Computational study of non-similar magneto-convection from an isothermal surface in saturated porous media with induction effects

Beg, OA ORCID: https://orcid.org/0000-0001-5925-6711, Vasu, B, Beg, TA, Leonard, HJ, Jouri, W, Kadir, A and Gorla, RSR 2021, 'Computational study of non-similar magneto-convection from an isothermal surface in saturated porous media with induction effects' , Computational Thermal Sciences . (In Press)

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Abstract

We study theoretically and numerically the forced convection magnetohydrodynamic (MHD) boundary layer flow of an electrically conducting fluid along a non-conducting isothermal wall adjacent to a porous medium, with magnetic field aligned with the plate direction. Induced magnetic field effects are incorporated. The transformed hydrodynamic, thermal and magnetic boundary layer equations are solved using the Chebyschev spectral collocation method with a MATLABbased code, MAGNASPEC. Super-Alfven flow is considered for which the magnetic force parameter () has values less than unity, following the approach of Glauert [J. Fluid Mechanics, 10, 276-288 (1956)). The effects of Darcian porous drag force parameter (ND), magnetic Prandtl number (Prm), magnetic force number (), Prandtl number (Pr) and also various thermal boundary conditions at the wall, on the distribution of dimensionless velocity (f/), dimensionless induced magnetic field (g/ i.e. gradient of the magnetic stream function, g), dimensionless temperature (), shear stress function ( 2 f/ 2 ), and wall temperature gradient function (/), are investigated. Increasing ND values decelerate the flow and decrease temperatures through the boundary layer but increase the induced magnetic field values. Increasing magnetic Prandtl number (Prm) slightly reduces the velocity in the boundary layer and similarly has a weak effect in reducing the wall shear stress. No noticeable response is computed for the effect of magnetic Prandtl number on the temperature distribution; however, increasing Prm values are found to reduce magnetic induction values near the plate surface but enhance them further towards the freestream. An increase in the magnetic force number, (which expresses the ratio of the square of the Alfven speed to the free stream velocity) is shown to fractionally reduce the shear stress but considerably increases the induced magnetic field values along the entire plate length i.e. with -coordinate. Negligible modification is witnessed for the surface temperature gradient (/) with a large increase in  from 0.01 to 0.5. The present spectral solutions are also benchmarked with Sparrow-Quack-Boerner local non-similarity method (LNM) and He’s variational iteration method (VIM) and furthermore demonstrate excellent correlation with steady state nonpermeable (purely fluid) finite difference solutions in the literature. Applications of the study arise in materials processing and plasma aerodynamics.

Item Type:	Article
Schools:	Schools > School of Computing, Science and Engineering
Journal or Publication Title:	Computational Thermal Sciences
Publisher:	Begell House Publishers
ISSN:	1940-2503
Depositing User:	OA Beg
Date Deposited:	29 Apr 2021 11:56
Last Modified:	16 Feb 2022 07:06
URI:	http://usir.salford.ac.uk/id/eprint/60132

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