Heat Exchange between Film Condensation and Porous Natural Convection across a Vertical Wall

Abstract

Conjugate heat transfer across a vertical solid wall separating natural convection in a cold fluid-saturated porous medium and film condensation in a saturated-vapour medium is analyzed. The analysis reveals that this thermal interaction process is mainly controlled by the thermal resistance ratio of wall to porous-side natural convection and that of condensate film to natural convection. Asymptotic and numerical results of interest are obtained for the local and mean overall Nusselt number as functions of these two thermal resistance ratios. Nomenclature g gravitational acceleration lc scale of convection layer thickness l f scale of condensate film thickness H wall height Ja Jacob number, cf., Eq. (7) k thermal conductivity K permeability of porous medium Nu mean overall Nusselt number Nux local overall Nusselt number Pr Prandtl number, = ν / α Rac Rayleigh number of porous-side natural convection, cf., Eq. (22) Ra f Rayleigh numberof condensate film, cf., Eq... (6) T temperature Tc∞ free temperature of cold porous medium Ts saturation temperature u,v dimensional velocity components U,V dimensionless velocity components 1 College of Technological Studies, Kuwait 70453, P.O. Box 64268 2 Prof. On leave from Mech. Power Eng. Dept., Mansoura university, Egypt, mosaad77@hotmail.com 52 Copyright © 2011 Tech Science Press FDMP, vol.8, no.1, pp.51-67, 2011 x,y dimensional vertical and horizontal coordinates X ,Y dimensionless vertical and horizontal coordinates w wall thickness Greek letters ∆ f dimensionless thickness of condensate film α thermal diffusivity β thermal expansion coefficient Γ thermal resistance ratio of condensate film to natural convection layer η inverse Oseen function ν kinematic viscosity θ dimensionless temperature δ f dimensional thickness of condensate film ew thermal resistance ratio of wall to natural convection