Ntd

N

ity o

m 127

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comethod for computation of glass cover temperature and top heat loss coecient has been followed. A modied equation from Akhtar

types, simple in design, few mechanical parts, low costand easy installation, the at plate solar collectors are more

balance and thus large time consumption since many thou-sands of solutions may be required (Due and Beckman,

been developed (Mullick and Samdarshi, 1988; Samdarshiand Mullick, 1991; Akhtar and Mullick, 1999, 2007), whichallows to accurately evaluate the top heat loss coecientdirectly from the energy balance.

Corresponding author. Address: 1 rue Mostafa Ben Chouia, 07000Biskra, Algeria. Tel.: +213 779530866.

E-mail address: cmahboub@lgm-ubiskra.net (C. Mahboub).

Available online at www.sciencedirect.com

Solar Energy 86 (2012appropriate techno-economically for the low temperaturesolar energy applications than the more complex ones.Although these collectors are classied into the mediumto low temperature category which limits their use, theyhave been popularized after the inclusion of some substan-tial improvements on their structural design. The design ofsuitable solar collectors, which leads to increase the usefulenergy gain and consequently to reduce the heat lossesthrough principally the upper side, is the main subject ofmany researches which recommend the use of ns or corru-gated surfaces as extended heat transfer area to get highesteciencies.

1991). To solve this problem, empirical equations for topheat loss coecient based on measurement data were rstdeveloped by Hottel and Woertz (Due and Beckman,1991; Klein, 1975). Later, in a series of papers, severalcorrected expressions for the accurate computation of thetop heat loss coecient have been proposed (Due andBeckman, 1991; Klein, 1975; Garg and Rani, 1980;Malhotra et al., 1981; Agarwal and Larson, 1981; Gargand Datta, 1984). However, because of the large errorsresulting from the regrouping of the convective and radia-tive terms in the previous relations, improved equationforms for computing the glass cover temperature of atplate solar collectors with single and double glazing haveand Mullicks relation was proposed. The predicted values of the glass cover temperature and the top heat loss coecient were comparedwith the results obtained by iterative solution of the energy balance equations over a wide range of operating conditions. A good accu-racy is provided by the proposed equation which is recommended to be used in the energy analysis of the present conguration. 2011 Elsevier Ltd. All rights reserved.

Keywords: Flat plate solar collector; Vee corrugated absorber plate; Glass cover temperature; Top heat loss coecient

1. Introduction

Because of their advantages over the other collectors

The energy analysis of such collectors requires theknowledge of the top heat loss coecient which is necessar-ily an iterative process to be calculated from the heatBrief

Calculation of the glass coverloss coecient for 60 vee corrugate

Chawki Mahboub ,Department of Mechanical Engineering, Univers

Received 17 August 2011; received in revised forAvailable online

Communicated by: Asso

Abstract

In this paper, the top heat losses from a 60 vee corrugated solar0038-092X/$ - see front matter 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.solener.2011.11.019ote

emperature and the top heatsolar collectors with single glazing

oureddine Moummi

f Biskra, B.P. 145, R.P. 07000 Biskra, Algeria

0 November 2011; accepted 30 November 2011December 2011

te Editor Brian Norton

llector with single glazing have been investigated. An approximate

www.elsevier.com/locate/solener

) 804808

e emissivity/ half opening angle of the vee corrugation ()h collector tilt angle ()r StefanBoltzmann constant (W/m2 K4)

Subscripts

a ambient, apparentg glass coverp plates sky

olar Energy 86 (2012) 804808 805However, all these proposals have been developed pri-marily for collectors with at absorber plate, which makesthem inappropriate for use to predict the top heat lossesfrom collectors with corrugated absorber plate. For thisreason and for the aim of making a better assessment ofthe top heat losses dependence on the absorber plategeometry, we investigate through the present study theeect of the geometrical characteristics of a 60 vee corru-gated plate on the top heat losses from solar collectors withsingle glazing over a wide range of operating conditions. Amodied version from the equation proposed by Akhtarand Mullick (1999), that provides good predictions forthe glass cover temperature of the present conguration,was derived. The accuracy of the results obtained fromthe proposed model was veried by comparison with thoseobtained from the iterative solution of the heat balanceequations.

