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Research Papers

# Momentum and Heat Transfer in MHD Stagnation-Point Flow Over a Shrinking Sheet

[+] Author and Article Information
T. Ray Mahapatra1

Department of Mathematics, Visva-Bharati University, Santiniketan 731 235, Indiatrmahapatra@yahoo.com

S. K. Nandy

Department of Mathematics, A.K.P.C Mahavidyalaya, Bengai, Hooghly 712 611, India

A. S. Gupta

Department of Mathematics, Indian Institute of Technology, Kharagpur 721 302, India

1

Corresponding author.

J. Appl. Mech 78(2), 021015 (Nov 10, 2010) (8 pages) doi:10.1115/1.4002577 History: Received December 06, 2009; Revised May 04, 2010; Posted September 17, 2010; Published November 10, 2010; Online November 10, 2010

## Abstract

The steady two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of an electrically conducting incompressible viscous fluid toward a shrinking sheet is investigated. The sheet is shrunk in its own plane with a velocity proportional to the distance from the stagnation-point and a uniform magnetic field is applied normal to the sheet. Velocity component parallel to the sheet is found to increase with an increase in the magnetic field parameter $M$. A region of reverse flow occurs near the surface of the shrinking sheet. It is shown that as $M$ increases, the tendency of this flow reversal decreases. It is also observed that the nonalignment of the stagnation-point flow and the shrinking sheet considerably complicates the flow structure. The effect of the magnetic parameter $M$ on the streamlines is shown for both aligned and nonaligned cases. The temperature distribution in the boundary layer is found when the surface is held at constant temperature. The analysis reveals that the temperature at a point increases with increasing $M$ in a certain neighborhood of the surface but beyond this, the temperature decreases with increasing $M$. For fixed $M$, the surface heat flux decreases with increase in the shrinking rate.

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## Figures

Figure 1

A sketch of the physical problem

Figure 2

Initial values F″(0) and h′(0) versus α

Figure 3

Variation of F(η) with η when α=−0.5 (shrinking) for several values of magnetic parameter M

Figure 4

Variation of h(η) with η when α=−0.5 (shrinking) for several values of magnetic parameter M

Figure 5

Variation of h(η) with η when M=1.0 for different values of α

Figure 6

Variation of u∗(ξ,η) with η when α=−0.5, ξ=0.5, and L=1.0 for several values of the magnetic parameter M

Figure 7

Streamlines for the shrinking sheet with α=−0.5, L=0 (aligned) for different values of M (solid line →M=0, short dashed line →M=1, long dashed line →M=2)

Figure 8

Streamlines for the shrinking sheet with α=−0.5, L=0.8 (nonaligned) for different values of M (solid line →M=0, short dashed line →M=1, long dashed line →M=2)

Figure 9

Variation of θ(η) with η when α=−0.25, Pr=0.5, Ec=2.0, L=0.5, and ξ=1.0 for several values of magnetic parameter M

Figure 10

Variation of θ(η) with η for M=1.0, Pr=0.5, Ec=2.0, L=0.5, and ξ=1.0 for several values of negative α (shrinking)

Figure 11

Variation of θ(η) with η when M=1.0, α=−0.5, Pr=0.5, L=0.5, and ξ=1.0 for several values of Eckert number Ec

Figure 12

Variation of θ(η) with η when M=1.0, Pr=0.5, Ec=2.0, α=−0.5, and ξ=1.0 for several values of L(>0)

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