Average Air Temperature Inside a Room With a Semitransparent Wall With a Solar Control Film: Effect of The Emissivity

Transcription

1 Average Ar Temperature Insde a Room Wth a Semtransparent Wall Wth a Solar Control Flm: Effect of The Emssvty J. Xamán *, G. Álvarez, Y. Chávez, J.O. Agular, J. Arce Centro Naconal de Investgacón y Desarrollo Tecnológco. CENIDET-DGEST-SEP Prol. Av. Palmra S/N. Col. Palmra. Cuernavaca, Morelos, CP 69, Méxco. * xaman@cendet.edu.mx, Unversdad de Quntana Roo. UQROO Blvd. Bahía S/N, Esq. Ign. Comonfort, Col. del Bosque, Chetumal, Quntana Roo, C.P. 779, Méxco. ABSTRACT In ths paper a theoretcal study on conugated heat transfer (natural convecton, radaton and conducton) n a square room (cavty) wth turbulent flow s presented, tang nto account varaton on the opaque wall emssvty. The room s formed by an sothermal vertcal wall, two adabatc horzontal walls and a semtransparent wall wth and wthout a control solar radaton flm. The governng equatons for turbulent flow n D were solved usng a fnte volume formulaton and - turbulent model. Results for an sothermal wall at C and an external temperature of 5 C are presented. The sze of the room s. m length and heght and the solar radaton fallng drectly on the semtransparent wall was 75 W/m (AM). The emssvty of the opaque walls was vared between. *.. Results show that, based on the ar average temperature and the effectve heat flux nsde the room, the solar control flm under study was advantageous for energy savng purposes, for emssvty values of *.6. A correlaton on ths system for the heat transfer as a functon of the emssvtes was determned. Keywords: Conugate heat transfer, κ-ε turbulent model, emssvty. RESUMEN En este artículo se presenta un estudo teórco de la transferenca de calor conugada (conveccón natural, conduccón y radacón) en fluo turbulento de una habtacón cuadrada (cavdad), consderando la varacón de la emsvdad en la pared opaca. La habtacón consste de una pared vertcal sotérmca, dos paredes horzontales adabátcas y una pared semtransparente con y sn película de control de radacón solar. Las ecuacones gobernantes para fluo turbulento en dmensones se resolveron usando una formulacón de volumen fnto y el modelo de turbulenca -. Se presentan los resultados para una pared sotérmca a ºC y una temperatura exteror de 5ºC. Las dmensones de la habtacón son m de longtud y altura y la radacón solar que cae drectamente sobre la pared semtransparente es de 75W/m (AM). La emsvdad de las paredes opacas fue varando entre. *.. Los resultados muestran que, con base en la temperatura ambente del are y el fluo de calor efectvo dentro de la habtacón, la película de control solar bao estudo resultó ser desventaosa para propóstos de ahorro de energía, para valores de emsvdad de *.6. Se determnó para el sstema una correlacón para la transferenca de calor en funcón de las emsvdades. NOMENCLATURE C p specfc heat, J g - K - dfda da vew factor between elements - g * gravtatonal acceleraton, 9.8 m s - G solar radaton, W m -. G buoyancy producton/destructon of netc energy h ext convectve heat transfer coeffcent at the outsde glass wall, Wm - K - H heght of the cavty, m L length of the cavty, m L g thcness of the glass, m P pressure, Pa P K turbulence netc energy producton Q heat flux, W m - s g extncton coeffcent, m - T temperature, K T cold wall temperature, K T g-average nsde average temperature of the glass wall, K T reference temperature [(T g-average +T )/], K u, v dmensonal horzontal and vertcal veloctes, m s - x, y dmensonal coordnates, m Journal of Appled Research and Technology 7

2 Gree symbols * absorptvty thermal expanson coeffcent, K - rate of dsspaton of, m s - * emssvty turbulence netc energy, m s - thermal conductvty, W m - K - dynamc vscosty, g m - s - t turbulent vscosty, g m - s - densty, g m - * reflectvty Stefan-Boltzman constant, 5.67x -8 W m - K - Prandtl number for Prandtl number for * transmssvty Subscrpts a ar ext ambent cond conductve conv convectve f flm g glass wall nt nsde out outsde rad radatve total total quanttes. Introducton In an effort to reduce economc costs generated by electrcty consumpton used by ar condtonng systems n buldngs and rooms, dverse alternatves for passve acclmatzaton have been developed. One of these alternatves has to do wth the use of solar control flms appled on the wndows glass, whch are commonly used on many modern buldngs. The goal when usng control solar flms on the wndows glass s to reduce heat gans nsde the buldng, located clmates []. For mathematcal smulatons, rooms are often modeled as square cavtes. Several