Windows-1256 Design Optimization

8/8/2019 Windows-1256 Design Optimization

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so that the net collection coefcient is given by

F T F D F R . (9)

2.2. Solar cookers with south tilted glazed surface(for countries of northern hemisphere)

Now, for a south tilted glazed surface at an angleb with the horizontal, the length of glazed surfaceincreases to

L1 L

cos b. (10)

Since the lid mirror should cover the entire surface of thecooker, the lid will also be of the same length.

2.2.1. South facing booster mirror [Fig. 1(b)]For this case, various collection coefcients will be

F R1 R sin y a, (11a)

F R2 R cos b y 2a, (11b)

with

L01 L1cos 2a b y

sin y a. (12)

The best results are obtained, when the booster mirror iskept at

a 13

2y b p2 , (13)

where the various symbols have meanings and applicabil-ities as discussed for conventional cooker in Section 2.1.

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Fig. 1. (a) Conventional box type solar cooker with south facing mirror in its lid; (b) a cooker with south tilted collecting surface with south facing mirrorin its lid; (c) cooker with south tilted collecting surface and north facing mirror in its lid; (d) cooker with south tilted collecting surface and north facingmirror as lid of the cooker with a xed south facing vertical mirror.

U.S. Mirdha, S.R. Dhariwal / Renewable Energy 33 (2008) 530544532


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2.2.2. North facing booster mirror [Fig. 1(c)]The collection coefcients for this design are as follows:

F R1 R cos y a, (14a)

F R2 R sin b y 2a p=2, (14b)

with

L01 L1sin b y 2a p=2

cos a y, (15)

and the fractional enhancement, due to reected radiationby north facing mirror, will be maximum for a given y,when

a 13p 2y b. (16)

2.2.3. Trackable north facing booster mirror with vertical south facing mirror [Fig. 1(d)]

Since, we are looking for a window model of the cookerwith a rear opening, the south facing booster mirror is kept

at a xed vertical position without tracking along with anorth facing mirror in its lid, which can be tracked roundthe year. The height, h, of the south facing vertical mirror iskept such that in the extreme winter (maximum value of y,reections from the mirror cover the complete collectingglazed surface. In terms of y and b, the height h of thesouth facing vertical mirror is given by

h L1cos y b

sin y. (17)

The fractional enhancement of radiation collected by thesurface is given by

F Rh R hL1 sin y, (18)which has the highest value in the extreme winter, wheny ymax . This component will add to the collectioncoefcient F T .

2.3. A nal design

As a further improvements, a combination of north andsouth facing booster mirrors have been introduced asshown in Fig. 2 . In this model, a xed south facing verticalmirror of the same height, h, as for cooker described in

Section 2.2.3, has been kept and a north facing mirror isalso xed at an angle a p=2 ymax , so that, even in theextreme winter, the shadow of this mirror does not fall onthe collecting surface. The length of the north facingmirror, L2 , is kept such that the upper end of the mirrorand the box are at the same height. This has been kept forconvenience of design and also to allow mirror to be usefuleven in extreme summer. The length of this mirror is givenby

L2 L1sin bsin a

. (19)

The fractional enhancement in radiation collected by thecollecting surface, due to reection by this north facing

mirror is given by

F RN1 RL2L1 cos a y (20a)

and when only a part of reection is received by thecollecting surface; the fractional enhancement is given by

F RN2 R sin 2 a y b p2 (20b)withL02 L1

sin 2a y b p=2cos y a

. (21)

To this new box, a new lid with a south facing mirror hasbeen attached with the xed south facing vertical mirror, sothat when closed, it covers the upper end of the northfacing mirror, and has the length

L3

ffiffiffiffiffiffiffiffi ffih2 L21 cos b

sin b

tan a 2

s . (22)

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Fig. 2. Improved solar cooker with south tilted collecting surface having axed sized vertical south facing mirror and a xed north facing mirroralong with a trackable south facing mirror in its lid.

U.S. Mirdha, S.R. Dhariwal / Renewable Energy 33 (2008) 530544 533


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Here h is the height of south facing vertical xed mirror,given by Eq. (17) with y ymax for the extreme winter.

