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, 2018)
In this paper, the problem of magnetohydrodynamics (MHD) boundarylayer flow of nanofluid with heat and mass transfer through a porous media in thepresence of thermal radiation, viscous dissipation and chemical reaction is studied.Three types of nanofluids, namely Copper ($Cu$)-water, Alumina ($Al_2O_3$)-water and TitaniumOxide ($TiO_2$)-water are considered. The governing set of partial differentialequations of the problem is reduced into the coupled nonlinear system of ordinary differentialequations (ODEs) by means of similarity transformations. Finite element solutionof the resulting system of nonlinear differential equations is obtained using continuousGalerkin-Petrov discretization together with the well-known shooting technique.The obtained results are validated using MATLAB "bvp4c" function and withthe existing results in the literature. Numerical results for the dimensionless velocity,temperature and concentration profiles are obtained and the impact of various physicalparameters 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 thisstudy confirm the idea that the finite element method (FEM) is a powerful mathematicaltechnique which can be applied to a large class of linear and nonlinear problemsarising in different fields of science and engineering.