Abstract
Analytical 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 that the conduction front has constant speed or even accelerates. Finally, various solution forms are compared in detail to numerical simulations, and a good agreement is achieved.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
