Local Thermal Nonequilibrium and Anisotropy Effects on Convective Instability of Maxwell Fluid

Thermal convection in fluid-saturated porous media has attracted considerable attention due to its wide-ranging applications in engineering and geophysical systems, such as geothermal energy extraction, underground contaminant transport, nuclear waste disposal, and heat exchangers. In these systems, buoyancy-driven flow arises when a temperature gradient is imposed across the medium. The onset of convection is primarily governed by the Rayleigh number, which quantifies the balance between thermal driving forces and dissipative effects, including viscosity and thermal diffusion. Conventional studies often assume local thermal equilibrium (LTE) between the solid matrix and the saturating fluid. However, this assumption becomes inadequate in many practical situations where the heat exchange between the two phases is not instantaneous. To overcome this limitation, the concept of local thermal non-equilibrium (LTNE) has been introduced, wherein separate energy equations are employed for the solid and fluid phases, allowing a more realistic representation of interphase heat transfer. Moreover, porous media encountered in practical applications are frequently anisotropic, with permeability and thermal conductivity varying with direction. Such anisotropy significantly influences both fluid flow and heat transport characteristics. The complexity of the problem is further enhanced when non-Newtonian fluids, particularly Maxwell fluids, are considered. Due to their viscoelastic nature, these fluids introduce additional parameters, such as stress relaxation time, which play a crucial role in determining the stability behavior of the system. Therefore, a comprehensive analysis that simultaneously incorporates LTNE effects, anisotropy, and non-Newtonian fluid behavior is essential for accurately predicting the onset of convection and gaining deeper insight into the associated stability mechanisms in porous media systems.