UNSTEADY FREE-CONVECTION ADJACENT TO AN IMPULSIVELY HEATED HORIZONTALCIRCULAR-CYLINDER IN POROUS-MEDIA

An infinitely long circular cylinder embedded horizontally in a porous medium at the same temperature is suddenly heated to a constant tempe rature. The governing equations are solved numerically for small and l arge values of the Rayleigh number, and at small limes, the results ar e found to be in very good agreement with the analytical solution as o btained by Pop et al. [1], who used the method of matched asymptotic e xpansions. A plume region develops at the top of the cylinder, and two counterrotating vortices form adjacent to the sides of the cylinder. A novel feature of the results is that as convection becomes increasin gly more dominant, a single hot cell of fluid forms vertically above t he cylinder and rapidly moves away from the cylinder as time increases . The hot cell of fluid occurs at smaller times and distances from the surface of the cylinder as the Rayleigh number increases. The numeric al results indicate that the heat and flow penetrate farther upward in to the porous media as time increases, whereas the conservation of ene rgy principle shows that the heat penetrates infinitely into the porou s media. At very large times the numerical results show reasonable agr eement, in the vicinity of the cylinder, with the steady state solutio n obtained by Ingham and Pop [2], which should only be considered as a n inner solution to the problem.