Numerical modeling of hyperbolic heat conduction using an explicit TVD scheme

This dissertation presented a numerical solution to two-dimensional hyperbolic heat conduction (HHC) equations using a second-order explicit TVD scheme. For simplicity and comparison, the governing equations were nondimensionalized. The governing equations were also transformed from the physical coordinates to the computational coordinates, so that hyperbolic heat conduction problems of irregular geometry can be solved numerically by the present TVD scheme. The numerical solution of the HHC equations was extended from the Cartesian coordinates to the axisymmetric coordinates, in order to deal with a situation in which a solid surface is subjected to an axisymmetric heat source, or a situation in which heat is transported by wave propagation in an axisymmetric body.; In addition, the influence of temperature-dependent material properties on the thermal wave propagation was investigated in the dissertation. The HHC equations become nonlinear due to the temperature-dependent material properties, and were expressed in a vector form by assuming material properties locally constant. Consequently the thermal wave propagates at a changing speed, and Roe's average was used to calculate the wave speed at the interfaces of control volumes.; The thermal wave propagation in composite materials was studied as well by non-dimensionalize HHC equations in a way such that the material properties can be explicitly appeared in the equations. The interfacial calculations were performed by keeping both temperature and heat flux continuous at the interfaces.; Complicated boundary conditions such as convection and radiation were considered. For convective boundary the unknown temperature was calculated explicitly; for radiation boundary Newton's iteration method was applied to find the boundary temperature. Several numerical examples were employed to investigate the thermal wave phenomenon. As expected, wave reflection was observed due to insulated boundary, converging geometry, and material interface, and wave expansion was shown because of diverging geometry.