2. Analysis

The vee corrugating of the absorber plate surface isregarded as one of the most successful techniques thatare used to enhance the thermal performance of solar col-

Nomenclature

A aspect ratio (average gap spacing to vee height)f ratio of outer to inner thermal resistancehw wind convection coecient (W/m

2 K)H vee height (m)k thermal conductivity (W/m K)L average gap spacing, thickness (m)Nu Nusselt numberRa Rayleigh numberT temperature (K)Ut top heat loss coecient (W/m

2 K)

C. Mahboub, N. Moummi / Slectors. This technique is frequently implemented to deviseselective surfaces characterized by high solar absorbtance(Due and Beckman, 1991; Hollands, 1963) and on theother hand to provide heat transfer enhancement in theow passage area (El-Sebaii et al., 2011). Unfortunately,due to a cellular base ow occurs within the trough ofthe vee corrugations permitting better mixture of transferrate (El-Sherbiny et al., 1978), and also to the increase overthe plane emissivity of the absorbers surface (Hollands,1963), an increasing in top heat losses is expected.

During the calculation of these heat losses, it is commonpractice to linearize the problem then to convert it to asimple electrical network which allows us to develop theconcept of an overall top heat loss coecient for simplica-tion purpose (Due and Beckman, 1991). This coecientcould be determined more preferably by empirical model-ing rather than solving a non linear system of heat balanceequations. Therefore, in the following, an approximatemethod for computation of glass cover temperature andtop heat loss coecient of solar collectors with single glaz-ing as that described by Akhtar and Mullick (1999) isadopted and subjected to some modications correspond-ing to the present conguration (Fig. 1).

2.1. Glass cover temperature

According to Akhtar and Mullicks analysis, the glasscover temperature could be calculated as follows:

T g fT p CT af 1 1

where C = (Ts/Ta + hw/3.5)/(1 + hw/3.5) used when the skytemperature lower than ambient is considered for outerradiation using Swinbanks relation, or C = 1 when thesky and ambient temperatures are considered equal; and fis the ratio of outer to inner thermal resistance which stillhas to be determined for the present problem. Hence, bas-ing on the semi-analytical correlation developed by Akhtarand Mullick (1999), an examination of the eect of the veecorrugations on convection and radiation heat transferprocesses between the vee corrugated plate and the glass

cover yields to the following ratio of outer to inner thermalresistance, which is closely analogous to that proposed inthe previous reference:

Fig. 1. Cross section of 60 vee corrugated absorber plate and at glasscover.

Rac 1708 1 0:036A 2:69

A2 1:70

A3

8

K 2460Rac

1 0:195A

5:97A2

4:16A3

9

B 2:23 0:0123h 0:34 103h2 10Rah 113001 0:204 sin4:50h 37:8 11where the operator [ ]+ means that the value of the quantityis to be taken as zero if the argument inside the brackets isnegative but otherwise takes on the value of the argument.

cos h0:25 C1 2

olar Energy 86 (2012) 804808In which ea is the apparent emissivity of the vee corru-gated plate. Using the radiation analysis on an enclosurewith the fundamental relations of the view factor, theapparent emissivity for a vee corrugated plate of openingangle 2/ is given by the following expression which givesa good overall t with the data of Hollands (1963):

ea 1 1ep 1

sin/

13

And C is a dimensionless function developed by regres-sion analysis basing on the results obtained by numericalsolution of the heat balance equations of 60 vee corru-gated collector, using the convective heat transfer coe-cient correlation provided by El-Sherbiny et al. (1978):

C 1 0:6531 A0:38 0:014hw1 A0:09 4

It is worth mentioning that the geometrical parametersA and / of the vee corrugated plate are suitably includedin the Eq. (2) in such a way that this latter will be identicalto Akhtar and Mullicks relation in the case of at absorberplate, where A1 = 0 and / = 90 .

