Analytical study of thermal transport in periodic pressure-driven flow of a Newtonian fluid through a porous channel: Brinkman–Forchheimer model

The present study provides a theoretical analysis of the heat transport in a periodic, pressure-driven flow of a Newtonian fluid through a porous channel by employing a variable permeability model. The time-dependent Brinkman–Forchheimer and thermal equations govern the unsteady flow of a Newtonian fluid through a porous channel. The governing equations constitute a set of nonlinear partial differential equations arising from the inclusion of the unsteady (time-dependent) terms and the nonlinear inertial effects. The regular and singular perturbation techniques with matched asymptotic expansions are employed to derive the asymptotic solutions of the governing equations. A detailed analysis is performed graphically to examine the effect of key parameters such as porous medium parameters (e.g., permeability and Forchheimer number) and time variations on critical hydrodynamic and thermal quantities, including axial velocity, volumetric flow rate, flow resistance, wall shear stress, and temperature. To validate the parametric analysis, the NDSolve command in Mathematica software is employed to numerically verify the accuracy of the obtained asymptotic findings. The validity of the present asymptotic solutions is further established by demonstrating excellent agreement with previously reported results in limiting or special cases. A noteworthy observation from the analysis is that increasing the Forchheimer number and the variable permeability parameter results in a noticeable reduction in the flow rate, wall shear stress, and temperature distribution, where the effect is particularly pronounced when the Darcy number is small. A decrease in the temperature profile is noted as the viscosity ratio parameter increases, with the effect being more prominent at the crest compared to the trough for higher values of the Darcy number. A significant and distinctive contribution of the present investigation is the derivation of asymptotic solutions for both the flow and thermal transport equations, modeled using the Brinkman–Forchheimer formulation.