studes on cavtes wth dfferent confguratons and boundary condtons have been carred out. Nevertheless, ths wor has to do wth studes on conugated heat transfer n cavtes wth a semtransparent wall. Prevous studes have analyzed the effect of radatve exchange on natural convecton nsde a cavty and showed that the effect s sgnfcant and should not be neglected [-]. Few studes have consdered the effect of radatve exchange when a semtransparent wall s placed n the cavty. Behna et al. [5] consder a cavty wth one glass sheet wall and presented numercal results for a varety of Raylegh numbers n the range <Ra<x 5. The authors concluded that, n general terms, the external convecton weaens the nternal crculaton, radaton strengthens t, and n combnaton the overall effect s a strengthenng of the nternal crculaton. Kwon et al. [] presented a numercal study of combned lamnar natural convecton and radaton n a rectangular enclosure wth a transparent wndow. Ther results show that temperature dstrbutons of adabatc walls ncrease wth the transmttance of the transparent wndow, however, the effects of solar radaton are hgher than those of surface radaton and pure natural convecton. Álvarez and Estrada [6] publshed results of a transent computatonal model for combned lamnar natural convecton, conducton and radaton n a square cavty. The cavty s modeled wth a vertcal glass wall wth flm coatng. Results show that there s a dmnshed convectve regme due to the nfluence of the radatve exchange. The authors show that the total energy transferred through the glass/solar control coatng system s lower than the case that uses ust clear glass. Xamán and Álvarez [7] determned the nfluence of a semtransparent glazng, wth and wthout a SnS-Cu x S solar control coatng, on turbulent natural convecton n a square cavty where the effects of surface thermal radaton were neglected. Results show that the drect solar energy transmttance of the semtransparent glazng wth a flm coatng was much lower than the case wthout a solar control coatng and therefore, the total heat gan through the glazng wth the solar control coatng would be lower than the one wthout the solar control coatng. Subsequently, Xamán et al. [8] studed the conugate heat transfer (lamnar and turbulent natural convecton, surface thermal radaton and conducton) n a square cavty wth a glass wall. The Raylegh number was vared n the range of Ra. Results showed that the flow pattern was not symmetrc due to the combned effect of the non-sothermal glass wall and radatve exchange nsde the cavty. As well, the surface thermal radaton was neglected, a sgnfcant under estmaton of the total heat transfer was found. The authors presented a correlaton for the total Nusselt number for both lamnar and turbulent flow consderng conugate heat transfer. Recently, Xamán et al. [9] presented a detaled study of flud 8 Vol. No., June

3 flow and heat transfer caused by turbulent natural convecton and surface thermal radaton n a square cavty wth a semtransparent wall wth (case A), and wthout (case B), a solar control flm. The obectve of the study was: to obtan the thermal parameters for cases approachng real szed rooms and to evaluate the thermal effect of usng a semtransparent wall wth, and wthout, a solar control flm on the arflow n the cavty. A Raylegh number range from 9 to was chosen for the heat transfer study n a square cavty. Results showed that by usng the solar control flm coatng on the semtransparent wall, the total heat flux was reduced from 66. to. W/m, even though the temperatures of the flm coatng on the semtransparent wall (case A) were hgher than the ones obtaned wthout solar control flm (case B), also the ar temperature values n the cavty were hgher for case A than for case B. Accordng to prevous studes [8, ] the use of a SnS-Cu x S flm results n a lower heat gan nsde the cavty, but ar temperatures are hgher than the case wthout the flm. The authors beleved that the emssvty value of the opaque walls had an nfluence on the ar temperature and that, there mght be emssvty values for whch the average ar temperature nsde the cavty has an opposte behavor to that as descrbe above. Ths study shall extend the prevous wor carred out by Xaman et al [9], by tang nto account dfferent emssvty values for the opaque walls (gray-dffuse surfaces) of a square cavty wth a semtransparent wall, for the cases wth and wthout a solar control flm. Ths study ams to fnd the range for whch the emssvty value of the opaque walls gves a lower heat gan and correspondng ar temperatures nsde the cavty, as compared to those obtaned when not usng a