http://arxiv.org/abs/2104.08475
Analytic solutions to the nonlinear radiation diffusion equation with an instantaneous point source for a non-homogeneous medium with a power law spatial density profile, are presented. The solutions are a generalization of the well known solutions for a homogeneous medium. It is shown that the solutions take various qualitatively different forms according to the value of the spatial exponent. These different forms are studied in detail for linear and non linear heat conduction. In addition, by inspecting the generalized solutions, we show that there exist values of the spatial exponent such the conduction front has constant speed or even accelerates. Finally, the various solution forms are compared in detail to numerical simulations, and a good agreement is achieved.
M. Krief
Tue, 20 Apr 2021
62/72
Comments: The following article has been accepted for publication in Physics of Fluids