The Flow of Conducting power-Law Fluids in a Narrow Divergent Channel

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概要

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• The laminar flow of conducting and non-conducting power-law fluids has been studied by Sarpkaya, Kapur and others. The lubrication flow of these fluids has been recently studied by Shukla. Here the flow of a conducting power-law fluid in a divergent channel with a uniform magnetic field B_0 applied parallel to the walls of channel and perpendicular to the direction of the fluid motion, is sudied. The two walls of the channel act as electrodes and this geometry permits a current J_y to flow in the y-direction. The physical situation is explained in the Fig.1. Since the thickness of the liquid film in the channel is much smaller then its length L the assumptions of magneto-hydrodynamic lubrication are used. For simplication the inertia, curvature and end effects are considered negligible. Following Elco and Hughes the basic equations governing the steady flow of a conducting powerlaw fluid is 0=-dh/dx+m∂/∂y{|∂u/∂y|^<n-1>∂u/∂y }+J_yB_0 (1) where dh/dx and J_y are functions x alone and u, p,m,n denote the velocity, pressure, consistency index, flow behaviour index of the fluid respectively. Since in the upper half of the film u decreases as y increases, ∂u/∂y is negative. Hence (1) can be written as ∂/∂y{-∂u/∂y }^n=-1/m{dp/dx-J_yBo }・ (2) Integrating equation (2) and using the boundary conditions, u=O at y=h/2; au/ay=O at y=O (3) We get, u={-1/m(dp/dx-J_yBo) }^<1/n> (h/2)^<1+1/n>-y^<1+1/n>/1+1/n (4) The flow rate Q per unit width is given by Q=2∫^<k/2>_o udy (5) because u is symmetrical about the x-axis. Then equations (4) and (5) give Q={-1/m(dp/dx-J_yB_o) }^1/n ・ 2n/2n+1 ・ (h/2)^<2+1/n>. (6)

• 社団法人日本物理学会の論文
• 1964-06-05

著者

• Shukla J.b.

  Department Of Methematics Indian Institute Of Technology

• Shukla J.b.

  Department Of Mathematics Indian Institute Of Technology

関連論文

• The Flow of Conducting power-Law Fluids in a Narrow Divergent Channel
• Unsteady Flow Of a Conducting Fluid between Two Non-Conducting Porous Plates in the Presence of a Transverse Magnetic Field at Magnetic Prandtl Number I

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