solar control flm.. Physcal model and assumptons The heat transfer and flud flow n a twodmensonal closed square cavty was consdered. Assumng that the dmenson n z drecton s much longer than the other two, then a two dmensonal assumpton can be appled. (Fgure ). The thermal flud was assumed to be ar n turbulent regme, ntally at rest and wth a unform temperature. The cavty s formed by two horzontal adabatc walls, one vertcal sothermal wall and one semtransparent wall (a glass sheet) consstng of glass and a solar control flm adhered to the nsde surface. The left surface of the cavty s an sothermal opaque wall at ºC (T =9K); the top and bottom horzontal surfaces were consdered adabatc. On the semtransparent wall an ncomng normal unform and constant solar radaton flux (75 W/m ) was consdered and two dmensonal heat transfer by conducton was taen nto account. The semtransparent wall transmts, reflects and absorbs normal solar radaton flux. Absorbed solar radaton flux ncreases the glazng temperature and t s transferred by conducton to the nsde and outsde of the cavty. The semtransparent wall, as well as the opaque walls s consdered gray, dffusve, reflectve surface and an emtter of thermal radaton. The thermal flud was consdered radatvely nonpartcpatng. The thermophyscal propertes of the ar were assumed constant except for the densty n the buoyancy force term n the momentum equatons, accordng to the Boussnesq approxmaton. The optcal propertes consdered were the ntegrated solar spectrum values. The flm solar control coatng selected was SnS-Cu x S. Fgure. Physcal model of the square cavty wth a semtransparent wall. Mathematcal model. Turbulent natural convecton model The turbulent natural convecton consdered n the square cavty wth a semtransparent wall s descrbed mathematcally by the Reynolds averaged Naver Stoes (RANS) equatons. The RANS equatons for mass, momentum and energy conservaton are expressed n tensor form as: Journal of Appled Research and Technology 9

4 ( u ) x () ( u ) t P G x x x (7) ( u u ) P u ' ' * uu ( T T ) g ( u ) t x x x x C P C G C x x x () (8) ( u T) T ' ' u T x x C p x where, P and G are the producton of () turbulent netc energy by shearng and the generaton/destructon by buoyancy. The above system of equatons s not complete because of the presence of the unnown Reynolds The mathematcal velocty boundary condtons on ' ' stress tensor ( u u the walls are zero and the temperature boundary ) n the momentum equaton condtons are set as: adabatc horzontal walls and the turbulent heat vector ( u ' T ' ) n the energy (top and bottom), the left vertcal wall s sotherm and heat transfer by conducton s consdered at equaton. In the Eddy Vscosty Model (EVM) the the semtransparent wall (rght wall), that s Reynolds stress tensor s modeled through the Boussnesq hypothess as [-]: Bottom wall: u ' ' u u u t x x () The Hgh Reynolds Number model (HRN) establshes that the turbulent vscosty ( t ) can be obtaned as: t C (5) where C s a constant. The turbulent heat vector s modeled as follow: ' u T ' t T T x (6) where T s the turbulent Prandtl number and s the Kronecer delta. The turbulent vscosty can be related wth the turbulent netc energy () and the turbulent dsspaton of netc energy () through the emprcal equaton of Kolmorogov-Prandtl [8]. The turbulent netc energy and the turbulent dsspaton of netc energy can be obtaned usng ts correspondng transport equaton: q q (9) conv rad Isothermal vertcal wall: T(, y) T () Upper wall: q q () conv rad Semtransparent vertcal wall: q q q q () abs condg conv rad Where q conv, q conv and q conv are the convectve heat transfer fluxes from the nsde surface to the adacent flud on walls, and respectvely. The terms q rad, q rad and q rad are the net radatve heat transfer fluxes at walls, and. The term q abs s the thermal energy that s absorbed by the solar control flm of the glazng. Fnally, q condg s the heat flux by heat conducton through the semtransparent wall. The boundary condtons and coeffcent values for - turbulence model are: w =., w =, C =.9, C =., C =.9, =., =. and C = tanh v/u []. Vol. No., June

