EXPERIMENTAL EVALUATION OF SOLAR STILL MATHEMATICAL MODELS
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1 Furt Internatinal Water Tecnly Cnference IWTC 99, Alexandria, Eypt 97 EXPERIMENTAL EVALUATION OF SOLAR STILL MATHEMATICAL MODELS M Abd Elkader * A Safat Nafy ** A Abd Elmtalip *** A A Mabruk **** * Assciate Prfessr, Mecanical per Department, Faculty f Enineerin, Prt Said, Eypt ** Lecturer, Enineerin Science Department, Faculty f Petrleum & Minin Enineerin, Suez, Eypt *** Lecturer, Mecanical Per Department, Faculty f Enineerin, Prt Said, Eypt **** Researc Assistant, Enineerin Science Department, Faculty f Petrleum & Minin Enineerin, Suez, Eypt ABSTRACT Experimental evaluatin fr sme f te publised matematical mdels fr ater desalinatin by slar still is presented in tis rk Te validity and te applicability f tese mdels under te Eyptian eater cnditins are examined Usin a cmputer prram, te cnsidered mdels are evaluated at te same peratin cnditins Te cmputer results sed a ide rane f discrepancy beteen te evaluated mdels Experimental sinleslped slar still as cnstructed fr te utdr rk itin te city f Suez Te btained results are in a d areement it sme f te cnsidered mdels KEY WORDS: Slar desalinatin, Matematical mdels, Experimental still, Experimental evaluatin INTRODUCTION At te situatin f ater rld crisis, saline ater desalinatin tecnly uld becme te mst imprtant ay t face tis prblem Eypt is situated in a rein f te rld ere slar radiatin intensity is cnsiderably i At te same time in remte and arid areas f Eypt, te srtae f ptable ater is a cnsiderable prblem Fr tse reins, te slar desalinatin is a viable ptin t prvide fres ater frm te sea r brackis ater Te sinle slped slar still, mit assist in meetin drinkin ater requirements f tese reins Te predicted perfrmance f a sinle effect slar still as been in te tecnical literature and slar enery textbks fr sme times Mainly, te predictive f te slar still perfrmance is based n empirical relatins Te first termal mdel fr slar still as utlined by Dunkle (96, and tis mdel based in part n Sarply and Belter s experiments (938 n te evapratin f ater int quiescent air (Malik et al; 98 Clark (99 examined te validity f Dunkle s mdel Clark fund tat te Dunkle s mdel needs sme mdificatins fr te mass transfer relatins inside te slar still Clark s results ere btained frm an experimental sall basin it slar simulatr f sptlits bank Terefre, te applicability f Clark s relatins fr te utdr rk needs t be investiated Te applicability f Dunkle s riinal mdel fr a ide rane f peratin cnditins as
2 98 Furt Internatinal Water Tecnly Cnference IWTC 99, Alexandria, Eypt examined by Adikari et al (995 Adikari fund tat Dunkle s relatins need sme mdificatins fr ier rane f peratin temperatures In te rk f Malik et al (98, sme assumptins ere made t simplify te teretical derivatin f te e at transfer cefficient relatins Graba (987 btained eneral relatins f eat and mass transfer inside slar still Tese relatins ave te distinctin f cnsiderin sme f te desin parameters suc as te lass anle and te slar still dimensins Hever, Graba uses an immersed electrical eater as an enery surce Generally, in spite f te many publicatins n slar stills, tere appears t be little in te ay f carefully validated matematical mdels fr predictin ln term perfrmance ver a ide rane f real peratin cnditins and desin caracteristics Te bjective f tis rk is t examine te applicability and te validity f tese mdels under te Eyptian eater cnditins, teretically and experimentally MATHEMATICAL MODELS Incident slar radiatin Insulatin Glass cver Saline ater Feedin ater Over fl Fres ater jar Steel frame Fi A scematic diaram f te munted slar still