Solutions for heat conduction in a solid with temperature dependent thermal conductivity

Abstract

The study of heat transfer can be categorized into three different modes; they are conduction, convection and radiation. The project focused specifically on heat transfer by conduction. Heat conduction is the transfer of internal energy within a solid or a stationary fluid due to a temperature difference. Because of the temperature dependence in thermal conductivity, the heat conduction equation becomes a nonlinear partial differential equation. The author explored solutions for heat conduction in a solid with temperature dependent thermal conductivity by means of the Fourier series for such problems. Solutions were modeled using MATLAB to illustrate the temperature contour of a solid subjected to different thermal conductivities and boundary conditions. Comparisons were made between the results to identify the effect of temperature dependence in thermal conductivity. The author also discussed the importance of temperature dependence in thermal conductivity in real world applications. The report was concluded with the insights gained from the project.