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.

Variable thermal conductivity in context of Green‐Naghdi theory of thermo‐microstretch solids

“…Abouelregal [29] derived a new mathematical model for thermoelasticity with a fractional derivative of the classical Fourier law of thermal conductivity. Zhang et al [30] discussed the electro-magneto-hydrodynamic non-Newtonian natural convection through a vertical parallel plate duct containing an isotropic, homogenous non-Darcian porous medium. Abouelregal et al [31] presented the governing equations based on the nonlocal model and Euler-Bernoulli beam theory.…”

“…Zhang et al. [30] discussed the electro‐magneto‐hydrodynamic non‐Newtonian natural convection through a vertical parallel plate duct containing an isotropic, homogenous non‐Darcian porous medium. Abouelregal et al.…”

Artificial neural network simulation and sensitivity analysis for optimal thermal transport of magnetic viscous fluid over shrinking wedge via RSM

“…Gaffar et al (2017) examined the flow of non-Newtonian fluid with mixed convection and non-isothermal effects over a wedge. Numerous investigations on MHD flow in electrically conducting fluids were discussed by different researchers, such as Ali (2022), Elghabaty and Abdel-Rahman (1988), Hamid and Khan (2018), Hussain et al (2022a), Hayat (2017), Sharma et al (2022), Srinivasacharya (2015) and Zhang et al (2022), because of its importance in applied science, manufacturing and industrial applications. The investigation of heat transport phenomena in boundary layer flow over a porous wedge was examined by Koh and Hartnett (1961).…”

Mixed convection Casson polymeric flow from a nonlinear stretching surface with radiative flux and non‐Fourier thermal relaxation effects: Computation with CSNIS

“…There are different numerical methods (see refs. [34][35][36][37][38]) that can be used to solve such kind of problems, but the used numerical method has advantages over other numerical methods. In the proposed technique, we transform the domain of the proposed problem to [−1,1].…”