Numerical investigation for a hyperbolic annular fin with temperature dependent thermal conductivity

An annular fin of hyperbolic profile with temperature dependent thermal conductivity is studied by pseudospectral method. Graphs illustrating the effect of fin dimensions, surface convection characteristics and the thermal conductivity parameter on the thermal performance of the fin are presented and discussed. A comparison of the obtained numerical results is made with the closed form analytical solution available in the literature for the case of constant thermal conductivity. This comparison confirms the high accuracy of numerical results. When the thermal conductivity increases with temperature, the effect is to elevate both the temperature distribution in the fin and the fin efficiency. The converse is true when the thermal conductivity decreases with temperature.