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Effects of Transpiration and Internal Heat Generation/Absorption on the Unsteady Flow of a Maxwell Fluid at a Stretching Surface

[+] Author and Article Information
Swati Mukhopadhyay

 Department of Mathematics, The University of Burdwan, Burdwan-713104, West Bengal, Indiaswati_bumath@yahoo.co.in

Kuppalapalle Vajravelu1

 Department of Mathematics, Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida, Orlando, FL 32816-1364Kuppalapalle.Vajravelu@ucf.edu

1

Corresponding author.

J. Appl. Mech 79(4), 044508 (May 11, 2012) (6 pages) doi:10.1115/1.4006260 History: Received November 30, 2011; Revised January 16, 2012; Posted March 03, 2012; Published May 11, 2012; Online May 11, 2012

The effect of transpiration on unsteady two-dimensional flow of an MHD non-Newtonian Maxwell fluid over a stretching surface in the presence of a heat source/sink is investigated. The upper convected Maxwell fluid model is used to characterize the non-Newtonian fluid behavior. Using a similarity transformation the governing partial differential equations of the problem are reduced to a system of ordinary differential equations (ODEs), and the ODEs are solved numerically by a shooting method. The flow features and the heat transfer characteristics are analyzed and discussed in detail for several sets of values of the governing parameters. Though the velocity of the fluid initially decreases with increasing unsteady parameter but it increases finally. Quite the opposite is true with the temperature. Furthermore, the velocity of the fluid decreases with an increasing magnetic or Maxwell parameter. But the temperature is enhanced with an increasing Maxwell parameter. It is observed that the effect of the transpiration is to decrease the fluid velocity as well as the temperature. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Velocity profiles for different values of M. (b) Temperature profiles for different values of M.

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Figure 2

(a) Velocity profiles for different values of β for steady motion. (b) Temperature profiles for different values of β for steady motion. (c) Velocity profiles for different values of β for unsteady motion. (d) Temperature profiles for different values of β for unsteady motion.

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Figure 3

(a) Velocity profiles for different values of Ha. (b) Temperature profiles for different values of Ha.

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Figure 4

(a) Velocity profiles for different values of S. (b) Temperature profiles for different values of S.

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Figure 5

(a) Temperature profiles for different values of heat source/sink parameter λ. (b) Temperature profiles for different values of Prandtl number Pr.

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Figure 6

(a) Variation of skin-friction coefficient with Maxwell parameter β for two values of unsteadiness parameter M. (b) Variation of heat transfer coefficient with Maxwell parameter β for two values of unsteadiness parameter M. (c) Variation of skin-friction coefficient with transpiration parameter S for two values of magnetic parameter Ha. (d) Variation of heat transfer coefficient with transpiration parameter S for two values of magnetic parameter Ha.

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