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Casson Fluid Flow and Heat Transfer at an Exponentially Stretching Permeable Surface

[+] Author and Article Information
Swati Mukhopadhyay

Department of Mathematics,
The University of Burdwan,
Burdwan-713104, W.B., India
e-mail: swati_bumath@yahoo.co.in

Kuppalapalle Vajravelu

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

Robert A. Van Gorder

Department of Mathematics,
University of Central Florida,
Orlando, FL 32816-1364
e-mail: rav@knights.ucf.edu

Manuscript received June 11, 2012; final manuscript received December 20, 2012; accepted manuscript posted February 11, 2013; published online July 12, 2013. Assoc. Editor: Nesreen Ghaddar.

J. Appl. Mech 80(5), 054502 (Jul 12, 2013) (9 pages) Paper No: JAM-12-1222; doi: 10.1115/1.4023618 History: Received June 11, 2012; Revised December 20, 2012; Accepted February 11, 2013

The present paper deals with the boundary layer flow and heat transfer of a non-Newtonian fluid at an exponentially stretching permeable surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior, due to its various practical applications. With the help of similarity transformations the governing partial differential equations corresponding to the continuity, momentum, and energy equations are converted into nonlinear ordinary differential equations, and numerical solutions to these equations are obtained. Furthermore, in some specific parameter regimes, analytical solutions are found. It is observed that the effect of increasing values of the Casson parameter is to decrease the velocity field while enhancing the temperature field. Furthermore, it is observed that the effect of the increasing values of the suction parameter is to increase the skin-friction coefficient.

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Figures

Grahic Jump Location
Fig. 1

Sketch of the physical problem

Grahic Jump Location
Fig. 2

(a) Variation of velocity f'(η) with Casson parameter β in the absence of suction/blowing. (b) Variation of temperature θ(η) with Casson parameter β in the absence of suction/blowing.

Grahic Jump Location
Fig. 3

(a) Variation of velocity f'(η) with Casson parameter β in the presence of suction/blowing. (b) Variation of temperature θ(η) with Casson parameter β in the presence of suction/blowing.

Grahic Jump Location
Fig. 4

(a) Variation of velocity f'(η) for several values of suction/blowing parameter S. (b) Variation of temperature θ(η) with η for several values of suction/blowing parameter S.

Grahic Jump Location
Fig. 5

(a) Variation of temperature θ(η) for several values of Prandtl number Pr in the absence/presence of suction. (b) Variation of temperature θ(η) for several values of Prandtl number Pr in presence of blowing.

Grahic Jump Location
Fig. 6

(a) Variations of skin-friction coefficient against Casson parameter β for several values of suction/injection parameter S. (b) Variations of heat transfer coefficient θ'(0) against Casson parameter β for several values of suction/injection parameter S.

Grahic Jump Location
Fig. 7

Plots of the squared residual error E(ɛ,h) as a function of the convergence control parameter h for several values of ɛ

Grahic Jump Location
Fig. 8

Plots of the analytical approximations to F(ξ) for two values of ɛ. The primary (physical) solution is monotone increasing, while the secondary (nonphysical) solution is nonmonotone. The original solution function f may be recovered by use of the formulas f(η) = SF(ɛη) and ɛ = |S|(1 + (1/β))-1.

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