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Free Convection Heat and Mass Transfer Flow for Magnetohydrodynamic Chemically Reacting and Radiating Elastico-Viscous Fluid Past a Vertical Permeable Plate with Gravity Modulation

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Abstract

An analysis of a two-dimensional unsteady magnetohydrodynamic free convective heat and mass transfer flow of an electrically conducting, optically thin, incompressible, and radiating elastico-viscous fluid (characterised by Walters’ liquid \({B}'\)) past a vertical permeable infinite plate embedded in a uniform porous medium with gravity modulation is considered. It is assumed that there exists a homogeneous first-order chemical reaction. Analytical solutions for velocity, temperature and concentration field have been derived. The effects of gravity modulation, radiation, and chemical reaction on velocity profile and shear stress for both Newtonian and elastico-viscous fluid have been studied and presented graphically. It was observed that velocity distribution increases with an increase in gravity modulation parameter and radiation parameter for both Newtonian and elastico-viscous fluid, where as it shows reverse effects in the case of magnetic field parameter and viscoelastic parameter. It is seen that viscous drag on the plate is reduced under the effect of chemical reaction parameter, where as it shows reverse effect in the case of gravity modulation parameter and radiation parameter.

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Abbreviations

a :

Gravity modulation parameter

\(\overline{{C}}\) :

Species concentration

\(\overline{{C}}_\infty \) :

Species concentration in the free stream

\(\overline{{C}}_w \) :

Species concentration near the surface

\(C_p \) :

Specific heat at constant pressure

D :

Chemical molecular diffusivity

g :

Acceleration due to gravity

\(g_0 \) :

Constant gravity level in the space

\(g_1 \) :

Amplitude of the oscillating component of acceleration

Gr :

Grashof number for heat transfer

Gm :

Grashof number for mass transfer

\(K_r \) :

Dimensionless chemical reaction parameter

K :

Dimensionless porous permeability parameter

\(k_0 \) :

Co-efficient of elastic viscosity

M :

Magnetic parameter

Nu :

Nusselt number

\(\Pr \) :

Prandtl number

\(q_r \) :

Radiation heat flux

R :

Radiation parameter

Sc :

Schmidt number

Sh :

Sherwood number

T :

Fluid temperature

\(\overline{{T}}_w \) :

Fluid temperature at the surface

\(\overline{{T}}_\infty \) :

Fluid temperature in the free stream

\(\overline{{u}},\overline{{v}}\) :

Velocity components along x and y-axis respectively

U :

Scale of surface velocity

\(v_0 \) :

Suction velocity

\(\overline{{x}},\overline{{y}}\) :

Cartesian coordinates

\(\alpha \) :

Viscoelastic parameter

\(\beta \) :

Coefficient of volume expansion for heat transfer

\(\overline{{\beta }}\) :

Coefficient of volume expansion for mass transfer

\(\omega \) :

Dimensionless frequency of oscillation

\(\varepsilon \) :

Positive small parameter

\(\theta \) :

Dimensionless fluid temperature

\(\kappa \) :

Thermal conductivity

\(\upsilon \) :

Kinematic viscosity

\(\rho \) :

Fluid density

\(\sigma _1 \) :

Electrical conductivity

\(\overline{{\sigma }}\) :

Stefan–Boltzmann constant

\(\sigma \) :

Dimensionless shear stress

\(\phi \) :

Dimensionless species concentration

w :

Conditions on the surface

\(\infty \) :

Free stream conditions

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  1. Department of Mathematics, Rajiv Gandhi University, Doimukh, Arunachal Pradesh, 791112, India

    Utpal Jyoti Das

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Das, U.J. Free Convection Heat and Mass Transfer Flow for Magnetohydrodynamic Chemically Reacting and Radiating Elastico-Viscous Fluid Past a Vertical Permeable Plate with Gravity Modulation. Int. J. Appl. Comput. Math 3, 2021–2037 (2017). https://doi.org/10.1007/s40819-016-0222-3

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