Free Convective Heat Transfer Over a Nonisothermal Body of Arbitrary Shape Embedded in a Fluid-Saturated Porous Medium

The problem of free convective heat transfer from a nonisothermal two-dimensional or axisymmetric body of arbitrary geometric configuration in a fliud-saturated porous medium was analyzed 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 nonisothermal body of arbitrary shape can be 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 a corresponding class of surface wall temperature distributions which permit similarity solutions. Furthermore, a more straightforward and yet sufficiently accurate approximate method based on the Ka´rma´n-Pohlhausen integral relation is suggested for a general solution procedure for a Darcian fluid flow over a nonisothermal body of arbitrary shape. For illustrative purposes, computations were carried out on a vertical flat plate, horizontal ellipses, and ellipsoids with different minor-to-major axis ratios.