Te slar still is bt a eat and mass transfer device Mst f te incident slar radiatin transmitted tru te lass cver and absrbed by te basin liner Water vapr is frmed and cndensed n te underside f te lass cver t frm drplets Heat f cndensatin is transferred t te ambient air tru te transparent cver, and drplets are cllected in a tru as distilled ater as sn in Fi ( Heat transfer mecanism inside te slar still based n te natural cnvectin mde and radiatin frm ater surface t te lass cver Cnvectin current ccurs as a result f vapr density difference at te evapratin and cndensin surfaces (Blemer et al; 963 As different matematical mdels ave been prpsed t describe te simultaneus eat and mass transfer prcess inside slar stills, s, ne f tese mdels is selected as an example t s te applied numerical slutin tecnique Fllin te same apprac, ter mdels are cnsidered In tis rk, te mdel f Malik et al (98 is illustrated it te fllin assumptins; (i Termal temperature radient acrss te tickness f lass cver and basin ater are insinificant (ii Heat transfer cefficient is cnsidered t be cnstant at te selected interval time (iii Te eat capacity f te basin liner and te insulatin are nelected cmpared t tat f basin ater
3 Furt Internatinal Water Tecnly Cnference IWTC 99, Alexandria, Eypt 99 Te enery balance equatins fr te lass cver, saline ater and basin liner are presented as fll; IA α + A ( + + ( T T = A ( T T + ρcxa c e r a θ τ ( θ Iη A + 3 A ( Tb T = A ( c + e + r ( T T + ( m c ( τ Iη = 3( Tb T + U( Tb Ta (3 Were, η + η is te ptical efficiency (η f te slar still, and defined as te fractin f external incident beam radiatin ic is absrbed by te ater and basin liner Te value f η = 7, and η = 58, as stated by Cper (973 3 NUMERICAL SOLUTION Since, te climatic cnditins suc as ambient air temperature (T a, ind speed (V, and slar intensity (I vary durin te day perid, te slar still is cnsidered as an unsteady state prcess Hence te matematical mdel uld be represented by a set f nnlinear equatins at unsteady state cnditin as present in Eqs ( - (3 Tis nn-linearity because f variatin f te eat transfer cefficients inside slar still it temperature Terefre, it is difficult t btain an explicit slutin fr tese equatins Te mdel s equatins are interated numerically in time usin te finite difference tecnique, ten tese equatins are linearized by usin direct linearizatin metd, Nafey (988 Fr te first time interval ( τ, it te initializatin f te T, T and Tb, te cmputatin f individual eat transfer cefficients are perfrmed at a iven climatic cnditins Wit a reasnable specified accuracy, te slutin f te mdel s equatins is btained by iterative metd (Gauss-Seidel Ten, T, T and Tb are updated Te updated temperatures are used in te next time interval as initial values, and s n Fr eac time interval, te interval slar still prductivity is calculated Ten urly, daily yield and te termal efficiency are calculated as flls; Interval yield; m int e ( T T = τ (4 λ Hurly yield; mi = mint number f interval per ur (5 Daily prductivity; Y = summatin f urly yield = m i n i = (6 Termal efficiency; η t = n i = n i = I i m λ i 3 6 (7
4 Furt Internatinal Water Tecnly Cnference IWTC 99, Alexandria, Eypt 4 EXPERIMENTAL WORK In rder t examine bt te validity and te applicability f te cnsidered matematical mdels under te Eyptian eater cnditins, an experimental slar still f sinle slped lass cver as erected n te site f Faculty f Petrleum and Minin Enineerin, Suez Canal University Te still basin area is 5 m and cnstructed f steel seet f mm tick Te internal alls ere painted it ite clr t prvide a deree f reflectin t increase te slar lad n te ater surface Te external surfaces are insulated it