Projection Methods for the Finite Element Solution of the Dual-Porosity Model in Variably Saturated Porous Media

2010 ◽  
pp. 97-125 ◽  
Author(s):  
Giuseppe Gambolati ◽  
Mario Putti ◽  
Claudio Paniconi
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Projection Methods ◽  
Finite Element Solution ◽  
Dual Porosity ◽  
Saturated Porous Media ◽  
Element Solution ◽  
Dual Porosity Model ◽  
Porosity Model

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

2017 ◽  
Vol 9 (4) ◽  
pp. 904-923 ◽  
Author(s):  
Shafqat Hussain
Keyword(s):  
Mass Transfer ◽  
Finite Element ◽  
Porous Media ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Heat And Mass Transfer ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Finite Element Solution ◽  
Element Solution

AbstractIn 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 (Al2O3)-water and Titanium Oxide (TiO2)-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 parameterM, 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.

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