5 . Conducton model of the semtransparent wall In order to obtan the temperature profle nsde the semtransparent wall formed by glass (L g = 6 mm) wth a thn solar control flm coatng, a dfferental energy balance was carred out. The model soluton s used to determne the conductve heat flux of wall ( q condg ). The heat transfer conducton equaton for the dfferental element of the semtransparent wall s gven by: x g C pg T x g C pg d dx () where s the attenuaton energy functon by absorpton and scatterng, whch depends of the extncton coeffcent (s g ) as follows [9]: ( x) G exp [ s ( L x)] () g g The outsde boundary condton for the semtransparent wall at (x=l+l g ) can be expressed as: * T g Tamb g T g T Tg g hext amb (5) x Where, T amb s the outsde ambent temperature. The flm thcness ( 6 m) was consdered neglgble wth regard to the glass thcness (6 mm). In order to obtan the flm temperature (T f ) at (x=l), the followng energy balance at the flm was carred out: * * Tg T f g G g a qrad (6) x x where T f = T g (,y) The boundary condtons are adabatc for the horzontal walls.. Surface thermal radaton model The net radatve method was used to calculate the resultng heat fluxes from the radatve exchange [9]. The thermal radatve exchange between the cavty surfaces s shown n Fgure, usng two dfferental areas on surfaces and. The cavty surfaces are assumed opaque and dffuse except the vertcal rght wall whch s a semtransparent wall. The radatve heat transfer from a surface s defned as the dfference between the outgong thermal radaton (radosty) and the ncomng thermal radaton (rradance). Therefore, mang an energy balance over the dfferental element da, located n r poston on wall (Fgure ), we can obtan the resultng heat radatve flux for wall : q rad ( x out n ) q ( x ) q ( x ) (7) Where the radosty s defned for a dffuse opaque surface as the sum of emtted energy and reflected energy, what can be formulated for the th element as: q out ( x * * ) T ( x ) q ( x ) (8) n The rradance s defned as the sum of energy fractons outgong from cavty surfaces dfferental elements that arrves to the analyzed surface. The rradance mathematcal formulaton for a surface element on wall s gven by: q n ( x m A ) q ( x ) df out da da (9) Where the summaton over the th surface element s to be taen for those elements over the boundary for whch nteracts radatvely. df da da s the correspondng dfferental vew factor. Smlar equatons can be derved for the remanng opaque cavty walls.. Thermal parameters The average Nusselt number s a parameter used to quantfy total heat transfer nsde the cavty. The total heat transfer nvolves the contrbuton of the convectve and radatve Nusselt numbers; thus, the total convectve and radatve Nusselt numbers can be expressed as: Nu total Nu Nu () conv rad Journal of Appled Research and Technology

6 where: Nu Nu conv rad H T dy q x cond H () qrad dy q () cond T T L q cond / () where T s the average temperature on the nsde surface of the semtransparent wall and T as the temperature on the left wall (wall ). momentum and contnuty equatons s made wth the SIMPLEC algorthm []. The algebrac equatons system s solved by applyng the lne by lne method (LBL) wth alternatng drecton (ADI). Furthermore, under-relaxaton s ntroduced usng the false transent strategy. If the resdual values of the dfferent equatons and the mass balance for every control volume are suffcently low, overall convergence s obtaned (typcally - ). Ths convergence crteron assures an acceptable soluton. A radatve balance at the walls s solved usng an teratve approach n order to couple turbulent natural convecton to surface thermal radaton effects at the boundares. The vew factors between the elements were determned by usng the equatons reported by Álvarez and Estrada [6]. da r y v n N N v n N r x W u w v s S P u e E u w P S ue E W v s P S E q n, qout, y (a) (b) (c) x Fgure. Radatve balances n dfferental areas 5. Methodology for the numercal soluton 5. Dscretzaton q rad, da The coupled ellptc partal dfferental equatons of the convectve and conductve model descrbed above are dscretzed wth the fnte volume method []. The equatons are ntegrated over elementary control volumes located around each node of a grd. The poston of the nodes s calculated usng a stretchng functon so that the nodes are closer to each other near the walls of the cavty. The velocty components are calculated at a staggered grd whle the scalar varables are calculated at the man grd (not-staggered) (Fgure ). The convectve terms are dscretzed applyng the hybrd scheme and the dffusve terms wth the central dfference scheme. Couplng between the Fgure. Cartesan grd showng placement of control volume boundares: (a) control volume for a scalar varable (P, T, etc ), (b) control volume for horzontal velocty u e and (c) control volume for vertcal velocty v n. The general procedure for the conugate heat transfer n a cavty can be summarzed n the followng steps: ) Intal guess values of all varables (u, v, T,...) n the cavty were gven; ) Equatons (7)-(9) were computed for each wall n order to get the local radatve heat flux on the walls ( q rad, q rad and q rad ); ) The conductve model to obtan q condg was solved; ) The pressure-velocty (u, v, p) were calculated by the SIMPLEC algorthm; 5) Wth the new calculated values of local radatve heat flux and velocty, the temperature (T), the turbulent netc energy () and the turbulent dsspaton of netc energy () feld n the cavty were obtaned; 6) A convergence crteron was appled; and, 7) the process was repeated teratvely untl the convergence crteron was acheved. Vol. No., June

