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Combined heat and mass transfer by mixed convection MHD flow along a porous plate with chemical reaction in presence of heat source

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Abstract

An exact and a numerical solutions to the problem of a steady mixed convective MHD flow of an incompressible viscous electrically conducting fluid past an infinite vertical porous plate with combined heat and mass transfer are presented. A uniform magnetic field is assumed to be applied transversely to the direction of the flow with the consideration of the induced magnetic field with viscous and magnetic dissipations of energy. The porous plate is subjected to a constant suction velocity as well as a uniform mixed stream velocity. The governing equations are solved by the perturbation technique and a numerical method. The analytical expressions for the velocity field, the temperature field, the induced magnetic field, the skin-friction, and the rate of heat transfer at the plate are obtained. The numerical results are demonstrated graphically for various values of the parameters involved in the problem. The effects of the Hartmann number, the chemical reaction parameter, the magnetic Prandtl number, and the other parameters involved in the velocity field, the temperature field, the concentration field, and the induced magnetic field from the plate to the fluid are discussed. An increase in the heat source/sink or the Eckert number is found to strongly enhance the fluid velocity values. The induced magnetic field along the x-direction increases with the increase in the Hartmann number, the magnetic Prandtl number, the heat source/sink, and the viscous dissipation. It is found that the flow velocity, the fluid temperature, and the induced magnetic field decrease with the increase in the destructive chemical reaction. Applications of the study arise in the thermal plasma reactor modelling, the electromagnetic induction, the magnetohydrodynamic transport phenomena in chromatographic systems, and the magnetic field control of materials processing.

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Abbreviations

B 0 :

uniform magnetic field

\( \bar b_x \) :

induced magnetic field along the x-direction

\( \bar C \) :

species concentration, kg·m−3

C f :

skin-friction coefficient

c p :

specific heat at a constant pressure, J·kg−1·K−1

\( \bar C_\infty \) :

species concentration in the free stream, kg·m−3

\( \bar C_w \) :

species concentration at the surface, kg·m−3

D :

chemical molecular diffusivity, m2·s−1

Ec :

Eckert number/dissipative heat

g :

acceleration due to gravity, m·s−2

Gr :

thermal Grashof number

Gr m :

mass Grashof number

J :

electric current density

K :

chemical reaction parameter

M :

Hartmann number/magnetic parameter

N :

number of cells

Nu :

Nusselt number

\( \bar p \) :

pressure, Pa

Pr m :

magnetic Prandtl number

Pr :

Prandtl number

Q :

heat source/sink

Sc :

Schmidt number

Sh :

Sherwood number

\( \bar T \) :

temperature, K

\( \bar T_w \) :

fluid temperature at the surface, K

\( \bar T_\infty \) :

fluid temperature in the free stream, K

u :

dimensionless velocity component in the x-direction, m·s−1

U :

dimensionless free stream velocity, m·s−1

ν 0 :

dimensionless suction velocity, m·s−1

α :

heat generation/absorption parameter

β :

coefficient of volume expansion for heat transfer, K−1

\( \bar \beta \) :

coefficient of volume expansion for mass transfer, K−1

η :

magnetic diffusivity

θ :

dimensionless fluid temperature, K

λ :

thermal conductivity, W·m−1·K−1

μ :

magnetic permeability, H·m−1

υ :

kinematic viscosity, m2·s−1

ρ :

density,kg·m−3

σ :

electrical conductivity, S·m−1

τ :

shearing stress, N·m−2

ϕ :

dimensionless species concentration, kg·m−3

w:

conditions on the wall

∞:

free stream conditions

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Authors and Affiliations

  1. ETS Ingeniería Industrial, Departamento de Ingeniería Térmicay Fluidos, Universidad Politécnica de Cartagena, Cartagena (Murcia), 30202, Spain

    J. Zueco

  2. Fluid Dynamics Research, Department of Mathematics, Goalpara College, Goalpara, Assam, 783101, India

    S. Ahmed

Authors
  1. J. Zueco
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  2. S. Ahmed
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Correspondence to J. Zueco.

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Communicated by Zhe-wei ZHOU

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Zueco, J., Ahmed, S. Combined heat and mass transfer by mixed convection MHD flow along a porous plate with chemical reaction in presence of heat source. Appl. Math. Mech.-Engl. Ed. 31, 1217–1230 (2010). https://doi.org/10.1007/s10483-010-1355-6

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  • DOI: https://doi.org/10.1007/s10483-010-1355-6

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