Performance of Asymmetrically Heated Extended Surface With Temperature Dependent Thermal Conductivity

The effect of temperature dependent thermal conductivity on the performance of an asymmetrically heated extended surface which is commonly encountered in compact heat exchangers is studied both analytically and numerically. The surface is assumed to extend between two primary surfaces at different temperatures and to operate in a convective environment. The nonlinear differential equation governing the thermal performance of the extended surface is solved by carrying out a perturbation analysis in which the perturbation parameter is the dimensionless measure of thermal conductivity variation with temperature. Two-term analytical solutions for the temperature distribution and the convective heat dissipation are presented. The problem is also solved numerically for a range of conventional fin parameter, thermal asymmetry parameter, and thermal conductivity-temperature variation parameter to assess the accuracy of the perturbation solutions. Graphical results illustrating the effect of these parameters on the temperature distribution, heat transfer rates from the end primary surfaces, and the total heat transfer from the extended surface are provided and discussed. For the thermal conductivity variations encountered in compact heat exchangers, the two-term perturbation solutions are accurate with 2% of the numerical solutions.