Numerical study of natural convection dissipative electro‐magnetic non‐Newtonian flow through a non‐Darcy channel

Abstract

Inspired by simulating duct thermal processing of novel functional polymers, a novel mathematical model is developed for buoyancy‐driven heat transfer in non‐Newtonian Williamson fluid flow in a vertical parallel plate duct containing a permeable medium, under mutually orthogonal electrical and magnetic fields. The momentum equation features electrical and magnetic body force terms, and the Darcy–Brinkman–Forchheimer mode is used for non‐Darcy effects. The energy balance equation includes thermal buoyancy (natural convection body force) and a modified viscous dissipation term. The conservation equations with associated boundary conditions are reframed into a system of coupled non‐linear ordinary differential equations via appropriate similarity transformations. The emerging dimensionless boundary value problem is then solved with a differential transform method (DTM). Validation of DTM solutions with the bvp4c MATLAB collocation solver is included. The influence of key parameters on velocity, temperature and average Nusselt number, are computed and illustrated graphically. With elevation in Weissenberg (non‐Newtonian) number, velocity and temperature are reduced. Velocity is suppressed with increasing non‐Darcian parameter (Forchheimer effect) whereas it is enhanced with increment in buoyancy convection parameter. With increasing Forchheimer, Darcy number and Hartmann number, the average Nusselt number is boosted whereas it is decreased with higher values of buoyancy convection parameter, Brinkman number and Weissenberg number. A strong reduction in temperature is computed with increment in ratio of Joule electrical heating to heat conduction parameter. DTM is shown to be an exceptionally accurate and versatile approach for simulating non‐Newtonian electromagnetohydrodynamic transport in ducts.