Irt. J. oJ Appliecl Mechanics and Engineering, 200l, vol.9, No.3, pp.47I_4gl THERMOPHORESIS FREE CONVECTION FROM A VERTICAL CYLINDER EMBEDDED IN A POROUS MEDIUM A.J. CHAMKHA Manufacturing Engineering Department The PublicAuthorityfbr AppliedEducation andTraining P. O. Box 42325, Shuweikh, i0654, KUWAIT M. JARADAT and I. pop- Facuity of Mathematics, University of Cluj R-3400 Clui. Cp 253, ROMANIA e-mail : popi @ math.Lrbbclul.rcr This paper deals with the stcady free convection over rrnisothernral rcrtjcal circulrr crlinder enrbedilcd in a fluid-saturated porousrnediumin the presence of the therrnophoresi' plrrric).- dr-nosiriun eff'ect. 'l'he governine partialdifferential equatiorrs are tritnsformed into a sct ol'non-sirnilar equations. rvhichare sol'cd nurnericall. usingan implicit finite-difference melhod. Comparisons with the previously published work are perfbrmecl ancl the resultsare found to be in excellent agrecment. Many resultsare obtainedand a representative set of these results is displayedgraphically to illustratc the intluencc of the various physical paramcters on the wall thermophoretic deposition velocity and concentration profiles. Key words: free convection, thermophoresis, vertical cylincler. boundary layer, porous medium. 1. Introduction Convective heat transfer in fluicl-saturated porousmedia has beenstudied quite extensively dulng -'e last few decades- This has beenmotivated by its importance in many naturaland industrial pioblems. 'i:ominent amongthese are the utilizationof geothermaL energy, chemical engineering, thermalinsulation " slems' nuclear wastemanagement, erain storage. fruits and vegetable, migrition of moisture throughair - ntained in fibrous insulation, food processing and storage and conraminani rransport in groundrvater and : :ny others. A detailed review of the subject of convective florv in porous media, includingan exhaustive 't of references, was recently <lone by Nield ancl Bejan(1999), Ingham and pop (1998; z}}r),Vafai (2000), r p andIngham (2001), and Bejanand Kraus(2003). Fiee convection from a vertical or horizontal cylinderembedded in a porousmedium is the principal " rde of heattransfer in numerous applications suchas in connection with oiVgas lines,insulation of horizontal - ]es. cryogenics as well as in the context of waterdistribution lines, underground electrical power transmission : :s and burial of nuclear waste, to name just a few applications. The case of a free and mixed convection flow ' in a vertical cylinder placed in a porous medium has been studied extensivelyboth anaiytically ancl '-:nerically. It appears that Minkowyczand Cheng(1996)were the first to present a numerical solutionof the - i-'lem of the free convective boundary layer flow induced by a heated verticalcylinderembedded in a i-luicj- -'-ratedporous mediumwhen the sutface temperature of the cylinder is taken to be proportional to .r.-"' . r'here.l 'ire distance from the leadingedge/base of the cylinder andm is a constant. The resultsrlere obtaineci tbr --:'rus values of m lying between 0 and l. Sirnilarity andlocalnon-sirnilarity rnethods of solution ri ereused. The ' "iem was laterextended by Merkin (1986), Kumari et at. (1986), lnghamand pop (19g6). \Ierkin and pop -'-i. Kuntari andNath (1986), Yiicel (1990), Chen er al. (1992), Hossain ancl Nakarama (1993), Bassom and ... 1996), Pop and Na (1998), Yih (1998) and Chen iurd IIom (1999). iromcorrespondence should be adclressed