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Magnetohydroynamic Free Convection from a Disk Rotating in a Vertical Plane

IP.com Disclosure Number: IPCOM000128721D
Original Publication Date: 1988-Dec-31
Included in the Prior Art Database: 2005-Sep-16
Document File: 8 page(s) / 26K

Publishing Venue

Software Patent Institute

Related People

William Thacker, Layne: AUTHOR [+4]

Abstract

The non-axisymmetric motion (produced by a buoyancy induced cross flow) of a fluid in contact with a rotating disk and in the presence of a magnetic field normal to the disk is studied. Using modern quasi-Newton techniques, B-splines, and a Galerkin approximation to the fluid motion equations, numerical solutions are obtained. for a wide range of magnetic field strengths and Prandtl numbers (ratio of kinematic viscosity to thermal conductivity). Results are presented both in tabular and graphical form in terms of two non-dimensional parameters. There is excellent agreement with previous work.

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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

Magnetohydroynamic Free Convection from a Disk Rotating in a Vertical Plane

William Thacker, Layne T. Watson and S. Kishore Kumar

TR 88 MAGNETOHYDRODYNAMIC FREE CONVECTION FROM A DISK ROTATING IN A VERTICAL PLANE

William I. Thacker Department of Computer Science Winthrop College Rock Hill, SC 29733

Layne T. Watsonfi Department of Computer Science Virginia Polytechnic Institute and State University Blacksburg, VA 24061

S. Kishore Kurnar$ Department of Mathematics and Statistics and Department of Production Technology Massey University Palmerston North, New Zealand

Abstract.

The non-axisymmetric motion (produced by a buoyancy induced cross flow) of a fluid in contact with a rotating disk and in the presence of a magnetic field normal to the disk is studied. Using modern quasi-Newton techniques, B-splines, and a Galerkin approximation to the fluid motion equations, numerical solutions are obtained. for a wide range of magnetic field strengths and Prandtl numbers (ratio of kinematic viscosity to thermal conductivity). Results are presented both in tabular and graphical form in terms of two non-dimensional parameters. There is excellent agreement with previous work.

1. INTRODUCTION.

The axisymmetric character in rotating flows is destroyed when there are translational velocities imposed on a symmetric flow. Rott and Lewellen (1) studied a class of such flows. Their case belongs to the class of exact solutions of the Navier-Stokes equations discussed by Lin (2). Recently, Chawla and Verma (3] obtained a solution to the free convective flow of a viscous incompressible fluid caused by a heated disk rotating in a vertical plane. Although this problem belongs to the class discussed in (21, the energy equation coupled with the momentum equation through buoyancy must be considered. The non-axisymmetric fluid motion is composed of the primary von Karman axisymmetric flow and a secondary buoyancy induced cross flow. Chawla and Verma (3) found transformations that uncouple the momentum and energy equations resulting in independent sets of equations that govern the

a) primary von Karman flow,

b) energy (dependent on the primary flow),

f Supported in part by AFOSR Grant $5-0250. Supported by University Grants Committee.

1 <> c) secondary cross flow (depends on both the primary von Karman flow and the energy).

Virginia Polytechnic Institute and State University Page 1 Dec 31, 1988

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Magnetohydroynamic Free Convection from a Disk Rotating in a Vertical Plane

The present study extends the scope of the work in (3) by imposing a magnetic field normal to the disk surface. Using the transformations in (31 for the flow variables, the governing momentum and energy equations uncouple resulting in a) primary axisymmetric flow with an axial magnetic field (studied by Sparrow and Cess j41), b) an energy equation (dependent on the primary flow),

c) secondary cross flow (depends on both th...