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Research Papers

Flow of a Biomagnetic Visco-Elastic Fluid in a Channel With Stretching Walls

[+] Author and Article Information
J. C. Misra1

School of Medical Science and Technology, Indian Institute of Technology, Kharagpur-721302, Indiamisrajc@rediffmail.com

G. C. Shit

Department of Mathematics, Jadavpur University, Kolkata-70032, Indiagcs@math.jdvu.ac.in

1

Corresponding author.

J. Appl. Mech 76(6), 061006 (Jul 23, 2009) (9 pages) doi:10.1115/1.3130448 History: Received October 04, 2007; Revised March 25, 2009; Published July 23, 2009

The flow of a visco-elastic fluid in a channel with stretching walls under the action of an externally applied magnetic field generated by a magnetic dipole was studied in this paper. As per an experimental report, the variation in magnetization M of the fluid with temperature T was approximated as a linear equation of state M=K1T, where K1 is a constant called the pyromagnetic coefficient. In this investigation the model used is that of Walter’s liquid B fluid, which includes the effect of fluid visco-elasticity. By introducing appropriate nondimensional variables, the problem is reduced to solving a coupled nonlinear system of ordinary differential equations subject to a set of boundary conditions. The problem is solved by developing a suitable numerical technique based on finite difference approach. Computational results concerning the variation in the velocity, pressure and temperature fields, skin friction and the rate of heat transfer with magnetic field strength, Prandtl number, and blood visco-elasticity are presented graphically. The results presented reveal that the velocity of blood in the normal physiological state can be lowered by applying a magnetic field of sufficient intensity. The study bears the promise of important applications in controlling the flow of blood during surgery and also during treatment of cancer by therapeutic means when it involves magnetic drug targeting (hyperthemia).

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Physical sketch of the problem

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Figure 2

Variation of f′(η) for different values of B

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Figure 3

Variation of −f(η) for different values of B

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Figure 8

Distribution of temperature (nondimensional) θ1(η) for different values of B

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Figure 9

Variation in temperature θ1(η) for different values of Pr

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Figure 11

Variation in pressure P2(η) for different values of Pr

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Figure 4

Variation of f′(η) for different values of Pr

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Figure 5

Variation of −f(η) for different values of Pr

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Figure 6

Variation of f′(η) for different values of α

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Figure 7

Variation of −f(η) for different values of α

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Figure 10

Distribution of pressure (nondimensional) P2(η) with η for different values of B

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Figure 12

Variation of f′(η) with η when B=0, K=0.005, and Pr=1 in the present study

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