Transient natural convection in a spherical enclosure containing a central core fluid and a porous shell fully saturated with the same fluid is investigated numerically. Simulations are based on a mathematical model consisting of the Navier-Stokes equations for the fluid region, the Brinkman equation for flow through porous media, a convective diffusion equation for energy transport, and the Boussinesq approximation for buoyancy. Solutions are obtained by a hybrid spectral method which combines the concepts of Galerkin and collocation methods with Legendre and Chebyshev polynomials employed as basis functions, respectively. Time advancement is accomplished by a combined Adams-Bashforth and backward Euler schemes. The numerical results exhibit remarkable effects along the porous-fluids interface;however, the overall heat flux is only sensitive to the thermal conductivity ratio of the solid matrix to the fluid.