Due to this south facing mirror, which is attached to thelid, the fractional enhancement in radiation received by thecollecting surface of the cooker is calculated for two cases.Firstly, when the reected radiation covers only a part of

the length of collecting surface, we have

F RS1 RL3L1 sin f a1. (23)

Secondly, when reected radiation from only a part of themirror,

L03 L4sin 2a1 ymax y

sin y a1(24)

is received by the collecting surface, where L4 is the lengthshown by dotted line in Fig. 2 and is given by

L4 L1cos b

sin ymax . (25)

The fractional contribution in collection coefcient, due tothe lid mirror is given by

F RS2 RL03L3

L3L1 sin y a1, (26a)

which can be rewritten as

F RS2 Rsin 2a1 ymax ycos b

sin ymax. (26b)

The net collection coefcient of this cooker is then given by

F T F D F Rh F RS F RN . (27)

The F RS and F RN are the lower values of the two valuesF RS1 , F RS2 and F RN1 , F RN2 , respectively.

Normalized with respect to the at horizontal surface,the collection coefcients for all designs discussed abovecan be written as

F T_norm F TL1L . (28)

2.4. Comparison of cooker designs

In Fig. 3 , curves 15 correspond to cooker designsconsidered in Section 2. The calculations have been donefor cookers kept at f f can (the tropic of Cancer, which issituated typically near cities like Ahmadabad in India). Fordesigns discussed in Sections 2.2 and 2.3, the tilt angle of the glazed surface, b, has been xed to be equal to f can .Further, in these calculations, lids of the cookers are fullytracked round the year.

The collection coefcients are calculated at the mid dayposition, when the sun is in the northsouth plane and arenormalized with respect to a similar glazed surface kepthorizontally. The reectivity of mirrors, R , is assumed to be88%. As is clear from Fig. 3 , collection coefcient of theconventional cooker, shown in Fig. 1 (a), is about 1.33 inwinter and about 1.45 in summer. Therefore, the maindrawback of the conventional cooker is that it gives lowercollection coefcient in winter, when the ambient is also at alower temperature. The collection coefcient of the cooker,shown in Fig. 1 (b), with inclined glazed surface with southfacing booster, improves the collection coefcient in

summer. Compared to these, the cooker with north facingbooster mirror, shown in Fig. 1 (c), gives better results in

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Cooker design 5 (Fig 2)Cooker design 4 (Fig 1(d))Cooker design 3 (Fig 1(c))Cooker design 2 (Fig 1(b))Cooker design 1 (Fig 1(a))

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Fig. 3. Normalized collection coefcients for solar cooker designs, discussed in Section 2, at noon position under lid mirror tracking condition. For thesecalculation, f 23:45 b 23:45 and R 88% have been taken. The xed north facing mirror of Fig. 2 is placed at 43 :1 .



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winter, but is poorer for use in summer. The cooker of Fig. 1 (d) overcomes these deciencies and combines thebenets of the north and south facing mirrors. However, thebest results are obtained for design shown in Fig. 2 , whichgives a large collection coefcient in winter and some whatlower value in the summer. However, in summer, due to

higher ambient temperatures even this much collectionshould sufce for cooking purpose.Though the solar intensity is continuously varying

throughout the day, to understand the relative importanceof the two designs; conventional box type solar cooker(Fig. 1 (a)) and new improved solar cooker ( Fig. 2 ), theirperformance is compared by assuming a steady statecondition corresponding to the noon position of the sun,for which the energy balance equation is given by

F T ta eI U L T T A . (29)

The steady state cooker temperature for this case is, given

by

T F T ta eI

U L T A , (30)

where T A is ambient temperature, U L is overall heat losscoefcient under one node assumption, ta e is effectiveabsorptance transmittance product for absorbing surface of the cooker and I denotes the intensity of incident radiationon a at surface perpendicular to the direction of insolation.

