LINEAR AND NONLINEAR STABILITY ANALYSIS OF AN ANISOTROPIC FLUID-SATURATED POROUS MEDIUM WITH THROUGHFLOW USING THE LTNE MODEL

The objective of this study is to examine how throughflow influences the stability of an anisotropic, fluid-saturated porous medium subjected to bottom heating, under the condition of local thermal nonequilibrium between the fluid and solid phases. The mathematical model with anisotropic thermal conductivity and permeability properties is formulated using two energy equations for the fluid and the solid phases in this study. Linear instability analysis is performed using the normal mode approach to determine the threshold for the onset of instability within the system. Additionally, a nonlinear stability analysis is carried out using the energy method. The Galerkin method is employed to calculate the critical Rayleigh number and also the corresponding wave numbers numerically for various values of throughflow (Pe), porosity-modified conductivity ratio (γ), the interphase heat transfer coefficient (H), anisotropic permeability parameter (ζ), the anisotropic thermal parameter for the fluid phase (ηf), and the solid phase (ηs). The parameters ζ, ηf , ηs, and Pe have a stabilizing effect on the system. The critical Rayleigh number becomes independent at H ⟶ 0 of both γ and η2. The convection cells reduce in size as the upward throughflow increases. This investigation highlights the potential existence of subcritical regions of instability.