Free Convection around a Body of Arbitrary Shape in a Porous Medium

Abstract

The problem of free convective heat transfer from a non-isothermal two dimensional or axisymmetric body of arbitrary geometrical configuration in a fluid saturated porous medium is analysed on the basis of boundary layer approximations. Upon introducing a similarity variable (which also accounts for a possible wall temperature effect on the boundary layer length scale), the governing equations for a non-isothermal body of arbitrary shape are reduced to an ordinary differential equation, which has been previously solved by Cheng and Minkowycz for a vertical flat plate with its wall temperature varying in an exponential manner. Thus, it is found that any two dimensional or axisymmetric body possesses its corresponding class of the surface wall temperature distributions which permit similarity solutions. A more straightforward and yet sufficiently accurate approximate method based on the Karman-Pohlhausen relation is also suggested for a general solution procedure for a Darcian fluid flow over a non-isothermal body of arbitrary shape. For illustrative purposes computations are performed on a vertical flat plate, horizontal ellipses and ellipsoids with different minor to major axis ratios.