By assuming I 800W =m 2 , U L 8 W =m 2 K and ta e 61:44% the attainable temperatures are shown for conven-tional box type cooker and new improved cooker in Fig. 4 ,

under fully tracked condition. It is worth a mention here, that

these results are calculated for a steady state at mid dayinsolation. Such a steady state is usually possible only insummer when the radiations are sufciently intense and theday is sufciently long. In winter, the actual attainabletemperatures will be lower than those shown in the gure,because of the shorter duration of the day during which the

steady state may not be actually attained. Therefore, theseresults should be taken only as indicators of the trend andmore exact evaluations of the transients become necessary forprediction of the actual performance throughout the day [22].

In the improved design, the glazed surface angle, b , hasbeen kept at f can , which corresponds to the central part of India. However, cookers so designed should work evenwhen they are moved to other latitudinal positions.Therefore, variations in the collection coefcient bymoving the cookers up and down in its latitudinal positionby 5 from the tropic of Cancer have been studied and areshown in Fig. 5 . For increasing latitudinal angle, an overallimprovement in the performance of cooker is found. Theexperimental work reported in Section 4 has beenperformed at our laboratory in Jodhpur (India), which issituated at latitude of 26 :3 , which is nearly 3 above f can .Response of the cooker designed with b f can , as placedat the latitudinal position of Jodhpur is also shown in thegure. A theoretical improvement in the performanceduring summer is established. However, when one goesdown in latitudinal position, losses occur and it isrecommend that for such cases, cooker be designed bykeeping the angle of glazed surface, b, equal to the actuallatitudinal angle or the cooker designed by keeping b f can be tilted northward, as a whole, by an angle equal to

the difference in latitudinal position and f can .

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Cooker design 5 (Fig 2)Cooker design 1 (Fig 1(a))Typical ambient temperature t e

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Fig. 4. Calculated plate temperatures at noon under steady state assumption for fully tracked new cooker ( Fig. 2 ) and conventional box type cooker areshown. For these calculations, I 800W =m2 , U L 8 W =m2 K and ta e 61:44% have been assumed. Other parameters are similar to those given inFig. 3 .



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3. Calculations with respect to eastwest plane

The design considerations discussed in Section 2 arebased on the calculations for mid day solar insolation,when the sun is in the northsouth plane. Foroptimum collection throughout the day eastwest trackingis also required. In conventional design, it is done byhourly movement of the cooker from east to west as thesun changes its position. This is a difcult proposition anduser, in practice, is not in a position to follow such anhourly tracking. As an alternative option, side mirrorshave been proposed by some workers [4,5,7,10] , whichseems to be a better option for practical operation of thedevice. Movement of the cooker especially, when it isloaded, is not convenient and should be avoided. Withthis objective in view, two side mirrors to the improveddesign are attached; so that it becomes a complete box typedesign and when closed become leak proof for heatlosses. The height of side mirrors at the south facing endis equal to the height of the vertical south facing xedbooster mirror, whereas at the north facing end it isequal to that of north facing xed booster mirror.Combinations of these side mirrors are to be kept suchthat the collection becomes optimum, throughout the day,when hour angle, o , changes from p=2 to p=2. Todetermine these, the following combination of the sidemirrors are considered. For simplicity the declination of the sun is assumed to be zero.

The combination of side booster mirrors as shown inFig. 6 (a); corresponds to a horizontal collecting surface

with a vertical side mirror and an inclined side mirror at anangle g with respect to the horizontal. Under this type of combination, three different reections will be received bythe collecting surface and hence three different collectioncoefcients have been analytically calculated:

(i) Contribution of vertical wing mirror : As sun goesupwards from hour angle jo j equal to 90 in themorning to 0 in the noon, contribution in energy bythe side vertical mirror comes from the length,

L05 W

tan jo j, (31)

and the fractional enhancement in radiation collectedby this length of vertical mirror is given by

F RSide 1 RL05W sin jo j. (32)

This partial contribution of vertical side mirror lengthcontinues up to o tan 1W =L5and after that as oreduces further, full length of side vertical mirror willbe in use.

