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Effects of Chemical Reaction and Heat Source on MHD Oscillatory Flow of a Viscoelastic Fluid in a Vertical Porous Channel

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Abstract

This paper deals with the MHD oscillatory flow of an incompressible and electrically conducting visco-elastic fluid in a vertical channel in the presence of chemical reaction and heat source. The unsteadiness in the flow is due to an oscillatory pressure gradient across the ends of the channel. A closed form solutions for velocity, temperature and concentration profiles as well as skin friction coefficient, rate of heat and mass transfers are obtained by using appropriate mathematical techniques. The analytical outcomes are assessed numerically and then are presented graphically to confer the effects of diverse parameters arriving in the problem. It is witnessed that the fluid velocity profile is parabolic in nature with extreme scale along the channel centerline and least at the walls and therefore, the oscillatory flow enhance the heat transport system by various magnitudes as compared with normal conduction.

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Abbreviations

\(B_0\) :

Uniform magnetic field

\(C^{*}\) :

Concentration

\(c_p \) :

Specific heat at constant pressure

\(C_0 \) :

Uniform concentration

d :

Mean half width of the channel

\(D_a \) :

Darcy number

g :

Acceleration due to gravity

\(G_r \) :

Grashof number

\(G_c \) :

Modified Grashof number

Q :

Heat source parameter

\(H_0 \) :

Intensity of magnetic field

Kr :

Chemical reaction parameter

k :

Thermal conductivity

\(K^{*}\) :

Permeability of the porous medium

M :

Hartmann number

R :

Radiation parameter

Nu :

Nusselt number

\(P_e \) :

Peclet number

\(p^{*}\) :

The pressure

q :

Radiative heat flux

\(R_e \) :

Reynolds number

S :

Porous medium shape factor

\(\theta \) :

Fluid temperature

\(\beta _T \) :

Coefficient of thermal expansion

\(\beta _C \) :

Coefficient of mass expansion

\(\mu \) :

Magnetic permeability

\(\sigma \) :

Electric conductivity

\(\rho \) :

Fluid density

\(\omega ^{*}\) :

Frequency of oscillations

\(\vartheta _1 \) :

Kinematic viscosity coefficient

\(\vartheta _2 \) :

Viscoelasticity

\(\gamma \) :

Viscoelastic parameter

\(\lambda \) :

Pressure gradient

\(\alpha \) :

Mean radiation absorption coefficient

\(\tau \) :

Skin friction

Sc :

Schmidt number

Sh :

Sherwood number

\(T^{*}\) :

Temperature

\(T_0 \) :

Uniform temperature

\(t^{*}\) :

Time

\(u^{*}\) :

Axial velocity

U :

Flow mean velocity

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Authors and Affiliations

  1. Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle, AP, India

    B. Venkateswarlu

  2. Fluid Dynamics Division, SAS, VIT University, Vellore, TN, 632 014, India

    P. V. Satya Narayana

  3. Department of Mathematics, Gitam University, Bangalore, Karnataka, India

    B. Devika

Authors
  1. B. Venkateswarlu
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  2. P. V. Satya Narayana
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  3. B. Devika
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Correspondence to B. Venkateswarlu.

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Venkateswarlu, B., Narayana, P.V.S. & Devika, B. Effects of Chemical Reaction and Heat Source on MHD Oscillatory Flow of a Viscoelastic Fluid in a Vertical Porous Channel. Int. J. Appl. Comput. Math 3 (Suppl 1), 937–952 (2017). https://doi.org/10.1007/s40819-017-0391-8

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