A General Telegraph-type Model for Heat Conduction with Self-similar Behaviour of Solutions
In our former studies we introduced a modified Fourier-Cattaneo law and derived a non-autonomous telegraph-type heat conduction equation which has desirable self-similar solution. Now we present a detailed in-depth analysis of this model and discuss additional analytic solutions for different parameters. The solutions have a very rich and interesting mathematical structure due to various special functions.
Keywords: Heat transfer, heat conduction, telegraph-type, self-similar solution