Natural Convection Around a Heated Cylinder in a Saturated Porous Medium

Numerical solutions are presented for the natural convection heat transfer from a heated cylinder buried in a semi-infinite liquid-saturated porous medium. The governing equations are expressed in the stream function–temperature formulation and finite difference equations are obtained by integrating the governing equations over finite cells. The heat transfer characteristics of the heated cylinder are studied as functions of the Rayleigh number and the vertical depth of the cylinder center from a permeable surface. The numerical scheme involves the use of a cylindrical network of nodes in the vicinity of the cylinder with a Cartesian mesh covering the remainder of the flow domain. The results are of use in the design of underground electrical cables, power plant steam, and water distribution lines, among others.