Heat conduction analysis in solids with temperature dependent thermal conductivity

Abstract

Heat transfer (or heat) is thermal energy in transit due to a spatial temperature difference and it occurs through three different modes: conduction, convection, or radiation. In this project, heat transfer through conduction will be the focus as the author analyses the effects of temperature on thermal conductivity of a solid and consequently, the effects of heat conduction through the solid. Fourier’s law is the cornerstone of conduction heat transfer and it is an xpression that defines an important material property, the thermal conductivity [1]. To analyse the temperature dependence in thermal conductivity, the Heat Diffusion Equation is used and the resulting heat conduction equation changes from a linear partial differential equation to a non-linear partial differential equation. The non-linear partial differential equation with different thermal conductivity equations is then solved, modelled, and analysed through MATLAB by the author. The author analyses two cases in this project – Two-dimensional steady state heat conduction and One-dimensional time-dependent heat conduction. In this project, the author also highlights the importance of the temperature dependence in thermal conductivity in specific engineering applications such as metal quenching. The insights gained form this project was also concluded in this report.