Regularity and analysis of solutions for a MHD flow with a p-Laplacian operator and a generalized Darcy–Forchheimer term

Abstract

The modeling of fluid flows with a p-Laplacian operator has attracted the interest of researchers to describe non-Newtonian fluids. One of the main reasons is the possibility of obtaining values for p (in the p-Laplacian) based on experimental settings. The main contributions of our study consist in providing analytical assessments of weak solutions, together with a numerical validating analysis, to a one-dimensional fluid in magnetohydrodynamics (MHD) flowing in porous media. We define a new Darcy–Forchheimer term and a generalized form of a constitutive kinematic that provides a p-Laplacian operator. Firstly, we discuss about the regularity and boundedness of weak solutions to support the existence and uniqueness analyses. Afterward, we explore solutions based on a selfsimilar profile. The resulting elliptic equation is solved based on the analytical perturbation technique. Eventually, a numerical analysis is provided with the intention of validating the analytical solution obtained. As a remarkable outcome, we establish minimum values in the selfsimilar variable for which the global distances between the analytical and the numerical solutions are below 10 ^− 2 and 10^− 3. Indeed, the convergence between both solutions is given under an asymptotic approach, where the decaying rates in the obtained solutions are sufficiently close