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Diffusion-Thermo and Radiation Effects on Unsteady MHD Flow Through Porous Medium Past an Impulsively Started Infinite Vertical Plate with Variable Temperature and Mass Diffusion

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Abstract

The objective of this study is to investigate diffusion-thermo (Dufour effect) and radiation effects on unsteady MHD free convection flow past an impulsively started infinite vertical plate with variable temperature and uniform mass diffusion in the presence of transverse applied magnetic field through porous medium. At time t > 0, the plate is given an impulsive motion with constant velocity u 0 in the vertical upward direction against to the gravitational field. At the same time, the plate temperature is raised linearly with time t and the level of concentration near the plate is raised to \({{C}_{\rm w}^{\prime}}\). A magnetic field of uniform strength B 0 is applied normal to the direction to the flow. The dimensionless governing equations are solved in closed form by Laplace transform technique. The effect of flow parameters on velocity, temperature, concentration, the rate of heat transfer and the rate of mass transfer are shown through graphs.

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Abbreviations

a*:

Absorption coefficient

B 0 :

External magnetic field

C′:

Species concentration

\({C_{\rm w}^{\prime}}\) :

Concentration of the plate

\({C_{\infty}^{\prime}}\) :

Concentration of the fluid far away from the plate

C :

Dimensionless concentration

C p :

Specific heat at constant pressure

C s :

Concentration susceptibility

g :

Acceleration due to gravity

Gr :

Thermal Grashof number

Gm :

Mass Grashof number

M :

Magnetic field parameter

Nu :

Nusselt number

Pr :

Prandtl number

q r :

Radiative heat flux in the y-direction

D m :

Coefficient of mass diffusivity

R :

Radiative parameter

Sc :

Schmidt number

T′:

Temperature of the fluid near the plate

\({T_{\rm w}^{\prime}}\) :

Temperature of the plate

\({T_{\infty}^{\prime}}\) :

Temperature of the fluid far away from the plate

t′:

Time

t :

Dimensionless time

u′:

Velocity of the fluid in the x′-direction

u 0 :

Velocity of the plate

u :

Dimensionless velocity

y′:

Co-ordinate axis normal to the plate

y :

Dimensionless co-ordinate axis normal to the plate

\({\kappa}\) :

Thermal conductivity of the fluid

α :

Thermal diffusivity

β :

Volumetric coefficient of thermal expansion

β * :

Volumetric coefficient of expansion with concentration

μ :

Coefficient of viscosity

ν :

Kinematic viscosity

ρ :

Density of the fluid

σ :

Electric conductivity

θ :

Dimensionless temperature

erf:

Error function

erfc:

Complementary error function

w:

Conditions on the wall

∞:

Free stream conditions

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Authors and Affiliations

  1. Department of Mathematics, University of Botswana, Private Bag 0022, Gaborone, Botswana

    J. Prakash

  2. Department of Mathematics, S.V. University, Tirupati, AP, India

    D. Bhanumathi & S. V. K. Varma

  3. Department of Mathematics, Sree Vidyanikethan Engineering College, Tirupati, AP, India

    A. G. Vijaya Kumar

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  1. J. Prakash
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  2. D. Bhanumathi
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  3. A. G. Vijaya Kumar
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  4. S. V. K. Varma
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Prakash, J., Bhanumathi, D., Vijaya Kumar, A.G. et al. Diffusion-Thermo and Radiation Effects on Unsteady MHD Flow Through Porous Medium Past an Impulsively Started Infinite Vertical Plate with Variable Temperature and Mass Diffusion. Transp Porous Med 96, 135–151 (2013). https://doi.org/10.1007/s11242-012-0078-x

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