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MHD viscoelastic fluid flow through porous medium over a stretching sheet in the presence of non-uniform heat source/sink

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Abstract

The boundary layer flow, heat and mass transfer of an electrically conducting viscoelastic fluid over a stretching sheet embedded in a porous medium has been studied. The effect of transverse magnetic field, non-uniform heat source and chemical reaction on the flow has been analyzed. The Darcy linear model has been applied to account for the permeability of the porous medium. The method of solution involves similarity transformation. The confluent hypergeometric function (Kummer’s function) has been applied to solve the governing equations. Two aspects of heat equation namely, (1) prescribed surface ure and (2) prescribed wall heat flux are considered. The study reveals that the loss of momentum transfer in the main direction of flow is compensated by increasing in transverse direction vis-à-vis the corresponding velocity components due to magnetic force density. The application of magnetic field of higher density produces low solutal concentration and a hike in surface temperature.

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Abbreviations

\(A,d,a_0 ,b_0 \) :

Constants

u :

Non-dimensional velocity in x-direction

v :

Non-dimensional velocity in y-direction

\(k_0 \) :

Co-efficient of viscoelasticity

\(\kappa \) :

Thermal conductivity

Rc :

Visco-elastic parameter

Kc :

Chemical reaction parameter

Sc :

Schmidt number

M :

Magnetic field parameter

T :

Non-dimensional temperature

\(T_w \) :

Temperature of the wall

\(T_\infty \) :

Ambient temperature

\(\theta \) :

Temperature profile in PST case

\(\psi \) :

Temperature profile in PHF case

\(\phi \) :

Concentration profile

b :

Stretching rate

Ec :

Eckert number

\( \Pr \) :

Prandtl number

\(A^{*}\) :

Space dependent parameters

\(B^{*}\) :

Temperature dependent parameters

\(c_p \) :

Specific heat at constant pressure

\(\mu \) :

Viscosity

\(q_w \) :

Heat flux

\({q}'''\) :

Space and temperature dependent internal heat generation/absorption

l :

Characteristic length

\(\upsilon \) :

Kinematic viscosity

\(\rho \) :

Density

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Authors and Affiliations

  1. Department of Mathematics, Siksha ‘O’ Anusandhan University, Bhubaneswar, Odisha, 751030, India

    S. R. Mishra, R. S. Tripathy & G. C. Dash

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  1. S. R. Mishra
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  2. R. S. Tripathy
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  3. G. C. Dash
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Mishra, S.R., Tripathy, R.S. & Dash, G.C. MHD viscoelastic fluid flow through porous medium over a stretching sheet in the presence of non-uniform heat source/sink. Rend. Circ. Mat. Palermo, II. Ser 67, 129–143 (2018). https://doi.org/10.1007/s12215-017-0300-3

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