Natural convection non-Newtonian EMHD dissipative flow through a microchannel containing a non-Darcy porous medium: Homotopy perturbation method study

Bhatti, MM; Beg, OA; Ellahi, R; Abbas, T

Abstract

Non-Newtonian thermal processing in microchannel systems, is emerging as a
major area of interest in modern thermal engineering. Motivated by these developments, in
the current paper, a mathematical model is developed for laminar, steady state fully
developed viscoelastic natural convection electro-magnetohydrodynamic (EMHD) flow in a
microchannel containing a porous medium. Transverse magnetic field and axial electrical
field are considered. A modified Darcy-Brinkman-Forchheimer model is deployed for porous
media effects. Viscous dissipation and Joule heating effects are included. The primitive
conservation equations are rendered into dimensionless coupled ordinary differential
equations with associated boundary conditions. The nonlinear ordinary differential boundary
value problem is then solved using He’s powerful homotopy perturbation method (HPM).
Validation with the MATLAB bvp4c numerical scheme is included for Nusselt number.
Graphical plots are presented for velocity, temperature and Nusselt number for the influence
of emerging parameters. Increment in thermal Grashof number and electric field parameter
enhance velocity. Increasing Brinkman number and magnetic interaction number boost
temperatures and a weak elevation is also observed in temperatures with increment in thirdgrade non-Newtonian parameter and Forchheimer number. Nusselt number is also elevated
with thermal Grashof number, Forchheimer number, third-grade fluid parameter, Darcy
parameter, Brinkman number and magnetic number.

Citation

Bhatti, M., Beg, O., Ellahi, R., & Abbas, T. (2022). Natural convection non-Newtonian EMHD dissipative flow through a microchannel containing a non-Darcy porous medium: Homotopy perturbation method study. Qualitative Theory of Dynamical Systems, 21, https://doi.org/10.1007/s12346-022-00625-7

• Journal Article Type: Article
• Acceptance Date: Jun 8, 2022
• Publication Date: Jul 11, 2022
• Deposit Date: Jul 13, 2022
• Publicly Available Date: Jul 12, 2023
• Journal: Qualitative Theory of Dynamical Systems
• Print ISSN: 1575-5460
• Electronic ISSN: 1662-3592
• Publisher: Springer Verlag
• Volume: 21
• DOI: https://doi.org/10.1007/s12346-022-00625-7
• Publisher URL: https://doi.org/10.1007/s12346-022-00625-7