(ii) Contribution of tilted wing mirror : The inclined sidemirror reects to the collecting area, when the hourangle jo j has value lower than p=2 g. Reectionsfrom it will either be collected directly by the cooker

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Improved cooker atlatitude 23.45 degreelatitude 23.45 + 5 degreelatitude 23.45 - 5 degreelatitude 26.3 degree (Jodhpur)

Conventional cooker atlatitude 23.45 degreelatitude 23.45 + 5 degreelatitude 23.45 - 5 degreelatitude 26.3 degree (Jodhpur)

Fig. 5. Effect of variation in latitudinal position by 5 from f f can on improved solar cooker designed with b f can and on conventional box typesolar cooker. Predicted performances at Jodhpur ( f 26:3 ) are also shown.



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surface or through re-reection from vertical sidemirror as described below.

The collection coefcient of tilted side mirror isgiven by

F RSide 2 RL5W cos g j o j. (33)

This equation is valid till the hour angle jo j isgreater than jo 0j, obtained by the followingequation:

L5W

sin 2g j o 0j p=2

cos g j o 0j, (34)

at this position, reections from full length of sidetilted mirror cover the glazed collecting surface.Thus, tilted side mirror contribute completely inradiation enhancement, when jo 0jo jo jo p=2 g.For the values of hour angle jo j less than jo 0j, thelength of side tilted mirror for radiation enhance-ment reduces to

L05 W sin 2g j o j p=2

cos g j o j(35)

and the collection coefcient becomes

F RSide 2 RL05W

cos g j o j. (36)

(iii) Combined effect of side mirrors : The reection by theremaining part of tilted side mirror, L005 L5 L

05 , will

be received by the vertical side mirror, as shown inFig. 6 (b). These reections on the side vertical mirrorwill cover the length of mirror given by

L6 L5 sin g W L5 cos gtan 2g j o j p=2.(37)

The length L6 increases from zero to full length of vertical mirror L5 as o moves towards noon. Thereected radiation received by this length will again

re-reect. Therefore, enhancement in collection by

re-reection is given by

F RSide 3 R2 L005L

06

WL 6 cos g j o j. (38)Here L06 is a part of the length L6 , from wherereections are collected by the collecting surface of thecooker and is given by

L06 W tan 2g j o j p=2. (39)

Thus, when jo j becomes less than jo 0j, radiations willbe reected twice before being collected at the surfaceof the cooker; the radiation will be rst reected fromtilted side mirror and then from vertical side mirror.This combination of side booster mirrors will be

effective till jo j4

p=2 2g. When jo j becomes equalto or less than p=2 2g, the re-reected energy willnot be received by the cooker surface.

The net enhancement in collection by these side mirrorsis given by

F T_RSide F RSide 1 F RSide 2 F RSide 3 . (40)

Hence, the side vertical mirror will be in effective modeupto noon position while the tilted side mirror and theircombination will contribute during p=2 2go jo jop=2 g. The sun before noon lies in eastward directionand therefore an east facing vertical side mirror with atilted west facing side mirror at the inclination g is requiredand in afternoon position of sun, the east and west facingmirror positions will be interchanged to give the sameeffect.

The above calculations cannot be used rigorously forthe calculation of increase in the collection coefcient;as for this purpose declination of the sun, the actualduration of the day and trapezoidal shape of the mirrorswill have to be taken in to account. However, thesecalculations help us in determining the angles at which theside mirrors can be placed for their optimal use. Thus,if one assumes the solar noon at 12:00 am and chooseto track the mirrors, instead of the hourly movement

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Fig. 6. Schematic diagram showing positions of booster wing mirrors: (a) shows direct reections from vertical and tilted side booster mirror to thecollecting surface, whereas (b) shows re-reections, due to the combined effect of side mirrors.



