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Finite Element Solution for MHD Flow of Nanofluids with Heat and Mass Transfer through a Porous Media with Thermal Radiation, Viscous Dissipation and Chemical Reaction Effects

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Incompressible viscous fluids Partial differential equations

Published online by Cambridge University Press:  18 January 2017

Shafqat Hussain
Shafqat Hussain*
Affiliation:
Department of Mathematics, Capital University of Science & Technology, Islamabad, Pakistan
*
*Corresponding author. Email:shafqat.hussain@cust.edu.pk (S. Hussain)
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Abstract

In this paper, the problem of magnetohydrodynamics (MHD) boundary layer flow of nanofluid with heat and mass transfer through a porous media in the presence of thermal radiation, viscous dissipation and chemical reaction is studied. Three types of nanofluids, namely Copper (Cu)-water, Alumina (Al 2 O 3)-water and Titanium Oxide (TiO 2)-water are considered. The governing set of partial differential equations of the problem is reduced into the coupled nonlinear system of ordinary differential equations (ODEs) by means of similarity transformations. Finite element solution of the resulting system of nonlinear differential equations is obtained using continuous Galerkin-Petrov discretization together with the well-known shooting technique. The obtained results are validated using MATLAB “bvp4c” function and with the existing results in the literature. Numerical results for the dimensionless velocity, temperature and concentration profiles are obtained and the impact of various physical parameters such as the magnetic parameter M, solid volume fraction of nanoparticles 𝜙 and type of nanofluid on the flow is discussed. The results obtained in this study confirm the idea that the finite element method (FEM) is a powerful mathematical technique which can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering.

Keywords

Boundary layer flownanofluidmagnetohydrodynamicsstretching sheetporous mediumheat and mass transferfinite element method (FEM)continuous Galerkin-Petrov (cGP) discretizationnumerical comparison

MSC classification

Secondary: 35A25: Other special methods 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 76D05: Navier-Stokes equations
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 4 , August 2017 , pp. 904 - 923
Copyright
Copyright © Global-Science Press 2017 

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