In the present work, the convective flow and thermal pattern, associated heat transport rates of buoyant convection in an annular geometry is theoretically analyzed. The inner cylindrical wall has finite thickness and is kept at high temperature, while the outer cylindrical wall is held at low temperature. The vorticity-stream function form of model equations are solved using FDM based on ADI and SLOR techniques. The numerical simulations for various parameters are presented. In particular, this analysis focused on the effects of conjugate heat transport characteristics.