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# Dual Solutions in Magnetohydrodynamic Stagnation-Point Flow and Heat Transfer Over a Shrinking Surface With Partial Slip

[+] Author and Article Information
Tapas Ray Mahapatra

Department of Mathematics,
Visva-Bharati,
Santiniketan 731 235, India
e-mail: trmahapatra@yahoo.com

Samir Kumar Nandy

Department of Mathematics,
A. K. P. C Mahavidyalaya,
Bengai, Hooghly 712 611, India
e-mail: nandysamir@yahoo.com

Ioan Pop

Department of Mathematics,
Babeş-Bolyai University,
Cluj-Napoca 400084, Romania
e-mail: popm.ioan@yahoo.co.uk

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 18, 2012; final manuscript received May 15, 2013; published online July 2, 2014. Assoc. Phillip M. Ligrani.

J. Heat Transfer 136(10), 104501 (Jul 02, 2014) (6 pages) Paper No: HT-12-1230; doi: 10.1115/1.4024592 History: Received May 18, 2012; Revised May 15, 2013

## Abstract

In this paper, the problem of steady two-dimensional magnetohydrodynamic (MHD) stagnation-point flow and heat transfer of an incompressible viscous fluid over a stretching/shrinking sheet is investigated in the presence of velocity and thermal slips. With the help of similarity transformations, the governing Navier–Stokes and the energy equations are reduced to ordinary differential equations, which are then solved numerically using a shooting technique. Interesting solution behavior is observed for the similarity equations with multiple solution branches for certain parameter domain. Fluid velocity increases due to the increasing value of the velocity slip parameter resulting in a decrease in the temperature field. Temperature at a point increases with increase in the thermal slip parameter. The effects of the slips, stretching/shrinking, and the magnetic parameters on the skin friction or the wall shear stress, heat flux from the surface of the sheet, velocity, and temperature profiles are computed and discussed.

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## Figures

Fig. 1

Physical model and the coordinate system

Fig. 2

Variation of the skin friction coefficient F″(0) with α for different values of δ for M = 0.2

Fig. 3

Variation of heat transfer −θ′(0) with α for different values of δ when M = 0.2, Pr = 2.0, γ = 0.2, and Ec = 0.1

Fig. 4

Variation of heat transfer −θ′(0) with α for different values of γ when M = 0.2, Pr = 0.71, δ = 0.5, and Ec = 0.1

Fig. 5

Variation of heat transfer −θ′(0) with α for different values of M when Pr = 0.71, δ = 0.3, γ = 0.25, and Ec = 0.5

Fig. 6

Variation of heat transfer −θ′(0) with α for different values of Ec when Pr = 0.71, M = 0.3, γ = 0.3, and δ = 0.4

Fig. 7

Velocity profiles F′(η) for several values of δ with M = 0.3 and α = −1.3

Fig. 8

Temperature profiles θ(η) for several values of δ with α = −1.3, M = 0.3, γ = 0.15, Pr = 0.71, and Ec = 0.5

Fig. 9

Velocity profiles F′(η) for several values of M with δ = 0.3 and α = −1.4

Fig. 10

Temperature profiles θ(η) for different values M with α = −1.4, Pr = 0.71, δ = 0.3, γ = 0.25, and Ec = 0.5

Fig. 11

Temperature profiles θ(η) for different values of α with δ = 0.5, M = 0.3, γ = 0.3, Pr = 0.71, and Ec = 0.5

Fig. 12

Temperature profiles θ(η) for different values of Ec with α = −1.3, M = 0.3, γ = 0.3, Pr = 0.71, and δ = 0.4

## Errata

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