Heat Transfer Enhancement in channel with obstacles

Transcription

1 Proceedings o the nd WSEAS Int. Conerence on Applied and Theoretical Mechanics, Venice, Italy, Noveber 0-, eat Transer Enhanceent in channel with obstacles M. Nazari M.. Kayhani Departent o Mechanical Engineering Departent o Mechanical Engineering University o Tehran Shahrood University o Technology Y. Khazraii Departent o Mechanical Engineering Shahrood University o Technology Abstract: Analysis o lid low and heat transer in an obstacle channel has lots o indstrial applications. In this paper, incopressible lid low in a channel has been stdied two diensionally and the eects o obstacle arrangeent on heat transer have been investigated. The heights o channel and obstacle size are variables to ind ot the ore properly odel or description o heat transer s iproveent in a channel. The nerical inite vole ethod has been developed and the Mean Nsselt nber has been calclated throgh the channel incorporating the eects o obstacle geoetry. The nerical reslts have good agreeent with orer experiental and nerical data. Key Words: Convective eat Transer, Enhanceent, CFD Noenclatre Dh Channel hydralic diaeter, h Obstacle height, hc Convective heat transer coeicient, W. K Channel height, k Theral condctivity, W. k L Obstacle streawise length, N Nsselt nber q eat lx, W D h ynolds nber, s Obstacle spacing, Velocity, s W Channel width, μ Dynaic viscosity, ( N. s ) θ Diensionless teperatre Sbscripts e Entrance Flid s Solid Mean Introdction eat transer enhanceent in channel has extensive engineering applications inclding heat exchanger design and cooling technology. The orced convective cooling o a two-diensional array o ltiple heated obstacles located pon one wall o an inslated channel was experientally investigated by Vaai et al. [1]. For an air low range o 800<<13000 and inpt heat lx o 950<q <000 W/, the dierent geoetric arrangeents that were eployed to stdy the eects pon the heat transer inclde changes in channel height and se o an individal obstacle or an array o siilar obstacles. The characterization o trblent low and convective heat transport o single isolated two and three-diensional obstacles in a channel were perored by Roeller et al. []. Larger obstacle widths increase the low acceleration by blocking ore channel low area while saller widths have ore intense threediensional transport eects. The se o an oddsized rectanglar obstacle within a threediensional array o sqare obstacles, with axi heat lxes o 6700 W/, was ond to enhance the heat transer p to 40 percent by Jbran et al.[3]. Sparrow et al. [4] also investigated the eects o height dierences within threediensional arrays o sqare obstacles and ond, sing the naphthalene sbliation techniqe, heat transer enhanceents o p to 80 percent copared with an array o nior height. The

2 Proceedings o the nd WSEAS Int. Conerence on Applied and Theoretical Mechanics, Venice, Italy, Noveber 0-, two-diensional conjgate heat transer proble or lainar low over an array o three obstacles was solved, tilizing a control vole orlation by Davalath et al. [5].Their analysis inclded the eects o obstacles spacing. In this stdy eat transer characteristics in an inslated channel with heated obstacles or developed lainar low o air are investigated by Finite vole ethod. The silation work has been carried ot or variant ynolds nbers, 600<<1400, and the inpt heat lx to the obstacles ranged ro 950 p to 000 W/. The reslts are presented in the or o ean Nsselt nber at the length o obstacles. In this work aects o dierent variables as Size and Geoetry o obstacles, Channel height, obstacles nber, inpt heat lx and low rates on Nsslet Nber are investigated. Finding teperatre distribtion and the convective heat transer coeicient on the obstacle sraces or dierent arrangeents o the and easring the iproveent or decrease o heat transer in the channel are the ost iportant isses reslted ro this research. Data reslted throgh odelling will be copared with the experiental reslts and proper coents or iproving the heat transer in channels with obstacle can be oered. This can be a sicient soltion or an accrate designing and constrction o copact heat exchanger. Geoetry o proble The geoetry o proble has been shown in Fig. 1. As is shown in this igre the channel walls are copletely isolated and the constant heat lx iposed at the botto srace o obstacle. The length and height o channel are considered L,. In this stdy the height o channel ( ) is varied between To decrease the end eect, channel width has considered W 305. In this stdy the channel height varied between the range o 1.< L <3.11. Governing Eqations and Bondary Conditions In nerical analysis o convective heat transer in a channel with arrays o heated obstacles, Navier-Stocks eqations or a lainar low in a Newtonian lid, steady incopressible low with constant therodynaic properties is solved. Coplete condctive heat transer in solid is also considered. Governing eqation are the conservation o ass, incopressible Navier-Stokes and Energy eqation, presented in the ollowing nondiensional or: + (1) 0 dp 1 () + dx dp + dy θ θ 1 θ Pe 1 v (3) With assing an incopressible low and one diensional velocity proile and constant heat lx on the obstacles sraces, bondary conditions will be deined as below: Entrance: 1, v 0, θ 0 (4) Otlet: ν θ (5) 0, 0, 0 Fig. 1: the geoetry o proble The strawise length o obstacles, L, was chosen to nondiensionalize the geoetric data. Flid/solid interaces: 0, ν 0, θ θ Channel walls: θ 0, ν 0, 0 s (6) (7)