2.2. Top heat loss coecient

Once the glass cover temperature is determined from theprevious relations, the top heat loss coecient could bereadily obtained from (Akhtar and Mullick, 1999):

Ut Lgkg hw regT 4g T 4s T g T a

0@

1A

1264

kNuL

rT 2p T 2g

T p T g1=ea 1=eg 1

0@

1A

13751

5

In which, the Nusselt number of an enclosed gapbounded by one 60 vee corrugated and one at surfaceis given by the following correlation (El-Sherbiny et al.,1978):

Nu Nuc K 1Racsin 1:8h1:6

Ra cos h

!1 Rac

Ra cos h

f 12 108T a 0:2T p3 hw1 0:3Lg

6 108ea 0:028T p 0:5T a3 0:6L0:2T p T a

806 C. Mahboub, N. Moummi / S B Ra cos hRah

1=3 1

" #6

where

Nuc 11 0:3025=A 0:06825=A2

A ln2A 12A 1

73. Results and discussion

The predicted values of the glass cover temperatureobtained from the present model are presented in graphicalform along with the results obtained by iterative methodbased on the convective heat transfer coecient correlationdue to El-Sherbiny et al. (1978) for many inuential param-eters. The comparison between these results was performedover a range of wind convection coecient varying from 5to 50 W/m2 K, plane emissivity of the absorber plate from0.05 to 0.95, collector tilt angle from 0 to 60 and absorberplate temperature from 353 to 423 K.While, an average gapspacing of 25 mm, ambient temperature of 293 K, glasscover thickness, emissivity and thermal conductivity of5 mm, 0.88 and 0.78 W/m2 K respectively were considered.For outer radiation, the Swinbanks relation for the skytemperature was used.

It can be seen from Figs. 25 that all results are in verygood agreement over the entire investigated range ofvariables and for two values of the aspect ratio A.Fig. 2. Variation of the glass cover temperature with the wind convectioncoecient.

olarC. Mahboub, N. Moummi / SThe maximum error between the iterative results of theglass cover temperature and those given by the presentmodel is about 3 C; and it can be noted that the best pre-dictions are given for non selective absorber plate. Sincethe natural convection in the enclosed gap dependsstrongly on Rayleigh number (temperature dierence,Tp Tg) which is in turn sensitive to the wind convectioncoecient, the eect of this latter has been included inthe approximation of the natural heat transfer correlationthrough the dimensionless function C, which signicantlyreduces the computational error of the glass cover temper-ature. As it is expected, at the same operating conditionsthe glass cover temperature as well as the top heat losscoecient increase with the decreasing aspect ratio.

A comparison between the results of the top heat losscoecient obtained from the present model and thoseobtained by iterative method was also carried out (notshown here), by which an excellent agreement was

Fig. 3. Variation of the glass cover temperature with the plane emissivityof the absorber plate.

Fig. 4. Variation of the glass cover temperature with the collector tiltangle.observed. It was found that the relative error from the eval-uation of the top heat losses, using the previous empiricalrelations for estimating the glass cover temperature, is lessthan 1% over the whole range of variables, which may con-rm that the followed approximate method described in(Akhtar and Mullick, 1999) provides more accurate predic-tions of heat losses than the single equation methods. Atsome extreme conditions, an increasing in the top heatlosses by up 40% relative to the at plate collectors couldbe reached. Therefore, the use of the present model in theenergy analysis of the 60 vee corrugated solar collectorsis justied.

Acknowledgements

The authors would like to thank Mr. Said Benramache

Fig. 5. Variation of the glass cover temperature with the absorber platetemperature.

Energy 86 (2012) 804808 807and Ms. Meriem Djaalal for their help.

References

Agarwal, V.K., Larson, D.C., 1981. Calculation of the top loss coecientof a at-plate collector. Solar Energy 27, 6971.

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El-Sebaii, A.A., Aboul-Enein, S., Ramadan, M.R.I., Shalaby, S.M.,Moharram, B.M., 2011. Investigation of thermal performance of-double pass-at and v-corrugated plate solar air heaters. Energy 36,10761086.

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808 C. Mahboub, N. Moummi / Solar Energy 86 (2012) 804808

Calculation of the glass cover temperature and the top heat loss coefficient for 60 vee corrugated solar collectors with single glazing1 Introduction2 Analysis2.1 Glass cover temperature2.2 Top heat loss coefficient

3 Results and discussionAcknowledgementsReferences