A COMPREHENSIVE REVIEW ON NON-NEWTONIAN FLUIDS IN POROUS MEDIA UNDER LTNE MODEL

The study of non-Newtonian fluid flow and heat transfer in porous media under local thermal non-equilibrium (LTNE) conditions has become an important interdisciplinary research area due to its applications in geothermal systems, enhanced oil recovery, biomedical engineering, polymer processing, thermal insulation, catalytic reactors, energy storage devices, and chemical industries. Unlike Newtonian fluids, non-Newtonian fluids exhibit complex rheological characteristics such as viscoelasticity, shear thinning, shear- thickening, yield stress, and microstructural effects. Simultaneously, the classical local thermal equilibrium (LTE) assumption often fails in practical porous systems involving high heat fluxes, low porosity, rapid thermal transients, or large thermal conductivity differences between fluid and solid phases. Consequently, LTNE models employing separate energy equations for the fluid and solid phases provide a more realistic thermal framework. This review presents a detailed and critical survey of the existing literature on non-Newtonian fluids in porous media under LTNE conditions. The review discusses major rheological fluid models including Maxwell, Oldroyd-B, Jeffrey, Casson, power-law, micropolar, couple-stress, Williamson, Carreau, and nano-fluid models. The effects of visco-elasticity, anisotropy, magnetic fields, rotation, chemical reactions, double diffusion, internal heat generation, and Darcy-Brinkman corrections on convective instability and heat transfer are extensively analyzed. Analytical, numerical, and experimental approaches are summarized, and the role of important parameters such as conductivity ratio, Darcy number, interphase heat transfer coefficient, relaxation parameter, porosity, and thermal anisotropy is discussed in depth. Current challenges and future research opportunities are also identified.