Variable thermal properties and thermal relaxation time in hyperbolic heat conductionNumerical 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 (Crank-Nicolson 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.
Document ID
19890037898
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Glass, David E. (NASA Langley Research Center; Analytical Services and Materials, Inc. Hampton, VA, United States)
Mcrae, D. Scott (North Carolina State University Raleigh, United States)