Modelling and nonclassical symmetry analysis of a complex porous media flow in a dilating channel

This investigation focuses on the symmetry analysis and explicit solution of a fluid flow inside a channel filled with a porous material. The walls of the channel are weakly permeable and dilating vertically. There is an inflow through the pores of the walls that develops flow within the channel. The configuration pertains to the fluid flow, exhibiting either injection or suction across the porous walls at an absolute velocity while experiencing uniform expansion or contraction. The entire flow dynamics is modelled by the Darcy–Brinkman equations. The classical and nonclassical symmetry analysis based on the invariance principle, brings a fourth-order nonlinear ordinary differential equation. The analytical solution is obtained by a double perturbation method, and the comparison is carried out with the numerical solution calculated using the shooting method. A stronger wall expansion pushes the mean-flow through the channel and strengthens the flow rate. The velocity profiles are much fuller for relatively larger Darcy numbers, and behave like a Hartmann flow for the smaller Darcy numbers. Notably, a flow reversal phenomenon is noticed for a suction flow with strong wall dilation rates. Moreover, this study explores a set of conservation laws for the governing model.