7 The accuracy of the numercal results was verfed through numerous tests based on the grd sze effect. Based on numercal calculatons, the computatonal grd that gves grd ndependent solutons was 9x8 wth a maxmum devaton of % for the average Nusselt number. Therefore, a 9x8 grd was used for all cases heren consdered. The dscretzaton for the semtransparent wall (6 mm) was always nodes n the horzontal drecton for all the meshes. 5. Verfcaton of the numercal code The numercal code developed to solve ths problem has been verfed and valdated usng dfferent problems from lterature; comparsons have been reported on dverse publcatons by Xamán et al. [8-, 6-7]. Among these comparsons s the verfcaton and valdaton of the Benchma problem for natural convecton wth turbulent flow n a square cavty reported by Henes et al. [] for numercal results, and Ampofo et al. [5] for expermental results. Besdes, comparsons wth numercal [6] and expermental [7] results, for tall cavtes have been carred out, as well as verfcatons wth the conugated heat transfer problem (natural convecton-surface thermal radaton). As a complement to ths secton comparson results wth Velusamy et al. [] for natural convecton wth turbulent flow and surface thermal radaton n a square cavty dfferentally heated s presented. Comparson of results was made wth the followng two cases: Case (the walls have an emssvty equal to.9, T =8 K, T =8 K and Ra= ) and Case (the walls have an emssvty equal to.9, T =8 K, T =98 K and Ra= ). The comparson of results s analyzed for both cases n terms of the average Nusselt numbers (convectve (conv) and radatve (rad)) n the hot (h) and cold (c) walls. The maxmum and mnmum observed dfferences for Case are. % for Nu cf and. % for Nu hr respectvely. In Case, the maxmum dfference observed s.9 % for Nu cf and the mnmum dfference s. % for Nu hr. However the dfferences for average total Nusselt numbers (Nu total ) are % and.5 % for Case and Case respectvely (Table ). Nu h -conv Nu c -conv Nu h -rad Nu c -rad Nu t otal Case Case Velusa my et al. Ths wor * Velusa my et al (.8%) (.%) (.%) (.9%) (.78%) 89.9 * The values among parenthess are percentage absolute dfferences Ths wor* 6. (.5%) (.9%) 5.5 (.%) 5.89 (.%) (.5%) Table. Comparson of the present study wth reported results by Velusamy et al., () for the turbulent natural convecton and surface thermal radaton n a square cavty. 6. Results and dscusson 6. Parameter of study The parameters used to obtan the conugate heat transfer results for the square cavty wth a semtransparent wall usng a solar control flm are descrbed next. The cavty length consdered n ths wor s the. m. The solar radaton ncomng n a normal drecton over the semtransparent wall has a constant value of 75 W/m. The glass thcness was set at 6 mm wth a selectve coatng flm of SnS-Cu x S whose propertes were reported by Nar et al. [] and are shown n Table. The sothermal wall temperature was taen as ºC (9 K). The external condtons around the semtransparent wall were: the external convecton coeffcent was assumed constant at a value of 6.8 W/m K correspondng to a wnd velocty of m/s and the ambent temperature was fxed at a temperature of 5 C (8 K) (warm clmates). The emssvty of the semtransparent wall wthout the solar control flm was set to.85 and when the solar control flm was consdered, the emssvty was assumed to.. The emssvty of the remanng walls was vared n a range:. *. Journal of Appled Research and Technology