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of the cooker as a whole as required in the conventionalcooker, the following angle positions of side mirrors can bechosen:

(a) When the mirror positions are chosen to be

g2 90 and g1 0 for 6 : 00 am to 9 : 00 am ;45 for 9 : 00 am to 12 : 00 am :

(b) When the mirror positions are chosen to be

g2 90 and g1

0 for 6 : 00 am to 7 : 30 am ;22:5 for 7 : 30 am to 9 : 00 am ;45 for 9 : 00 am to 12 : 00 am ;

8>:where subscripts 1 and 2 are for mirrors placed in eastand west side, respectively, and are interchanged in the

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Net collection factor, due to side booster mirrorsDue to vertical east facing booster mirror Due to titled west facing booster mirror onlyDue to re-reflections by vertical east facing mirror of that by west faing booster mirror

Fig. 7. Effect of side booster mirrors in enhancing the energy collection is shown in (a) for combination of wing mirror positions as shown in inset I, while(b) for combination of wing mirror positions as shown in inset I upto 9:00 am and then as shown in inset II.



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afternoon. The above mentioned timings will have tobe corrected for difference in the local time andstandard time.

Fig. 7 (a and b) shows the fractional energy enhancement

by the side mirrors for tilt angles of combinations (a) and(b) described above. To reduce, the frequency of tracking;the early morning and late evening positions in the abovecombination are not of practical interest and can beavoided.

4. Experimental results

For a comparative study, solar cookers of the improveddesign, discussed above and of the conventional type havebeen fabricated. Photographs of these are shown in Fig. 8 .The bases of both the cookers are designed to have same

lengths and widths equal to 20 in each. Height of conventional cooker box is 6 in, whereas of improveddesign cooker varies from 6 in in front and 15 in at theback. The glazed surface of the improved cooker has beenkept at an angle b f can . Black painted aluminum sheet

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Fig. 8. Proposed improved solar cooker and conventional solar cooker of the same base dimensions installed at Jodhpur, India (73 010E, 26 180N).



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has been used as absorbing surface. The insulation isprovided by 1 in thick glass wool. Further 4 mm thickglasses have been used for doubly glazed radiationcollecting surface. In conventional solar cooker, the topopening has been provided by lifting up the glazed surfacewhereas in case of improved solar cooker, a 6 00 1600

double walled door has been provided at its back. The lidof both the cookers as well as side booster mirrors of theimproved solar cooker have been attached through hinges.Positions of the lid of improved cooker can be adjustedwith the help of a piano-hinge arrangement whose otherend has been xed on a virtual wall as shown in Fig. 8 (b).

For temperature measurement Pt-100 sensors have beenused.

All the experiments have been performed on Indianstandard time (IST) scale at Jodhpur (India). The localapparent time of Jodhpur (73 010E, 26 180N) can becalculated by using expressions given by Dufe andBeckman [23] and time correction for a particular set of observations has been given in gure caption.

Fig. 9 shows the experimental results of the improvedcooker, discussed above and of conventional solar cooker, inno load condition. In agreement with the theoreticalpredictions, one nds that the new design is much improved.

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Fig. 8. ( Continued )



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Date: May 12, 2005 with 500ml loadConventional cooker Improved cooker Ambient temperature

Date: May 11, 2005 without loadConventional cooker Improved cooker Ambient temperature

Fig. 10. Thermal performances of conventional cooker and improved cooker under passive load of 500 ml engine oil and without load are compared. Thehourly tracking of box type cooker has not been done, while combination (b) for side mirrors as discussed in Section 3 has been used for proposed design.The local apparent time legs behind the IST by 41 min.

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01 April 2005Jodhpur, India. ( = 26.3)

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Fig. 9. Experimental comparison of thermal performance of improved solar cooker with conventional box type solar cooker under no load condition. Thehourly tracking of box type cooker has not been done, while for the new design combination (b) for side mirrors as discussed in Section 3 has been used.Observations have been taken on Indian standard time (IST) scale and the local apparent time legs behind the IST by 33 min.



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Also, temperature above 100 C can be obtained from thisimproved design, even in the late evening. The effect of thermal load on these cookers has also been studied in Figs. 10

and 11. In Fig. 10 , the results correspond to both the cookersbeing loaded with 500 ml of engine oil throughout the day,whereas in Fig. 11 , a load of 1000 ml has been provided. For

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Fig. 12. Effect of active load of 1000ml on improved cooker and conventional box type cooker for 1 h loading from 11:00 am to 12:00 noon and againfrom 3:00 pm to 4:00 pm. Other conditions are as described in Fig. 11 . The local apparent time legs behind the IST by 37 min.

