The optimal dimensions of annular fins of constant and variable cross sectional area when subjected to both heat and mass transfer were investigated by a numerical scheme. A non-linear model representing both heat and mass transfer mechanisms was solved using finite difference over-relaxation scheme. Numerical solutions are obtained for the dimensionless heat transfer rate for completely wet conditions as a function of important dimensionless parameters (u,v,w) for annular fins. The results are presented in a graphical form as well as regression equations for rectangular, triangular, convex and concave parabolic annular fins. It is shown that these dimensionless parameters represent modified version of fin parameter(moL), non-dimensional fin material volume and fin base ratio (outer radius of tube to thickness of fin at its conjunction with tube). Keeping the two dimensionless parameters constant (u,v) and considering w as the only independent variable, the maximum heat dissipated from the fin is obtained.