The motion of a fluid in the closed annular cavity formed by two concentric vertical cylinders with externally finned tube has been analysed by a numerical solutions of the equation of momentum and energy. For the calculation procedure, the fluid is assumed to have constant thermo-dynamic and transporties except for the density, which is temperature-dependent in the buoyancy term of the vertical momentum equation (Boussinesq approximation). The govern ins equations for velocity and temperature are solved by a finite difference technique which incoorporates a scheme for treating the coupled variables. Results are presented for a range of the Rayleigh number and for various values of the fin height and the number of fins.