Natural Convection Non-Newtonian EMHD Dissipative Flow Through a Microchannel Containing a Non-Darcy Porous Medium: Homotopy Perturbation Method Study

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 third-grade 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.

Automated summary

This article focuses on the thermal flow problem in microchannels and proposes a mathematical model. The model is validated using numerical methods. The study finds that an increase in the thermal Grashof number and electric field parameter enhances the velocity, the Brinkman number and magnetic interaction number increase the temperature, and the Nusselt number is elevated with several parameters.