Transient heat diffusion with temperature-dependent conductivity and time-dependent heat transfer coefficient (Q955973)

The author considers an unsteady nonlinear heat diffusion problem modeling thermal energy storage in a medium with power law temperature-dependent thermal conductivity and subjected to a convective heat transfer to the surrounding enviromment at the boundary. In the description of the boundary-value problem he uses a rectangular cylindrical or spherical coordinate a system. Using the theory of Lie algebra he constructs the one-dimensional optimal system. Next, the invariant solution for such a system of equation is constructed. At the end, some graphical representation of the invariant solution is given. The invariant solution shows thermal decay due to heat losses by convection to the surrounding environment.