3 Proceedings o the nd WSEAS Int. Conerence on Applied and Theoretical Mechanics, Venice, Italy, Noveber 0-, Basic Theory Local convective heat transer coeicient is deined as below: h c q A ( T T ) C e (8) Where q is srace heat lx, is wetted srace area, Te and T are srace teperatre and ean teperatre siltaneosly that can be obtained with the ollowing eqation: 1 (9) T TdA UA hc x The local Nsslet nber is deined as N k and the ean Nsselt nber is ond as the average o the local vales, N Ac Ndx A C A C (10) The ynolds nber was deined as ρ Dh D where the ean lid h μ velocity was ond ro the voletric low rate within the channel and the channel hydralic diaeter is D W. h ( W +. ) All therophysical properties o the air were evalated at the entrance teperatre. In or stdy that heat lx distribtion is constant, lid ean teperatre can be calclated ro the energy balance in each selective point o channel. Nerical Procedre In or nerical analysis, inite vole ethod and SIMPLE algorith have been sed. An orthogonal esh is sed throgh the channel. This esh is iner near to obstacles to obtain critical properties o regions beore, ater and on the srace o obstacles and the nber o cells is varied ro 000 to 4000 in varios steps. It is ond that ater 3900 cells, rther increase in cells has less than 3% variation in Nsselt nber vale which is taken as criterion or grid independency. In nerical soltion o single obstacles in a channel soe dierent sections are deined to calclate lid ean teperatre, Then local convective heat transer coeicient will be calclated and average o this vales reslt in the h in the obstacles length. Calclated Mean Nsselt nber is copared with Vaai s data that are shown in igre. Shold be noted that igre (a) shows the reslts or h/l0.89 and /L3.11 and igre (b) Is also or h/l 0.44 and /L As shown in the igres, Nsselt vales calclated in or paper have a siilar trend to Vaai s experiental reslts. Mean Nsselt Nber Mean Nsselt Nber ynolds Nber (Fig. -a) ynolds Nber (Fig. -b) Nerical reslt present stdy Experiental reslt vai et al[1] Nerical reslt present stdy Experiental reslt vaai et al[1] Fig. (a,b): Mean Nsselt nber, coparison between the experiental and present nerical reslts

4 Proceedings o the nd WSEAS Int. Conerence on Applied and Theoretical Mechanics, Venice, Italy, Noveber 0-, Mltiple Obstacle Arrays: The nerical analysis was tilized to copare the ean convective heat transer behavior or the syste like conigration o an array o three heated obstacle o height h/l 0.44and interobstacle spacing s/l0.44 within a channel o height /L3.11. For the experients the inpt heat lx was 930W while the airlow was kept within the lainar regies. Figre 3 shows or the three obstacles, the ean Nsselt nber coparison between the experiental and nerical analyses. Fig.3c: Mean Nsselt Nber, h/l0.44, s/l0.44, /L3.11, q 930 W/, heat Flx iposed on obstacle 3 \ Fig.3a: Mean Nsselt Nber, h/l0.44, s/l0.44, /L3.11, q 930 W/, heat Flx iposed on obstacle1 Fig.3b: Mean Nsselt Nber, h/l0.44, s/l0.44, /L3.11, q 930 W/, heat Flx iposed on obstacle Conclsions In this paper, incopressible lid low in a channel has been stdied two diensionally and the eects o obstacle arrangeent on heat transer have been stdied. The heights o channel and obstacle size are variables to ind ot the ore properly odel or description o heat transer s iproveent in a channel. The nerical inite vole ethod has been developed and the Mean Nsselt nber has been calclated throgh the channel incorporating the eects o obstacle geoetry. The nerical reslts have good agreeent with orer experiental and nerical data and the obstacle lead to change the ean Nsselt nber in the channel. These nerical reslts can be sed in design and abrication o heat exchangers and the rate o heat transer can be predicted exactly. erences [1]K.Vaai, T.J, Yong, Experiental and Nerical Investigation o Forced Convective Characteristics o Arrays o Channel Monted Obstacles, ASME JOURNAL o EAT TRANSFER,Vol.11, pp.34-4, [] P.T.Roeller, J. Stevens, B.W. Webb, eat Transer and Trblent Flow Characteristics o Isolated Three-Diensional Protrsions in Channels, ASME JOURNAL o EAT TRANSFER,Vol.113,pp , 1991.

5 Proceedings o the nd WSEAS Int. Conerence on Applied and Theoretical Mechanics, Venice, Italy, Noveber 0-, [3] B.A. Jbran, S.A. Swiety, M. adan, Convective heat transer and pressre drop characteristics o varios array conigrations to silate the cooling o electronic odles, Int.J.eat andmass Transer, Vol.39, pp , [4] E.M. Sparrow, A.A Yanezoreno, D.R. Otis, Convective heat transer response to height dierences in an array o block like electronic coponents, Int.J.eat and Mass Transer,Vol.7,pp, , [5] J. Davalath, Y. Bayazitogl, Forced Convection Cooling Across ctanglar Blocks, ASME JOURNAL OF EAT TRANSFER,Vol.109, pp.31-38, 1987.