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Unsteady Radiative MHD Free Convective Flow and Mass Transfer of a Viscoelastic Fluid Past an Inclined Porous Plate

  • Research Article - Chemical Engineering
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Abstract

The present paper is related to the study of an unsteady radiative magnetohydrodynamic free convection flow of a viscoelastic fluid past an inclined plate embedded in a porous medium. The fluid is incompressible and optically transparent. The effects of chemical reaction, heat source and viscous dissipation are considered during the present study. The case of viscous flow has been discussed as a special case, and the reported results of previous authors have been highlighted also. The novelty of our study is not only to analyze the effect of elasticity but also to account for the viscous dissipation which is important in case of radiative and optically transparent flows. An approximate analytical solution has been obtained by applying perturbation method. Results of the present study are in good agreement with Reddy et al. (Asian J Curr Eng Maths 1(3):115–119, 2012) and Chen (Int J Heat Mass Transf 53:4263–4276, 2010). It is interesting to note that higher Prandtl number fluid under the influence of magnetic field reduces the velocity, whereas elasticity property increases it. Moreover, higher viscous dissipation leads to an increase in the fluid temperature and hence reduces the heat transfer rate from the inclined plate.

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Abbreviations

g :

Acceleration due to gravity

\({\beta^{\ast}}\) :

Volumetric coefficient of expansion with species concentration

\({\upsilon}\) :

Kinematic viscosity

B 0 :

Uniform magnetic field strength

K p :

Permeability parameter

C p :

Specific heat at constant pressure

q r :

Radiative heat flux

D :

Diffusion coefficient

T :

Non-dimensional temperature

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

Ambient temperature

u, v :

Component velocity along x and y directions

k 1 :

Mean absorption coefficient

C w :

Concentration at the surface of the plate

\({\theta }\) :

Dimensionless temperature

G c :

Grashof number for mass transfer

\({\mu }\) :

Dynamic viscosity

M :

Magnetic parameter

E c :

Eckert number

\({\omega}\) :

Frequency of excitation

\({\beta}\) :

Volumetric coefficient of expansion for heat transfer

\({\alpha}\) :

Angle of inclination

\({\sigma}\) :

Electrical conductivity

\({\rho}\) :

Density of the fluid

k 0 :

Elasticity of the fluid

k :

Thermal conductivity

S :

Heat source parameter

K c :

Chemical reaction parameter

T w :

Temperature at the surface of the plate

U 0 :

Characteristic velocity

\({\sigma_{1}}\) :

Stefan–Boltzmann constant

C :

Non-dimensional concentration

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

Ambient concentration

G r :

Grashof number for heat transfer

P r :

Prandtl number

S c :

Schimdt number

R c :

Elastic parameter

R :

Radiation parameter

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Authors and Affiliations

  1. Department of Physics, Radhakrishna Institute of Technology and Engineering, Biju Patnaik University of Technology, Rourkela, Odisha, India

    M. K. Nayak

  2. Department of Mathematics, I.T.E.R, Siksha ‘O’ Anusandhan University, Bhubaneshwar, Odisha, India

    G. C. Dash

  3. Department of Physics, Utkal University, Bhubaneshwar, Odisha, India

    L. P. Singh

Authors
  1. M. K. Nayak
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  2. G. C. Dash
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  3. L. P. Singh
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Correspondence to M. K. Nayak.

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Nayak, M.K., Dash, G.C. & Singh, L.P. Unsteady Radiative MHD Free Convective Flow and Mass Transfer of a Viscoelastic Fluid Past an Inclined Porous Plate. Arab J Sci Eng 40, 3029–3039 (2015). https://doi.org/10.1007/s13369-015-1805-8

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