A vectorized finite-difference code has been developed for the Cray-2 supercomputer which has the capability of simulating a wide class of three-dimensional coupled conduction-convection flows. This program numerically solves the transient form of the Navier-Stokes equations of motion for laminar flow using the vorticity-vector potential method. One problem that has been considered is three-dimensional natural convection from a heated horizontal cylinder with an attached circular conducting fin array. Numerical solutions have been obtained for a Rayleigh number of 106 and a Prandtl number of 5. A parametric study has been performed by varying the fin length, fin spacing, fin thickness, and the fin conductivity parameter. Plots showing the local surface heal flux distribution, temperature distributions, and flow fields were developed using color graphics packages available on the Cray-2 that revealed the existence of very complex fin-cylinder interactions. The local heat flux in the upper section of the fins is predicted to reverse direction under certain operating conditions. The integrated results indicated that for a particular fin material and thickness, an optimum fin spacing and length exist for which the total heat transfer per unit cylinder length is a maximum.