lass l f tickness 4 cm Te still cver is made f rdinary lass it 3 mm tick makin an anle f 5 it respect t te rizntal U-cannel, made f steel seet, as fixed inside te still fr cllectin and discarin distilled ater utside f te unit Te distilled ater is measured directly by a measured jar Silicn sealant is used t seal te edes f te lass t te frame In eac run, sea ater as fed int te basin t a specified dept f cm Amunt f cllected distilled ater as measured at urly intervals Te amunt f distilled ater btained durin nit as measured at te next mrnin Wind speed as measured by an anemmeter Te brine temperature is measured by a diital termcuple Slar enery intensity is measured by Silicn Pyrmeter it Interatr Slar 8 (mdel 8347 Fis ( and (3 s a typical climatic cnditins f slar radiatin intensity, ambient temperature and ind speed Tese cnditins are recrded in Suez city ic is situated at 3 latitude in te nrt east in Eypt at te Suez Gulf Slar intensity (W/m² Time (rs Fi A typical set f data fr te slar radiatin intensity f, 8, 998 Ambient temperature C ind speed m/s Ambient temperature C Time (rs Fi 3 Wind speed velcity and ambie6t temperature f, 8, ind speed m/s 5 RESULTS AND DISCUSSION Under te climatic cnditins sn in Fis ( and (3, all te cnsidered matematical mdels are slved numerically by usin te same cmputer prram and te same slutin tecnique Fr cmparisn, te cmputer results f te slar still prductivity, still efficiency
5 Furt Internatinal Water Tecnly Cnference IWTC 99, Alexandria, Eypt and te ater temperature fr te cnsidered mdels are present aainst te experimental rk results in Fis (4, (5, (6 and (7 respectively A cmparisn beteen te teretical and experimental results fr te urly and accumulative prductivity f te slar still is sn in Fis (4 and (5 Tis cmparisn is perfrmed under te same peratin cnditins Tese fiures illustrate tat te rate f distilled ater frm te mdel f Cper (973 is te iest ne Te minimal yield as btained by te mdel f Malik, (98 and Clark, (99 Fiure (5 ss tat te experimental daily prductivity f te slar still is amuntin by 55 (liter/m day Als, tis value is in a mderate areement it te results btained by Clark s mdel (99 and Malik s mdel (98 Te relatins f eat transfer cefficient fr bt mdels are present in te Appendix Yield (liter/m²r Blmer63 Cper7 Malik8 Graba87 Clark9 Adikari95 Exp Blmer63 Cper7 Malik8 Graba87 Clark9 Adikari95 Exp Yield ( Liter/m²day Time (rs 4 8 Time (rs 6 4 Fi 4 te urly utput variatian fr te slar still mdels Fi 5 te daily utput variatian fr te slar still mdels Cper (973 prved te upper limit f te teretical efficiency fr an ideal slar still as a value f 6 % At te same peratin cnditins, te averae value f te efficiency fr te mst f cnsidered mdels is less tan 6 %, ic arees it cper s findin Te minimum averae value f efficiency f 44 % as iven by Clark s mdel (99 and te maximum value f 6% as iven by te mdel f Cper (973 as sn in Fi (6 Te fiure ss tat, te averae teretical efficiency btained by Malik s mdel (98 is clse t te experimental results
6 Furt Internatinal Water Tecnly Cnference IWTC 99, Alexandria, Eypt % Efficiency 9 Blemer63 8 Cper73 7 Malik8 6 Graba87 Clark9 5 Adikari 95 4 Exp Time (rs Fi 6 Slar still efficiency fr bt te cnsidered mdels and te experimental results Fiure (7 indicates a mderate deviatin in te basin ater temperature fr te cnsidered mdels Te iest value f averae basin temperature as 596 C and btained by te mdel f Cper (973 Als, at te same peratin cnditins te mdel f Malik et al (98 ives te lest temperature it te averae value f 54 C Als, Fi (7 ss tat te averae brine temperatures ere calculated by Malik s mdel (98 are in a mderate areement it te experimental results Temperature ( C 9 Blemer63 8 Cper73 7 Malik8 Graba87 6 Clark9 5 Adikari 95 Exp Time (rs Fi 7 Basin ater temperature variatin Te ide rane f deviatin beteen te cnsidered mdels in te rate f distilled ater prductivity, slar still efficiency and basin ater temperature may be attributed t; (i Different frms f eat transfer relatins used in te cnsidered mdels; (ii Different ptical slar still efficiency values