8 Glass (6 mm) Flm (SnS-Cu x S) (Glass-Flm) * g =. A * =.6 * ysst = * g + * f =.69 * g =.78 T * =. * syst = - * sst - * sst =.5 * g =.8 R * =.6 * syst = R * / =.6 * g =.85 * f =. g =. W/mK Cp g = 75 J/gK * f = (- * g)a * / =.55 * f = * sst / * g =.9 g = 5 * g/m f = - * f - * f =.6 Table. Optcal and thermophyscal propertes of glass and SnS-Cu x S solar control coatng. The results of ths analyss are presented as sotherms and average ar temperatures as a functon of the surface emssvtes. As well, effectve heat gan nsde the cavty for the case of the semtransparent wall wth control solar flm (case A) and wthout control solar flm (case B) are presented. 6. Isothermals and average ar temperature n the cavty Fgure shows the sothermals nsde the cavty for Case A and Case B, for emssvty values of.,.5 and.9. In general, stratfcaton occurs n most of the cavty for all cases. Results for an (opaque wall) emssvty of. show that, for case B, the temperatures are hgher than those for case A. It can be seen that at m heght case A presents an sothermal of K and for case B of.5k. For an emssvty value of.5 results show that the values of the sothermals are slghtly hgher n case A than n case B. Sgnfcant dfferences for the sothermals values for an emssvty of.9 are observed; n case A sothermals are shown wthn an nterval from 5 to 5K and n case B from to 5K. It can be noted that average ar temperature nsde the cavty s hgher for case A. Summarzng, as observed from Fgure, ths results ndcated that there s an nterval of wall-emssvty values for whch the temperatures nsde the cavty are lower for case A when compared to case B and vce-versa. Fgure 5 shows the average ar temperature nsde the cavty as a functon of the emssvty values. In general, for both cases, the average ar temperature behavor s almost lnear and t dmnshes as the wall emssvty value ncreases. Ths ncrement on the average temperature as the emssvty ncreases can be explaned as follows: by the Krchoff law approxmaton the emssvty becomes approxmately equal to the wall absortvty ( * α * ), then f the cavty opaque walls absorb less energy (emssvty dmnshes absortvty dmnshes), more energy wll be gven n to the cavty flud by any of the energy transport phenomenon and as a consequence temperature wll ncrease. For case A the average temperature s between the nterval 5.7 to 7. C and for case B the nterval s 55. to 8. C. The average temperature values for both cases ntercept on an emssvty value of.6, below ths emssvty value average temperature for case A s lower than for case B. So, s n ths emssvty nterval ( *.6) where the use of the SnS.Cu x S solar control flm s recommendable to be used rather than the wndow glass wthout t. Ths result allows us to conclude that there mght be a range for each confguraton conformed by the wndow glass and the solar control flm. Table shows the average temperature nsde the cavty wth a sem-transparent wall for cases A and B that correspond to all the emssvty values consdered for ths study. It can be seen that for all the emssvty values the semtransparent wall temperature s hgher for case A than for case B, ths s due to the semtransparent wall confguraton of case A has a much hgher absortvty value due to the solar control flm (see Table ). In both cases, the sem-transparent wall temperature ncreases when the emssvty on the remanng walls dmnshes; physcally the result maes sense, due to the assumpton that when the emssvty on the opaque walls dmnshes so too does the absortvty reducng radaton exchange from the sem-transparent wall to the nteror walls. Vol. No., June

9 5 5 5 y(m) y(m) 5 5 x(m) 5 x(m) * = y(m) y(m) 5 x(m) * =.5 x(m) y(m) y(m) 5 x(m) x(m) * =.9 Case A Case B Fgure. Isotherms (K) for an emssvty of * =.,.5 and.9 for case A and case B Journal of Appled Research and Technology 5

10 T average (ºC) Fgure 5. Average ar temperature as a functon of the emssvty for case A and case B. * T g-average (ºC) Case A Case B (wth flm) (wthout flm) Table. Average temperature of the nteror surface of the semtransparent wall n functon of the emssvty for case A and case B. 6. Total heat flux n the cavty Case A Case B On prevous publcatons, Xamán et al. [8, ] confuson has emerged; n order to clarfy ths let us tae cases A and B wth a wall emssvty of *=.9. In Table, the average heat transfer fluxes of semtransparent wall for cases A and B are presented for * =.9. The nomenclature used s as follow: q = transmtted heat flux through the semtransparent wall toward the nteror of the cavty, q = absorbed heat flux by the semtransparent wall, q = reflected heat flux to cavty outsde, q nt = nsde heat flux by natural convecton and thermal radaton from the semtransparent wall to the cavty, q out = outsde heat flux by natural convecton and thermal radaton from the semtransparent wall toward the outsde of the cavty, q nt +q = nsde total heat flux, q out +q = outsde total heat flux. Confuson les manly when evaluatng results for the total heat flux nsde the cavty (q nt +q ) t can be apprecated that t s lower for case A (. W/m ) than for case B (66. W/m ); now, when results for the ar average temperature nsde the cavty are quantfed, t s observed that temperature for case A s hgher than for case B. So, how would t be possble