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Research Papers: Forced Convection

Heat and Mass Transfer on the Unsteady Magnetohydrodynamic Flow Due to a Porous Rotating Disk Subject to a Uniform Outer Radial Flow

[+] Author and Article Information
Mustafa Turkyilmazoglu

Department of Mathematics, Hacettepe University, 06532 Beytepe, Ankara, Turkeyturkyilm@hacettepe.edu.tr

J. Heat Transfer 132(6), 061703 (Apr 02, 2010) (6 pages) doi:10.1115/1.4000963 History: Received May 04, 2009; Revised December 14, 2009; Published April 02, 2010; Online April 02, 2010

An unsteady flow and heat transfer of an incompressible electrically conducting fluid over a porous rotating infinite disk impulsively set into motion are studied in the present paper. The disk finds itself subjected to a uniform normal magnetic field. The particular interest lies in searching for the effects of an imposed uniform outer radial flow far above the disk on the behavior of the physical flow. The governing Navier–Stokes and Maxwell equations of the hydromagnetic fluid, together with the energy equation, are converted into self-similar forms using suitable similarity transformations. A compact, unconditionally stable, and highly accurate implicit spectral numerical integration algorithm is then employed in order to resolve the transient behavior of the velocity and temperature fields. The time evolution and steady state case of some parameters of fundamental physical significance such as the surface shear stresses in the radial and tangential directions and the heat transfer rate are also fully examined for the entire family of magnetic interaction, radial flow, and suction/blowing parameters.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Configuration of the flow and geometrical coordinates

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Figure 2

The time progression of basic flow quantities for the rotating disk flow are shown for an MHD (M=1) and permeable wall case (s=1), respectively, in (a) the radial velocity profiles, (b) the circumferential velocity profiles, (c) the wall-normal velocity profiles, and (d) the temperature profiles. The snapshots are given at 0.5 increments in time. The dot-dashed curves correspond to the large time limit as well as the steady solution.

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Figure 3

The time progression of physically significant parameters are shown for the conducting flow case with M=1 and C=0, respectively, in (a) F′(0), (b) −G′(0), (c) H(∞), and (d) −θ′(0). A dashed line corresponds to the steady state value.

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Figure 4

Effects of the uniform outer radial flow on the basic flow quantities for the rotating disk flow are shown for a non-MHD and impermeable wall case, respectively, in (a) the radial velocity profiles, (b) the circumferential velocity profiles, (c) the wall-normal velocity profiles, and (d) the temperature profiles. The increment in C is 0.25 units.

Grahic Jump Location
Figure 5

The variation in physically significant parameters are shown against the radial flow parameter C for the conducting flow with a variety of M, respectively, in (a) F′(0), (b) −G′(0), and (c) −θ′(0). The increment in M is 2 units.

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