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Effects of thermal radiation on hydromagnetic flow over an unsteady stretching sheet embedded in a porous medium in the presence of heat source or sink

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Abstract

A boundary layer analysis is performed to study the effects of thermal radiation on the flow of an incompressible viscous electrically conducting fluid over an unsteady stretching sheet embedded in a porous medium in the presence of heat source or sink. The governing boundary layer equations are transformed to ordinary differential equations by using similarity transformation and solved numerically by Runge–Kutta fourth order method in association with quasilinear shooting technique. The effects of unsteadiness parameter, permeability parameter, magnetic parameter, thermal radiation parameter, Prandtl number, heat source or sink parameter and Eckert number are represented graphically on velocity and temperature profiles while local skin friction coefficient and local Nusselt number are represented numerically. The results for the non-magnetic case are in good agreement with earlier published work.

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Abbreviations

A :

Unsteadiness parameter

b :

Positive constant

\( B_{o} \) :

Uniform magnetic field

C f :

Local skin-friction coefficient

C p :

Specific heat at constant pressure

Ec :

Eckert number

f :

Dimensionless stream function

K :

Permeability

\( k^{*} \) :

Absorption coefficient

M :

Magnetic parameter

\( Nu_{x} \) :

Local Nusselt number

Pr:

Prandtl number

Q :

Heat source or sink

q r :

Radiative heat flux

R :

Thermal radiation parameter

\( \text{Re}_{x} \) :

Local Reynolds number

T :

Temperature of the fluid

t :

Time

T w :

Surface temperature

\( T_{\infty } \) :

Free stream temperature

U w :

Surface velocity

u :

Velocity component in the x-direction

v :

Velocity component in the y-direction

x :

Along the stretching surface distance

y :

Normal distance

γ :

Stretching rate

η :

Similarity variable

δ :

Heat source or sink parameter

\( \theta \) :

Dimensionless temperature

\( \kappa \) :

Thermal conductivity

λ :

Permeability parameter

μ :

Coefficient of viscosity

\( \upsilon \) :

Kinematic viscosity

ρ :

Fluid density

\( \sigma_{e} \) :

Electrical conductivity

\( \sigma^{*} \) :

Stefan–Boltzmann constant

ψ :

Stream function

′:

Differentiation with respect to \( \eta \)

w :

Surface conditions

\( \infty \) :

Conditions for away from the surface

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Authors and Affiliations

  1. Department of Mathematics, Malaviya National Institute of Technology, Jaipur, 302017, India

    Santosh Chaudhary & Mohan Kumar Choudhary

  2. Department of Electronics and Communication, Malaviya National Institute of Technology, Jaipur, 302017, India

    Ritu Sharma

Authors
  1. Santosh Chaudhary
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  2. Mohan Kumar Choudhary
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  3. Ritu Sharma
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Correspondence to Santosh Chaudhary.

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Chaudhary, S., Choudhary, M.K. & Sharma, R. Effects of thermal radiation on hydromagnetic flow over an unsteady stretching sheet embedded in a porous medium in the presence of heat source or sink. Meccanica 50, 1977–1987 (2015). https://doi.org/10.1007/s11012-015-0137-9

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