Lorenz and Ginzburg-Landau equations for thermal convection in a high-porosity medium with heat source

AbstractThe paper presents an investigation of a weakly non-linear stability analysis of thermal convection in a porous medium using the Lorenz model. The Ginzburg-Landau model is then obtained from the Lorenz model using which an expression for Nusselt number, Nu, is obtained in closed form. Such a procedure of obtaining an analytical solution is reported for the first time in the literature. It is found that heat source enhances amount of heat transport whereas heat sink diminishes the same. The influence of the thermal and mechanical anisotropies on Nu is to oppose each other in the case of both heat source and heat sink. It is observed that the anisotropic effects are prevalent only for short time whereas heat source(sink) has a sustained influence. Several limiting cases are obtained from the present study