to get a hgher average ar temperature on case A compared to case B, f for case A the heat flux s lower. The answer to ths possble nconsstency comes further. The sothermal wall was assumed to be an opaque wall, wth an emssvty of.9, s practcally the cause of the ncreasng temperatures of ar at nsde when the solar control flm s used (case A) regardng to the case when solar control flm s not used (case B), ths s explaned as follows: It can be seen from Table that for case A, the amount of total energy nsde the cavty (q nt +q ) s. W/m and 66. W/m for case B, then we thought how could t be possble that hgher temperatures were reached n case A, where the amount of energy was lower regardng to case B. The amount of total energy nsde the cavty s made up of the radaton and convecton energy (q nt ) plus the solar energy drectly transmtted through the semtransparent wall (q ). In Table we can observe that q nt s hgher for case A regardng to case B (case A: 9.5 W/m, case B: 6. W/m ), ths result seems to be logcal, as the average temperature of the semtransparent wall s hgher n case A (59. ºC) than the one reached n case B (8.5 ºC) (Table ). For the case of q, on Table t can be seen that ts value s lower for case A (case A: 7.9 W/m, case B: 585. W/m ); at ths pont the sothermal wall plays an mportant roll, due to the energy q, was consdered to fall n a drect form and perpendcular to the sothermal wall. As the sothermal wall was consdered to have an emssvty of.9 and accordng to Krchoff s Law emssvty equals absortvty (ε * = * ) then, the q energy that reached the sothermal wall n case A were 7.9, from ths amount.56 were absorbed for the sothermal wall (heat sn) and the rest of t, whch s.7 W/m returned to the nsde of the cavty by convecton or radaton, that s represented n Fgure 6. Summarzng, the total effectve energy nsde the cavty for case A s * qnt ( q q ) : q nt =9.5 W/m plus the percentage of q energy that was not absorbed by 6 Vol. No., June

11 the sothermal wall (.7 W/m ) equals to 7.88 W/m. Regardng to case B, the energy that reached the sothermal wall was 585., from whch 56.6 were absorbed for the sothermal wall (heat sn) and 58.5 W/m returned to the nsde of the cavty. In the same way, the total effectve energy nsde the cavty for case B s * qnt ( q q ) : q nt =6. W/m plus the percentage of q energy that was not absorbed by the sothermal wall (58.5 W/m ) equals to 9.6 W/m. Concludng, the amount of energy at the nsde cavty s hgher n case A (7.88 W/m ) regardng to case B (9.6 W/m ), for that reason temperature s hgher n case A. correlaton shows a maxmum percentage dfference of.% aganst the numercal results. Case A B q q q 6 q nt q out q nt +q. 66. q out +q Table. Average heat fluxes (W/m ) for case A and B for * =.9. q nt + ( - ) q (W/m ) Case A Case B Fgure 6. Schematc dagram of the total effectve energy nsde the cavty. Fnally, n order to show the heat gan that remans n the system consstng on the cavty and the sem-transparent wall, Fgure 7 shows the total effectve heat flux nsde the cavty for cases * qnt ( q q ) A and B as a functon of the emssvtes. In ths fgure t can be observed that both curves ntercept for an emssvty value of.6, ths value concde wth the one presented n Fgure for the average ar temperature. It s observed that for the emssvty value nterval of *.6 the total effectve heat gan for case A s lower than for case B and for ths nterval the use of the solar control flm under study s recommended. An average total Nusselt numbers as a functon of the emssvty for case A was obtaned. Usng least square regresson, a correlaton for the average Nusselt number for case A for. *. s: Nu total = *.556. The Nusselt number Fgure 7. Total effectve energy nsde the cavty as a functon of the emssvty for case A and case B. 7. Conclusons Ths wor presents a numercal study of the conugate heat transfer n a square cavty wth turbulent flow. The cavty has one vertcal sothermal wall, two horzontal adabatc walls and one vertcal semtransparent wall wth and wthout a SnS-Cu x S solar control flm coatng appled to control the solar radaton transmsson. Analyss on the sothermals as a functon of the emssvty, t was found that there exsts an emssvty nterval for whch temperatures on case A are lower compared to case B and vce versa. Ths nterval was determned from the ar average temperature results and the effectve energy flux nsde the cavty; results on each case concded on an emssvty nterval, where the use of the solar control flm SnS-Cu x S on the sem- Journal of Appled Research and Technology 7

