Numerical results of heat transfer rates and flow fields in a vertical annulus with longitudinal fins for various parameters [Rayleigh number (10(3) less than or equal to Ra less than or equal to 10(6)), radius ratio (1 less than or equal to kappa less than or equal to 5), fin ratio 0.25 less than or equal to FR less than or equal to 0.75, number of fins, and fin thickness angle (delta=2 degrees or 6 degrees)] have been obtained. Placing fins of fin ratio 0.5 and fin thickness angle 6 degrees on the inner cylinder of an annulus with radius ratio 2 increases the heat transfer by as much as 70%. For fixed Rayleigh number, radius ratio, aspect ratio, fin ratio and fin thickness angle, the heat transfer rate is maximum for a specific number of fins. The heal transfer rates increase as the fin ratio and radius ratio increase. In addition, the heat transfer rates decrease if the aspect ratio and the fin thickness angle increase. The maximum Nusselt number and optimum number of fins have been obtained as functions of various parameters. Heat transfer correlations have been provided in the range of the parameters considered.