, 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


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.


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

List of symbols


Magnetic field


Value of the magnetic field at x = 0


Local skin friction coefficient


Specific heat at constant pressure


Dimensionless stream function


Dimensionless velocity


Dimensionless function of X


Acceleration due to gravity


Gebhart number


Grashof number


Hartmann number


Thermal conductivity of the fluid


Characteristic length


Local Nusselt number


Prandtl number


Reynolds number


Local Reynolds number




Surface temperature at x = 0

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

Chebyshev polynomial

\( u, v \)

Velocity components in x and y directions, respectively


Velocity of the stretching surface at x = 0


Surface velocity

\( x, y \)

Distances along and normal to the stretching surface


Dimensionless distance

Greek symbols


Thermal diffusivity


Coefficient of thermal expansion


Similarity variable


Dimensionless temperature


Dimensionless relaxation parameter of Maxwell fluid


Relaxation parameter of Maxwell fluid


Dimensionless buoyancy parameter


Fluid viscosity


Kinematic viscosity


Transformed similarity variable


Density of the fluid


Electrical conductivity


Stream function


\( s, \infty \)

Conditions on the surface and in the quiescent fluid, respectively


Prime denotes derivative with respect to η or ξ



Chebyshev finite difference method



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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