Volume 9, Issue 4
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

Adv. Appl. Math. Mech., 9 (2017), pp. 904-923.

Published online: 2018-05

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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 ($Al_2O_3$)-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 flow, nanofluid, magnetohydrodynamics, stretching sheet, porous medium, heat and mass transfer, finite element method (FEM), continuous Galerkin-Petrov (cGP) discretization, numerical comparison.

35A25, 65M60, 76D05

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@Article{AAMM-9-904, author = {Shafqat Hussain , }, title = {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}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {4}, pages = {904--923}, 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 ($Al_2O_3$)-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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m793}, url = {http://global-sci.org/intro/article_detail/aamm/12182.html} }
TY - JOUR T1 - 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 AU - Shafqat Hussain , JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 904 EP - 923 PY - 2018 DA - 2018/05 SN - 9 DO - http://doi.org/10.4208/aamm.2014.m793 UR - https://global-sci.org/intro/article_detail/aamm/12182.html KW - Boundary layer flow, nanofluid, magnetohydrodynamics, stretching sheet, porous medium, heat and mass transfer, finite element method (FEM), continuous Galerkin-Petrov (cGP) discretization, numerical comparison. AB -

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 ($Al_2O_3$)-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.

Shafqat Hussain. (2020). 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. Advances in Applied Mathematics and Mechanics. 9 (4). 904-923. doi:10.4208/aamm.2014.m793
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