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Numerical investigation of Dufour and Soret effects on unsteady MHD natural convection flow past vertical plate embedded in non-Darcy porous medium

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Abstract

The Dufour and Soret effects on the unsteady two-dimensional magnetohydrodynamics (MHD) double-diffusive free convective flow of an electrically conducting fluid past a vertical plate embedded in a non-Darcy porous medium are investigated numerically. The governing non-linear dimensionless equations are solved by an implicit finite difference scheme of the Crank-Nicolson type with a tridiagonal matrix manipulation. The effects of various parameters entering into the problem on the unsteady dimensionless velocity, temperature, and concentration profiles are studied in detail. Furthermore, the time variation of the skin friction coefficient, the Nusselt number, and the Sherwood number is presented and analyzed. The results show that the unsteady velocity, temperature, and concentration profiles are substantially influenced by the Dufour and Soret effects. When the Dufour number increases or the Soret number decreases, both the skin friction and the Sherwood number decrease, while the Nusselt number increases. It is found that, when the magnetic parameter increases, the velocity and the temperature decrease in the boundary layer.

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Abbreviations

B 0 :

magnetic induction

C :

concentration

c p :

specific heat at constant pressure

c s :

concentration susceptibility

Da :

Darcy number

D m :

coefficient of mass diffusivity

Du :

Dufour number

F :

Forchheimer coefficient

g :

gravitational acceleration

Gr c :

modified solutal Grashof number

Gr t :

thermal Grashof number

k e :

effective thermal conductivity of porous medium

K p :

permeability of porous medium

K t :

thermal diffusion ratio

M :

magnetic field parameter

Nu :

Nusselt number

Pr :

Prandtl number

Sc :

Schmidt number

Sh :

Sherwood number

Sr :

Soret number

T :

temperature

t :

time

T ∞ :

free stream temperature

T m :

mean fluid temperature

T w :

wall temperature

U,V :

dimensionless velocity components in X- and Y-directions, respectively

u,v :

velocity components in x- and y- directions, respectively

u 0 :

velocity of plate

X :

dimensionless spatial coordinate along plate

Y :

dimensionless spatial coordinate normal to plate

x :

spatial coordinate along plate

y :

spatial coordinate normal to plate

α e :

effective thermal diffusivity

Γ:

Forchheimer parameter

ρ :

fluid density

φ :

dimensionless concentration variable

θ :

dimensionless temperature variable

τ :

dimensionless time

ν :

effective kinematic viscosity of fluid

σ :

electrical conductivity of fluid

β c :

concentration expansion coefficient

β t :

thermal expansion coefficient

w:

conditions at wall

∞:

free stream conditions

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Authors and Affiliations

  1. Mechanical Engineering Department, Faculty of Engineering, Umm Al-Qura University, Makkah, Kingdom of Saudi Arabia

    M. Q. Al-Odat & A. Al-Ghamdi

  2. Mechanical Engineering Department, Al-Huson University College, Al-Balqa Applied University, Irbid, Jordan

    M. Q. Al-Odat

Authors
  1. M. Q. Al-Odat
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  2. A. Al-Ghamdi
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Correspondence to M. Q. Al-Odat.

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Al-Odat, M.Q., Al-Ghamdi, A. Numerical investigation of Dufour and Soret effects on unsteady MHD natural convection flow past vertical plate embedded in non-Darcy porous medium. Appl. Math. Mech.-Engl. Ed. 33, 195–210 (2012). https://doi.org/10.1007/s10483-012-1543-9

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  • DOI: https://doi.org/10.1007/s10483-012-1543-9

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