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Mixed Convective Boundary Layer MHD Flow Along a Vertical Elastic Sheet

  • K. VajraveluEmail author
  • Ronald Li
  • M. Dewasurendra
  • K. V. Prasad
Original Paper

Abstract

The influence of magnetic field on flow and heat transfer of an electrically conducting fluid at an impermeable elastic sheet is analyzed. The governing nonlinear differential equations are solved analytically via homotopy analysis method. To validate the approximate-analytical method, comparisons are made with the available results in the literature for some special cases and the results are found to be in good agreement. The effects of physical parameters on the flow and temperature fields are analyzed graphically. We could obtain the residual errors \(\mathcal{E}_2^{f} =1.3\times 10^{-4}\) and \(\mathcal{E}_2^{\theta } =8.0\times 10^{-4}\) respectively for velocity and temperature fields only with second-order approximations. The velocity power index and the variable thickness parameters have strong effects on the shear stress and the Nusselt number.

Keywords

Mixed convection Homotopy analysis method Flow and heat transfer Variable thickness Skin friction Nusselt number 

List of symbols

Greek Symbols

\(\uprho \)

Density of the fluid (kg m\(^{-3}\))

\(\uptheta \)

Dimensionless temperature of the fluid

\(\upmu \)

Dynamic viscosity (N s m\(^{-2}\))

\(\upsigma \)

Electrical conductivity of the fluid(Sm\(^{-1}\))

\(\upnu \)

Kinematic viscosity (\(\hbox {m}^{2}\hbox {s}^{-1}\))

\(\uplambda \)

Mixed convection parameter

\(\upeta \)

Similarity parameter

\(\upkappa \)

Thermal conductivity of the fluid (W m\(^{-1}\) K\(^{-1}\))

\(\upalpha _{0}\)

Thermal diffusivity

\(\upbeta \)

Thermal expansion coefficient

\(\upalpha \)

Wall thickness parameter

Roman Symbols

Ab

Constants

xy

Direction of parallel and perpendicular to the surface, respectively

\(T_{\infty }\)

Free-stream temperature (K)

Nu

Nusselt number

Pr

Prandtl number

\(U_{0}\)

Reference velocity (\(\hbox {ms}^{-1}\))

Re

Reynolds number

\(C_{f}\)

Skin-friction coefficient

\(C_{p}\)

Specific heat at constant pressure (\(\hbox {J kg}^{-1} \hbox { K}^{-1}\))

\(u_{w}\)

Stretching/shrinking sheet velocity

\(T_{w}\)

Temperature at the surface(K)

T

Temperature of the fluid (K)

\(q_{r}\)

Thermal radiative heat flux

D

Thermal slip factor

\(B_{0}\)

Transverse magnetic field (tesla)

uv

Velocity components in the x- and y-direction, respectively

m

Velocity power index

Subscripts

w

Condition at surface

\(\infty \)

Free stream condition

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Copyright information

© Springer India Pvt. Ltd. 2016

Authors and Affiliations

  • K. Vajravelu
    • 1
    • 2
    Email author
  • Ronald Li
    • 1
  • M. Dewasurendra
    • 1
  • K. V. Prasad
    • 3
  1. 1.Department of MathematicsUniversity of Central FloridaOrlandoUSA
  2. 2.Department of Mechanical, Material and Aerospace EngineeringUniversity of Central FloridaOrlandoUSA
  3. 3.Department of MathematicsVSK UniversityBellaryIndia

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