Nonlinear thermal analysis of two-dimensional materials with memory

A nonlinear hyperbolic heat transport equation has been proposed based on the Cattaneo model without mechanical effects. We analyze the two-dimensional Maxwell-Cattaneo-Vernotte heat equation in a medium subjected to homogeneous and non-homogeneous boundary conditions and with thermal conductivity and relaxation time linearly dependent on temperature. Since these nonlinearities are essential from an experimental point of view, it is necessary to establish an effective and reliable way to solve the system of partial differential equations and study the behavior of temperature evolution. A numerical scheme of finite differences for the solution of the two-dimensional non-Fourier heat transfer equation is introduced and studied. We also investigate the attributes of the numerical method from the aspects of stability, dissipation and dispersive errors.