7 Furt Internatinal Water Tecnly Cnference IWTC 99, Alexandria, Eypt 3 6 CONCLUSION Te daily prductivity f a sinle-slped, slar still is determined experimentally as 55 (liter/m day, under te Eyptian climatic f Auust 998 Als, te averae termal efficiency f te unit is estimated as 4 % Under te same peratin cnditins f 5 lass anle and cm ater dept, te basin temperature ranes frm 3 C t 76 C Te cmputer results sed a ide rane f discrepancy beteen te cnsidered mdels fr te estimatin f te daily prductivity and termal efficiency f te slar still Als, tis deviatin is appeared in te brine temperature variatin aln te daytime 3 Bt slar still prductivity, ic are cmputed by te mdels f Malik et al (98 and Clark (99, are similar and in a d areement it te btained experimental results, under, te Eyptian eater cnditins NOMENCLATURE A A C I m m n T T T P P U v Y c r 3 i m T b ca ra int i a ρcx area f te lass cver, basin area, (m specific eat f ater, (J/k cnvective eat trans fer beteen lass and ambient, (W/m radiative eat trans fer cefficien t beteen lass and ambient, cnvective eat trans fer beteen ater and lass cver, (W/m radiative eat trans fer cefficien t beteen ater and lass cver, (W/m cnvectin eat trans fer cefficien t beteen liner and te ate slar radiatin intensity, distilled yield f te time interval, urly distilled yield, basin ater, (k/s te day peratin urs ambient temperature, lass temperatu re, ater temperature, liner temperature, saturatin pressure f ater at ater free suface, (Pa saturatin pressure f ater at te lass surface, (Pa verall eat trans fer cefficien t beteen te still and ind speed velcity, (m/s eat capacity f te lass daily yield ( ( (, (k /daym ( (m (k/m (W/m, (J/ r C (k/m (W/m, (W/m te surrundin, (W/m
8 4 Furt Internatinal Water Tecnly Cnference IWTC 99, Alexandria, Eypt Greek letters: λ la te n t e a t, (J / k η α θ θ σ τ τ τ se le c te d tim e in te rv a l, (s e c η η t T e rm a l e ffic ie n c y f t e s la r still la ss a b s rp itiv ity t + t T T ( C t + t T T ( C 4 S te fa n - B ltz m a n c n sta n t ( W / m k tim e in te rv a l f t e la ss, (se c tim e in te rv a l f t e a te r (s e c fra c ti n f e n e r y a b s rb e d b y a te r f fra c ti n e n e r y f t e lin e r REFERENCES - Adikari, R S, Asivini Kumar, and GD Sta, (995 Simulatin studies n multistae stacked tray slar still Slar Enery, 54, Blemer, J W, J A Eiblin, J R Irin and G O G Lf, (963 Anal Cmputer Simulatin f Slar Still Operatin ASME, 63-WA-33, -8 - Clark, JA, (99 Te steady- state perfrmance f a slar still Slar Enery, 44, Cper, P I (973 Te maximum efficiency f sinle - effect slar stills Slar Enery, 5, Graba, MM, (987 Teretical and experimental studies f eat and mass transfer inside sinle-slped slar stills PH D Tesis, Cair University - Malik, MA S, GN Tiare, A Kumar and MS Sda (98 Slar Distillatin Peramn Press, Oxfrd, UK - Nafy, ASMT, (988 Desin and simulatin f sea-ater termal desalinatin plants PD tesis, Leeds University Te mdel f Malik et al (98 APPENDIX c = ( T T i + ( p p T s s p s 3 e ( p s ps = c ( T T 4 4 r = 9 σ ( T T / ( T T
9 Furt Internatinal Water Tecnly Cnference IWTC 99, Alexandria, Eypt 5 Clark s mdel (99 c = ( T T i + ( p p T s s p s 3 e = c ( p s p s λ T T 4 4 r = 9 σ ( T T / ( T T
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