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Research Papers: Forced Convection

# Three-Dimensional Magnetic Fluid Boundary Layer Flow Over a Linearly Stretching Sheet

[+] Author and Article Information
E. E. Tzirtzilakis

Department of Mechanical Engineering and Water Resources, Technological Educational Institute of Messolonghi, 30 200 Messolonghi, Greecetzirtzi@iconography.gr

N. G. Kafoussias

Department of Mathematics, Section of Applied Analysis, University of Patras, 26 500 Patras, Greecenikaf@math.upatras.gr

J. Heat Transfer 132(1), 011702 (Oct 26, 2009) (8 pages) doi:10.1115/1.3194765 History: Received September 18, 2008; Revised June 23, 2009; Published October 26, 2009

## Abstract

The three-dimensional laminar and steady boundary layer flow of an electrically nonconducting and incompressible magnetic fluid, with low Curie temperature and moderate saturation magnetization, over an elastic stretching sheet, is numerically studied. The fluid is subject to the magnetic field generated by an infinitely long, straight wire, carrying an electric current. The magnetic fluid far from the surface is at rest and at temperature greater of that of the sheet. It is also assumed that the magnetization of the fluid varies with the magnetic field strength $H$ and the temperature $T$. The numerical solution of the coupled and nonlinear system of ordinary differential equations, resulting after the introduction of appropriate nondimensional variables, with its boundary conditions, describing the problem under consideration, is obtained by an efficient numerical technique based on the common finite difference method. Numerical calculations are carried out for the case of a representative water-based magnetic fluid and for specific values of the dimensionless parameters entering into the problem, and the obtained results are presented graphically for these values of the parameters. The analysis of these results showed that there is an interaction between the motions of the fluid, which are induced by the stretching surface and by the action of the magnetic field, and the flow field is noticeably affected by the variations in the magnetic interaction parameter $β$. The important results of the present analysis are summarized in Sec. 6.

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## Figures

Figure 1

Schematic representation of flow configuration

Figure 2

(a) Dimensionless velocity component f′(η) and (b) dimensional velocity component u(z) at the plane y=0 and for different positions of x

Figure 3

(a) Dimensionless velocity component g′(η) and (b) dimensional velocity component υ(z) at the plane x=0 and for different positions of y

Figure 4

Dimensionless velocity component −[f(η)+g(η)]

Figure 5

(a) Dimensionless fluid temperature Θ1(η) and (b) dimensional fluid temperature T(z)

Figure 6

Dimensional fluid pressure difference Δp1 in the hydrodynamic case

Figure 7

Dimensional fluid pressure difference Δp in the ferromagnetic case at the plane y=0 and for different positions of x

Figure 8

Dimensionless skin friction coefficient f″(0)

Figure 9

Dimensionless skin friction coefficient g″(0)

Figure 10

Dimensionless wall heat transfer coefficient Θ1′(0)

## Errata

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