In this chapter, we study the natural convection heat transfer in a saturated porous medium confined in a vertical annular porous medium. In this study Finite Element Method (FEM) has been used to solve governing partial differential equations. Results are presented interms of average Nusselt number (Nu), streamlines and Isothermal lines for various values of Rayleigh number (Ra), Cone angle (CA) and Radius ratio (Rr).