxtype cooker under load test condition (starting time 12:00 noon), both are in non-tracking mode.

The test for the second figure of merit, F2, involves operating the solar cooker with full load (i.e.pots containing 8 l/m2). The cooker is kept in the sun in the morning and the water temperature isallowed to rise gradually until it reaches the boiling point. The water temperature, ambienttemperature and solar radiation are measured and recorded simultaneously. F2 is calculated usingthe following equation:

1

F,=-As

ln1 -

F H

' -« H

(A.2)

where F1 is the first figure of merit of the cooker (obtained from the stagnation test), Mw is themass of water as load, Cw is the specific heat of water, Ta is the average temperature, H is theaverage solar radiation incident on the aperture of the cooker, Tw1 is the initial water temperature(~60 °C), Tw2 is the final water temperature (~90 °C), A is the aperture area and S is the time

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I

200

100

Fig. 18. Variation of the water temperatures with time under load test condition with the laboratory model of solarcooker stationary and conventional cooker with the booster mirror adjusted/tracked every half an hour.

difference between Tw1 and Tw2. It should be noted that both the stagnation and full load tests areconducted without the booster mirror because the effective contribution of the booster mirror onthe aperture of the cooker varies with the diurnal motion of the sun.

Appendix B. Uncertainty analysis in determination of F1 and F2

The uncertainty in the determination of F1 and F2 can be studied using the instrumentationerror analysis. Following the procedures outlined in Refs. [15,16], an error analysis has beenperformed for the instrumentation used for measuring the different performance parametersfor determining the values of F1 and F2. A commonly used root sum square (rss) formula hasbeen used for determination of the overall error for the instruments used. It states that if aquantity R is be computed which is a known function of n independent variablesu1 ; u2; u3 ; . . . ; un such that

24

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Twr rTwc cTa

500 a

200

100

Fig. 19. Variation of the water temperatures with time under load test condition with the laboratory model of solarcooker tracked horizontally and conventional cooker with the booster mirror adjusted/tracked every half an hour.

R = / ( « ] , W2,W3, ;un(B.I)

and if it is assumed that the u's are the measured quantities and have associated errors as±A«i, ±AM2, ±AM3, . . . ; ±Awn, respectively, these errors will cause an error DR in the computedresult R. If the Du's are considered as statistical bounds, such as probable errors, the uncertaintydetermination of the root square sum method is used to compute such errors. In this case, theoverall error can be expressed as

W =82?

8«i +oR

-W(H 2)(dR oR

-W(Hn;

1=2

(B.2)

where WR is the overall error.Following the above approach, from Eq. (B.1), the absolute attainable accuracy in the deter-

mination of F1, i.e. WF1, can be expressed as,

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B.S. Negi, I Purohit / Energy Conversion and Management xxx (2004) xxx-xxx

8,

I

12:00

Twr -Twc —•—Ta —•— Hs

25

Fig. 20. Variation of the water temperatures with time under load test condition with the concentrator of the labo-ratory model of solar cooker tilted at 24° and conventional cooker with the booster mirror adjusted/tracked every halfan hour.

8Fj

87L

1=2

(B.3)

where WÐTPSÞ, wðTasÞ and WÐHSÞ represent the accuracies in the measurement of Tps, Tas and Hs

respectively.Similarly, from Eq. (B.2), the absolute attainable accuracy in the determination of F2, i.e. WF2,

can be expressed as,

8F?-wðMw

oF2

Tw1

1=2

(B.4)

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13:30 14:00

Time [hrs]

Twr - Twc

200

100

Fig. 21. Variation of the water temperatures with time under load test condition with the concentrator of the labo-ratory model of solar cooker tilted at 32° and conventional cooker with the booster mirror adjusted/tracked every halfan hour.

Table 3Instrumental error analysis for evaluation of first figure of merit F1 of a box type solar cooker

S. no. Parameter measured Associated error Least count/ Associatedin measurement possible error error

by

Absolute WF1=F1 x 100accuracy [WF1] [%]

Stagnation platetemperature

Ambient temperature

Solar radiation

0.10 °C0.50 °C1.00 °C

0.10 °C0.50 °C1.00 °C

1.0 W/m2

1.5%2.5%

0.0020.0080.015

)0.002)0.008)0.015

)0.002)0.0029)0.0031

0.00030.00080.0160

0.00030.00080.0160

0.00030.00190.0031

0.230.651.25

0.230.651.25

0.231.512.51

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Table 4Instrumental error analysis for evaluation of second figure of merit F2 of a box type solar cooker

