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Meccanica

, Volume 49, Issue 5, pp 1263–1274 | Cite as

Steady mixed convection flow of Maxwell fluid over an exponentially stretching vertical surface with magnetic field and viscous dissipation

  • M. KumariEmail author
  • G. Nath
Article

Abstract

The steady mixed convection flow and heat transfer from an exponentially stretching vertical surface in a quiescent Maxwell fluid in the presence of magnetic field, viscous dissipation and Joule heating have been studied. The stretching velocity, surface temperature and magnetic field are assumed to have specific exponential function forms for the existence of the local similarity solution. The coupled nonlinear ordinary differential equations governing the local similarity flow and heat transfer have been solved numerically by Chebyshev finite difference method. The influence of the buoyancy parameter, viscous dissipation, relaxation parameter of Maxwell fluid, magnetic field and Prandtl number on the flow and heat transfer has been considered in detail. The Nusselt number increases significantly with the Prandtl number, but the skin friction coefficient decreases. The Nusselt number slightly decreases with increasing viscous dissipation parameter, but the skin friction coefficient slightly increases. Maxwell fluid reduces both skin friction coefficient and Nusselt number, whereas buoyancy force enhances them.

Keywords

MHD mixed convection Maxwell fluid Exponentially stretching surface Viscous dissipation Chebyshev finite difference method 

List of symbols

B

Magnetic field

B0

Value of the magnetic field at x = 0

Cfx

Local skin friction coefficient

cp

Specific heat at constant pressure

f

Dimensionless stream function

f′

Dimensionless velocity

F(X)

Dimensionless function of X

g

Acceleration due to gravity

Gb

Gebhart number

Gr

Grashof number

Ha

Hartmann number

k

Thermal conductivity of the fluid

L

Characteristic length

Nux

Local Nusselt number

Pr

Prandtl number

Re

Reynolds number

Rex

Local Reynolds number

T

Temperature

T0

Surface temperature at x = 0

\( \bar{T}\left( X \right) \)

Chebyshev polynomial

\( u, v \)

Velocity components in x and y directions, respectively

u0

Velocity of the stretching surface at x = 0

us

Surface velocity

\( x, y \)

Distances along and normal to the stretching surface

X

Dimensionless distance

Greek symbols

α

Thermal diffusivity

β

Coefficient of thermal expansion

η

Similarity variable

θ

Dimensionless temperature

λ

Dimensionless relaxation parameter of Maxwell fluid

λ*

Relaxation parameter of Maxwell fluid

λ1

Dimensionless buoyancy parameter

μ

Fluid viscosity

ν

Kinematic viscosity

ξ

Transformed similarity variable

ρ

Density of the fluid

σ

Electrical conductivity

ψ

Stream function

Subscripts

\( s, \infty \)

Conditions on the surface and in the quiescent fluid, respectively

Superscript

Prime denotes derivative with respect to η or ξ

Abbreviation

ChFDM

Chebyshev finite difference method

Notes

Acknowledgments

One of the authors (MK) is thankful to the University Grants Commission, India, for the financial support under the Research Scientist Scheme. The authors also thank the reviewers for comments and suggestions which resulted in considerable improvement in the quality of this paper.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  2. 2.SultanpurIndia

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