Analysis of local thermal non-equilibrium effects in three-dimensional flow over a stretching sheet embedded in a porous medium

This study conducts a numerical analysis of steady, three-dimensional laminar flow and related heat transfer of an incompressible viscous fluid over a stretching surface embedded in a homogeneous porous medium, considering local thermal non-equilibrium (LTNE) conditions. Unlike traditional local thermal equilibrium (LTE) assumptions, the LTNE framework independently models the temperature distributions of the fluid and solid phases, facilitating a more precise depiction of inter-phase heat transfer. The governing partial differential equations, generated using an extended Darcy-Brinkman-Forchheimer technique, are transformed into a set of non-linear ordinary differential equations (ODEs) by similarity transformations. The Keller-box method, recognized for its stability and efficacy in boundary layer flow problems, is employed to solve these equations. The impact of key dimensionless parameters, including the three-dimensional velocity ratio ((Formula presented.)), permeability parameter ((Formula presented.)), Prandtl number ((Formula presented.)), inter-phase heat transfer coefficient ((Formula presented.)), and porosity-scaled conductivity ((Formula presented.)), on the flow and temperature profiles is systematically analyzed. The results reveal the influence of LTNE conditions on thermal and hydrodynamic behavior and demonstrate the conditions under which the system transitions toward LTE.