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MHD flow and heat transfer of a UCM fluid over a stretching surface with variable thermophysical properties

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Abstract

In this paper we investigate the effects of temperature-dependent viscosity, thermal conductivity and internal heat generation/absorption on the MHD flow and heat transfer of a non-Newtonian UCM fluid over a stretching sheet. The governing partial differential equations are first transformed into coupled non-linear ordinary differential equation using a similarity transformation. The resulting intricate coupled non-linear boundary value problem is solved numerically by a second order finite difference scheme known as Keller-Box method for various values of the pertinent parameters. Numerical computations are performed for two different cases namely, zero and non-zero values of the fluid viscosity parameter. That is, 1/θ r →0 and 1/θ r ≠0 to get the effects of the magnetic field and the Maxwell parameter on the velocity and temperature fields, for several physical situations. Comparisons with previously published works are presented as special cases. Numerical results for the skin-friction co-efficient and the Nusselt number with changes in the Maxwell parameter and the fluid viscosity parameter are tabulated for different values of the pertinent parameters. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid phenomena, especially the UCM fluid phenomena. Maxwell fluid reduces the wall-shear stress.

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Abbreviations

a :

constant in (3)

b :

constant in (14) known as stretching rate b>0

B 0 :

uniform magnetic field

c p :

specific heat at constant pressure

C f :

skin friction coefficient

d ij :

deformation rate tensor

f :

dimensionless stream function

K :

thermal conductivity

L ij :

velocity gradient tensor

K ∞ :

thermal conductivity of the fluid far away from the sheet

Mn :

magnetic parameter

Nu x :

local Nusselt number

Pr:

Prandtl number

Q s :

temperature dependent volumetric rate of heat generation/absorption

q w :

heat transfer from the surface of the sheet

T :

fluid temperature

T r :

constant in (4)

T w :

temperature of the plate

T ∞ :

ambient temperature

U w (x):

velocity of the stretching sheet

u,v :

velocity components in the x and y directions

x,y :

Cartesian coordinates

α ∞ :

thermal diffusivity

α 0,β 0 :

unknown initial conditions

β :

Maxwell parameter

β 1 :

heat source/sink parameter

γ :

constant defined in (4)

ν :

kinematic viscosity

ρ :

density

σ :

electric conductivity

δ :

the coefficient of viscosity defined in (10)

λ :

relaxation time

ΔT :

characteristic temperature

\(\frac{\Delta}{\Delta t}\) :

upper convected time derivative

ε :

constant in (2) known as variable thermal conductivity parameter

η :

similarity variable

θ :

dimensionless temperature

θ r :

constant in (5) known as fluid viscosity parameter

μ :

viscosity

ψ :

stream function

τ ij :

tensor notation

τ w :

skin friction or shear stress

∞:

condition at infinity

w :

condition at the wall

′:

derivative with respect to η

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Acknowledgements

The authors appreciate the constructive comments of the reviewers which led to definite improvement in the paper. K. V. Prasad expresses his grateful thanks to DST authorities of India for providing with the financial support through BOYSCAST fellowship.

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Authors and Affiliations

  1. Department of Mathematics, Bangalore University, Bangalore, 560001, India

    K. V. Prasad & A. Sujatha

  2. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    K. Vajravelu

  3. Faculty of Mathematics, Babeş-Bolyai University, 400082, Cluj-Napoca, CP 253, Romania

    I. Pop

Authors
  1. K. V. Prasad
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  2. A. Sujatha
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  3. K. Vajravelu
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  4. I. Pop
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Correspondence to I. Pop.

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Prasad, K.V., Sujatha, A., Vajravelu, K. et al. MHD flow and heat transfer of a UCM fluid over a stretching surface with variable thermophysical properties. Meccanica 47, 1425–1439 (2012). https://doi.org/10.1007/s11012-011-9526-x

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