Fluid Flow and Heat Transfer in a Tube Partially Filled with Anisotropic Porous Medium under LTNE Conditions: Application to Cooling Systems

In microreactors and electronic cooling systems, fluid flow through tubes partially filled with a porous medium provides more effective thermal management than fully porous tubes. Analytical studies on such systems, particularly with anisotropic porous media under local thermal non-equilibrium (LTNE) conditions, are limited. In this article, the porous medium occupies the outer core, while the inner region contains a clear fluid with uniform wall heat flux. Flow is described by the Darcy-Brinkman-Forchheimer model in the porous domain and the Stokes equations in the clear region, coupled with a two-equation LTNE energy model. A numerical algorithm based on shooting and searching techniques is employed to address the nonlinearity from the Forchheimer term and handle general anisotropic permeability. The method is validated against asymptotic solutions for small and large Darcy numbers, corresponding to singular and regular perturbation limits, where Prandtl's matching condition connects inner and outer solutions. It is found that permeability ratio and orientation angle strongly influence velocity and temperature distributions, providing insights for optimizing compact thermal management systems with controlled porous-fluid interfaces.