The purpose of this paper is to numerically investigate the effects of some geometric parameters and flow variables on heat transfer augmentation in annuli with equi-spaced internal longitudinal fins along the external walls. A fully developed flow and a constant thermal boundary condition of uniform heat flux at the walls of the pipe were assumed. Continuity, momentum and energy transport equations were adopted for the solutions of the problem. A Q-BASIC code was written based on the finite difference scheme generated. Numerical experiments were conducted to ascertain the effects of Reynolds number Re, radius ratio, R.R, Prandtl number Pr, fin height H, and pipe inclination, on the rate of heat transfer and fluid flow. The results obtained show that for 50 ≤ Re ≤ 500, total Nusselt number NuT increases with increase in Re while for Re > 500, there was no significant increase in NuT. Nusselt number, average velocity and bulk temperature of the fluid increase with increasingin the range 0° ≤ ≤ 75° but for the range 75°≤  ≤ 90°  the effect is negligible. For R.R > 0.6, the heat transfer was observed to be almost independent of R; therefore for economic purposes, heat exchangers similar to the configuration studied should be run at a low pumping power. A numerical study was done to validate the program by test running it for the finless annuli for similar boundary conditions; the results obtained in the present work show the same trend as that of Kakac and Yucel.