Variable thermal properties and thermal relaxation time in hyperbolic heat conduction
Abstract
Numerical solutions were obtained for a finite slab with an applied surface heat flux at one boundary using both the hyperbolic (MacCormack's method) and parabolic (CrankNicolson method) heat conduction equations. The effects on the temperature distributions of varying density, specific heat, and thermal relaxation time were calculated. Each of these properties had an effect on the thermal front velocity (in the hyperbolic solution) as well as the temperatures in the medium. In the hyperbolic solutions, as the density or specific heat decreased with temperature, both the temperatures within the medium and the thermal front velocity increased. The value taken for the thermal relaxation time was found to determine the 'hyperbolicity' of the heat conduction model. The use of a time dependent relaxation time allowed for solutions where the thermal energy propagated as a high temperature wave initially, but approached a diffusion process more rapidly than was possible with a constant large relaxation time.
 Publication:

27th AIAA Aerospace Sciences Meeting
 Pub Date:
 January 1989
 Bibcode:
 1989aiaa.meetT....G
 Keywords:

 Conductive Heat Transfer;
 Hyperbolic Differential Equations;
 Relaxation Time;
 Thermodynamic Properties;
 CrankNicholson Method;
 Parabolic Differential Equations;
 Slabs;
 Specific Heat;
 Time Dependence;
 Fluid Mechanics and Heat Transfer