In this chapter, we concentrate on the study of heat transfer by natural convection in a saturated porous medium with a power law temperature variation on a vertical conical annular porous medium”. In this study Finite Element Method (FEM) has been used to solve the governing partial differential equations. There have been considerable interest in studying natural or buoyancy – induced flows in fluid saturated porous media adjacent to surfaces in recent years. This interest stems from numerous possible industrial and technological applications. Example of some applications include geothermal reservoirs, drying of porous solids, heat exchanger design, petroleum production, filtration, chemical catalytic reactor, nuclear waste repositories, and geophysical flows. The prediction and knowledge of heat transfer rate and temperature distribution from a heated horizontal surface to surrounding ground water in a subsurface environment has important applications in the assessment of geothermal resources and the design of a geothermal power plant.