Inclined wall plumes in porous media

We present a numerical solution of the natural convection from inclined wall plumes which arise from a line thermal source imbedded at the leading edge of an adiabatic plate with arbitrary tilt angle between 0 and n/2, and embedded in a fluid-saturated porous medium. An appropriate transformation of the governing boundary-layer equations is proposed and a very efficient novel numerical solution is proposed to obtain rigorous numerical solutions of the transformed nonsimilar equations over a wide range of tilt angle from the vertical to the horizontal. Graphs are presented showing the effect of the tilt angle on the velocity and temperature profiles, as well as on the wall velocity and wall temperature. As far as we know, this problem has not yet been studied in the available literature. Nomenclature G f g K L Q R. T T* bt~ /) X, y fl specific heat of fluid dimensionless stream function acceleration due to gravity permeability of the porous medium length of line source energy released from the line source Rayleigh number temperature equivalent temperature of the line source velocity components in the x, y directions coordinates along and normal to the plate, respectively effective thermal diffusivity of the porous medium coefficient of thermal expansion * Corresponding author. 0169-5983 / 97 / $17.00 © 1997 The Japan Society of Fluid Mechanics Incorporated and Elsevier Science B.V. All rights reserved. PII S0 1 6 9 5 9 8 3 ( 9 6 ) 0 0 0 1 1-7 304 J.-J. Shu, I. Pop/Fluid Dynamics Research 21 (1997) 303-317