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Date: May 13, 2005 with 1000ml loadConventional cooker Improved cooker Ambient temperature

Date: May 11, 2005 without loadConventional cooker Improved cooker Ambient temperature

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Fig. 11. Thermal performance comparison of conventional cooker and new solar cooker under passive load of 1000ml engine oil and without load. Otherconditions are same as given in Fig. 10 .



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higher thermal load, the performance of new design issubstantially improved and the plate temperature above100 C can be retained even beyond 17:00 hours (IST). Also

during the day, the response curve becomes quite at which isan indication of good performance. The above two loads arepassive, ones kept once throughout the day. The responses of

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Fig. 13. Seasonal variation of maximum attained plate temperature of conventional box type solar cooker and of the new improved cooker without loadcondition.

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Ambient temperature on June 02, 2005Ambient temperature on June 03, 2005Ambient temperature on June 04, 2005

Fig. 14. Effect of side booster mirrors in improving the performance of proposed solar cooker ( Fig. 8 (b)) without load for combination (a) and (b) asdescribed in Section 3 and when no side boosters are used. The local apparent time during the measurements legs behind the IST by 40 min.



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cookers to active loads have also been shown in Fig. 12 . Boththe cookers were provided with a load of 1000ml engine oil.For the rst time, the load was put at 11:00 am andwithdrawn at 12:00 am and again for the second time, put at3:00 pm and withdrawn at 4:00 pm. The loading shows atransient dip in plate temperature as should be expected due to

heat extraction by the load. However, while the conventionalcooker does not recover from the loss of heat during thesecond loading, the present cooker has recovered fairly well.This clearly shows that while the conventional cooker issuitable only for cooking in the early part of the day andtherefore useful for a single cooking, the improved cooker canbe used to cook meals twice in a day. Further, since the platetemperature remains fairly high even after second loading, bykeeping suitable storage materials in this cooker, it would bepossible to keep higher temperature in late evening.

The above results are for response of cookers onparticular days. Seasonal variations in the response of cookers are shown in Fig. 13 in terms of maximum attainedplate temperature. Trends are similar to those predictedtheoretically in Section 2.4. However, the exact compar-isons cannot be made as the theoretical results are based onthe steady state, whereas the experimental results corre-spond to maxima of the daily variations arising due totransients in solar intensity and ambient temperature.

The above results are for the improved cooker with sidebooster mirrors discussed in Section 3. To study as to howeffective these side mirrors have been, experiments on thenew cooker with combinations of side mirrors discussed inSection 3; (a) and (b) and with no side mirrors have alsobeen done. Fig. 14 shows plate temperatures of improved

design under these different side mirrors combinations asdiscussed and veries the theoretical predictions.

5. Conclusion

Various possible designs of solar cookers to optimizetheir thermal performances with respect to north and southfacing booster mirrors have been analyzed theoretically.Based on these calculations, an improved design wasnalized and a solar cooker of this design was fabricated.For comparison, a conventional box type solar cooker of exactly the same material and dimensions was alsofabricated. Comparison of experimental results, showclearly that the proposed new cooker can provide highertemperature throughout the day and round the year. It canbe used successfully for preparation of two meals in a dayand can be used to keep the food warm in late evening.Further the design allows the cooker to be installed in asouth facing window and can be operated from a rearopening from inside the kitchen. Thus, a more efcient anduser friendly solar cooker has been developed successfully.

Acknowledgment

U.S. Mirdha is thankful to the CSIR, New Delhi, India forgranting a fellowship. The authors are grateful to Dr. N.M.

Nahar, Dr. P.C. Pande and Dr. P.B.L. Chaurasia of CAZRI,Jodhpur for useful discussions. Abhishek Mirdha, Jasa Ramand Manu Smrity are also acknowledged with thanks.

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