12 transparent wall s recommended rather than the wall wthout t. Ths result allows us to conclude that there mght be a range for one and each of the unque confguratons conformed by the wndow glass and the solar control flm. A correlaton for the heat transfer as a functon of the emssvty was determned. Results from ths study also let us to observe the nfluence on havng an sothermal wall as a heat sn, whch should be replaced for a heat conductve wall n future wors. As future wor smlar studes for dfferent solar control flms should be carred out due to ts optcal behavor s not an only conclusve element to determne f ts use would gve us lower temperatures nsde rooms, the selecton for a solar control flm should be accompaned by a thermal study. Fnally, the developed -D numercal model of conugate turbulent heat transfer n a cavty wth semtransparent wall was capable of studyng n detal the heat transfer phenomena. Ths may represent an advance n the nowledge of what we can have n real rooms wth a wndow havng or not, solar control flm coatng. Acnowledgements The authors are grateful to Conseo Naconal de Cenca y Tecnología (CONACYT) - Thematc Research Networs: Energy Sources (REDFE), whose fnancal support made ths wor possble. References [] M. Nar, P. Nar, SnS-CuxS thn flm combnaton: a desrable solar control coatngs for archtectural and automoble glazngs. J. Physcs D: Appled Physcs (99) 5-5. [] N. Ramesh, S.P. Venateshan, Effect of surface radaton on natural convecton n a square enclosure. J. Thermophyscs Heat Transfer (999) 99-. [] K. Velusamy, T. Sundararaan, K. Seetharamu, Interacton effects between surface radaton and turbulent natural convecton n square and rectangular enclosures. J. Heat Transfer () 6-7. [] Anl Kumar Sharma, K. Velusamy, C. Bala, S.P. Venateshan, Conugate turbulent natural convecton wth surface radaton n ar flled rectangular enclosures. Int. J. Heat Mass Transfer 5 (7) [5] M. Behna, J. Rzes, G. De Vahl Davs, Combned radaton and natural convecton n a cavty wth a transparent wall and contanng a non-partcpant flud. Int. J. Numercal Methods Fluds (99) 5-5. [6] G. Álvarez, C. Estrada, Numercal heat transfer n a cavty wth a solar control coatng deposted to a vertcal semtransparent wall. Int. J. Numercal Methods Fluds () [7] J. Xamán, G. Álvarez, Effect of heat conducton of SnS-Cu X S solar control coated semtransparent wall on turbulent natural convecton n a square cavty. Numercal Heat Transfer Part A 5 (6) [8] J. Xamán, J. Arce, G. Álvarez, Y. Chávez, Lamnar and turbulent natural convecton combned wth surface thermal radaton n a square cavty wth a glass wall. Int. J. Thermal Scences 7 (8) [9] J. Xamán, G. Álvarez, J.F. Hnoosa, J. Flores, Conugate turbulent heat transfer n a cavty wth a solar control coatng deposted to a vertcal semtransparent wall. Int. J. Heat Flud Flow (9) 7-8. [] R. Henes, F. Van-Der-Vlugt, C. Hoogendoorn, Natural-convecton flow n a square cavty calculated wth low-reynolds-number turbulence models. Int. J. Heat Mass Transfer (99) [] J. Van Doormaal, G. Rathby, Enhancements of the SIMPLE method for predctng ncompressble flud flow. Numercal Heat Transfer 7 (98) 7-6. [] J. Xamán, G. Álvarez, L. Lra, C. Estrada, Numercal study of heat transfer by lamnar and turbulent natural convecton n tall cavtes of facade elements. Energy Buldngs 7 (5) [] J. Xamán, J.F. Hnoosa, J. Flores, R. Cabanllas, Effect of the surface thermal radaton on turbulent natural convecton n tall cavtes of façade elements. Heat Mass Transfer, 5 (8) [] R. Henes, C, Hoogendoorn, Comparson exercse for computatons of turbulent natural convecton n enclosures. Numercal Heat Transfer, Part B, 8 (995) Vol. No., June

13 [5] F. Ampofo, T. Karayanns, Expermental benchmar data for turbulent natural convecton n an ar flled square cavty. Int. J. Heat Mass Transfer 6 () [6] C.D. Pérez-Segarra, A. Olva, M. Costa, F. Escanes, Numercal experments n turbulent natural and mxed convecton n nternal flows. Int. J. Num. Meth. Heat Flud Flow 5 (995) -. [7] P.L. Betts, I.H. Bohar, Experments on turbulent natural convecton n an enclosed tall cavty. Int. J. Heat Flud Flow () [8] S. Pope,. Turbulent Flows, Cambrdge Unversty Press, UK. [9] M. Modest, 99. Radatve heat transfer, McGraw- Hll, New Yor. [] S. Patanar, 98. Numercal Heat Transfer and Flud Flow, Hemsphere Publshng Corporaton, Washngton DC. [] S. Kwon, Y. Kwon, J. Par, Numercal study of combned natural convecton and radaton n a rectangular enclosure wth a transparent wndow on the center regon of rght wall. In: 6th Internatonal Symposum on Transport Phenomena n Thermal Engneerng, Seoul, Korea, 99, pp. 99. Journal of Appled Research and Technology 9