S. No. Parameter measured Associated errorin measurementof F2 by

Least count/possible error

Associated Absoluteerror accuracy

[WF2]

WFjF2x 100

1 Mass of water WÐMWÞ

2 Specific heat of water wðCwÞ

3 First figure of merit WÐF1Þ

Cooking time

5 Area

Solar radiation

V(A)

6 Ambient temperature wðTaÞ

1 Initial water temperature wðTw1Þ

Final water temperature

wðHÞ

0.001 kg0.010 kg0.100 kg

0.04%0.08%1.00%

0.00030.0050.008

1.00 s10.0 s60.0 s

0.001x0.0010.005x0.0050.1x0.1 m2

0.10 °C0.50 °C1.00 °C

0.10 °C0.50 °C1.00 °C

0.10 °C0.50 °C1.00 °C

1.0 W/m2

1.5%2.5%

0.00030.00270.0267

0.00160.00320.0040

)0.0010)0.0016)0.0032

)0.0001)0.0007)0.0040

0.0010.00.0050.0

)0 .0017

)0.0010)0.0049)0.0098

)0.0010)0.0049)0.0098

0.00190.00970.0194

)0.0012)0.0120)0.0200

0.00330.00420.0269

0.00330.00430.0049

0.00330.00360.0046

0.00330.00330.0052

0.00330.00330.0037

0.00330.00590.0104

0.00330.00590.0104

0.00330.01030.0197

0.00330.0124000.02

0.781.016.41

0.781.021.17

0.780.871.09

0.780.801.23

0.780.780.88

0.781.412.47

0.781.412.47

0.782.444.69

0.782.964.82

where wðMwÞ, wðCwÞ, wðF1Þ, WÐSÞ, WÐAÞ, wðTw1Þ, wðTw2Þ, wðHÞ and wðTaÞ represent the accuracies in themeasurements of mass, specific heat, first figure of merit, time, aperture area, initial and finalwater temperatures, average solar radiation and the average ambient temperature, respectively.

The uncertainty associated with the evaluation of F1 and F2 by the measurements of the indi-vidual parameters are given in Tables 3 and 4, respectively. The values of WÐTPSÞ, W ^ ) and WÐHSÞ

have been assumed to be equal to the least counts of the respective measuring instruments. Theabsolute value of error in determining F1 was found as 0.0003, and hence, the maximum attainableaccuracy in the determination of F1 is around 0.23%. For the determination of uncertainty in themeasurement of F2, the value of the possible error in the evaluation of specific heat has been takenfrom Proctor [15], i.e. 0.04%. The maximum attainable accuracy for the determination of F2 isaround 0.78%, which is higher than that for F1. The absolute value of error in F2 was found as

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0.0033 in the present analysis. Some possible variation in errors in the measurements have alsobeen considered in order to study the effect of variations on the absolute accuracies of F1 and F2.

References

[1] Lof GOG. Solar Energy 1963;7(3):125.[2] Natarajan Murthy S, Narasingh. Solar Energy 1985;34:279.[3] Khalifa AMA, Akyurt M, Taha MMA. Appl Energy 1986;24:77.[4] Morrison GL, Mills DR. In: Proceedings of Conference of International Solar Energy Society, 1987. p. 13-18.[5] Mills R David, Maoyin Qin. Sun World 1987;11(2):44.[6] Schwarzer K, Hafner B, Von Meer A, Kings T. In: Proceedings of Conference of International Solar Energy

Society, 1987. p. 13-18.[7] Biermann E, Grupp M, Palmer R. Solar Energy 1999;66(6):401.[8] Suharta Herliyani, Abdullah K, Sayigh A. Solar Energy 1998;64(4-6):121.[9] Mullick SC, Kandpal TC, Sexana AK. Solar Energy 1987;39:353.

[10] Mullick SC, Kandpal TC, Kumar S. Solar Energy 1991;46:139.[11] IS 13429 (Parts 1, 2 & 3), Indian Standard: Solar Cooker, Bureau of Indian Standards, New Delhi, 1992.[12] Annual Report, Ministry of Non-conventional Energy Sources, Government of India, New Delhi 11003, 2002-

2003.[13] Negi BS, Kumar A, Tripathi TC. J Solar Energy Soc Ind (SESI) 2001;11(2):73.[14] Purohit Ishan, Negi BS. In: Proceedings of International Conference on New Millennium—Alternative Energy

Solutions for Sustainable Development, held at Coimbatore, India, 17-19 January 2003. p. 163.[15] Proctor D. Solar Energy 1984;32:377.[16] Doblein ED. Measurement systems. New York: McGraw Hill Publishing Co; 1990.

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