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

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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.

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Acknowledgements

The authors would like to thank the anonymous reviewers and the editor for their comments and kindness in reviewing the article.

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Authors and Affiliations

  1. Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad, Pakistan

    Saeed ur Rahman

  2. Department of Mathematics and Education, Universidad a Distancia de Madrid, 28400, Madrid, Spain

    José Luis Díaz Palencia

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Correspondence to José Luis Díaz Palencia.

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Rahman, S.u., Palencia, J.L.D. Regularity and analysis of solutions for a MHD flow with a p-Laplacian operator and a generalized Darcy–Forchheimer term. Eur. Phys. J. Plus 137, 1328 (2022). https://doi.org/10.1140/epjp/s13360-022-03555-0

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