Linear and Non-Linear Stability Analysis for Thermal Convection in A Bidispersive Porous Medium with Thermal Non-Equilibrium Effects


The linear instability and nonlinear stability analyses are performed for the modelof bidispersive local thermal non-equilibrium flow. The effect of local thermal nonequilibriumon the onset of convection in a bidispersive porous medium of Darcytype is investigated. The temperatures in the macropores and micropores areallowed to be different. The effects of various interaction parameters on the stabilityof the system are discussed. In particular, the effects of the porosity modifiedconductivity ratio parameters, p  and s  , with the inter-phase momentum transferparameters 1  and 2  , on the onset of thermal Convection are also considered.Furthermore, the nonlinear stability boundary is found to be below the linearinstability threshold. The numerical results are presented for free-free boundaryconditions.