Chaotic Cattaneo-LTNE porous convection

Abstract

The chaotic convection in a porous medium has been studied with a local thermal nonequilibrium (LTNE) model and hyperbolic-type heat transport equation in the solid arising due to Cattaneo heat flux law. The Brinkman-extended Darcy model is considered to describe the flow in a porous medium. A system of autonomous nonlinear ordinary differential equations is derived by using a truncated double Fourier series expansion such that the linear stability theory results are the same as those for the full two-dimensional problem. The stability of equilibrium points of the system is discussed in detail for the governing parameters involved therein. The transition to chaos in different phase planes and the transient behavior of heat transfer are analyzed by solving the model equations numerically using the Runge-Kutta-Fehlberg technique. The effect of increasing scaled solid thermal relaxation time parameter is to speed up the transition to chaos and to decrease the heat transfer.