Abstract
Flow and temperature fields in an annulus between two rotating cylinders have been examined in this study. While the outer cylinder is stationary, the inner cylinder is rotating with a constant angular speed. A homogeneous and isotropic porous layer is press fit to the inner surface of the outer cylinder. The porous sleeve is saturated with the fluid that fills the annulus. The Brinkman-extended Darcy equations are used to model the flow in the porous layer while the Navier–Stokes equations are used for the fluid layer. The conditions applied at the interface between the porous and fluid layers are the continuity of temperature, heat flux, tangential velocity, and shear stress. Analytical solutions have been attempted. Through these solutions, the effects of Darcy number, Brinkman number, and porous sleeve thickness on the velocity profile and temperature distribution are studied.
Issue Section:
Porous
Media
1.
Vafai
, K.
, and Kim
, S. J.
, 1990, “Analysis of Surface Heat Transfer Enhancement by a Porous Substrate
,” ASME J. Heat Transfer
0022-1481, 112
, pp. 700
–706
.2.
Huang
, P. C.
, and Vafai
, K.
, 1994, “Analysis of Flow and Heat Transfer Over an External Boundary Covered With a Porous Substrate
,” ASME J. Heat Transfer
0022-1481, 116
, pp. 768
–771
.3.
Kuznetsov
, A. V.
, 2000, “Fluid Flow and Heat Transfer Analysis of Couette Flow in a Composite Duct
,” Acta Mech.
0001-5970, 140
, pp. 163
–170
.4.
Nield
, D. A.
, and Kuznetsov
, A. V.
, 2003, “Boundary-Layer Analysis of Forced Convection With a Plate and Porous Substrate
,” Acta Mech.
0001-5970, 166
, pp. 141
–148
.5.
Nield
, D. A.
, Kuznetsov
, A. V.
, and Xiong
, M.
, 2003, “Thermally Developing Forced Convection in a Porous Medium: Parallel Plate Channel With Walls at Uniform Temperature, With Axial Conduction and Viscous Dissipation Effects
,” Int. J. Heat Mass Transfer
0017-9310, 46
, pp. 643
–651
.6.
Capone
, E.
, 1970, “Lubrication of Axially Undefined Porous Bearings
,” Wear
0043-1648, 15
, pp. 157
–170
.7.
Diprima
, R. C.
, and Stuart
, W. H.
, 1972, “Flow Between Eccentric Rotating Cylinders
,” ASME J. Lubr. Technol.
0022-2305, 94
, pp. 266
–274
.8.
Cusano
, C.
, 1973, “The Effects of Variable Permeability on the Performance Characteristics of Porous Bearings
,” Wear
0043-1648, 23
, pp. 55
–62
.9.
Gururajan
, K.
, and Prakash
, J.
, 1999, “Surface Roughness Effects in Infinitely Long Porous Journal Bearings
,” ASME J. Tribol.
0742-4787, 121
, pp. 139
–147
.10.
Channabasappa
, M. N.
, Ranganna
, G.
, and Rajappa
, B.
, 1984, “Stability of Viscous Flow in a Rotating Porous Medium in the Form of an Annulus: The Small-Gap Problem
,” Int. J. Numer. Methods Fluids
0271-2091, 4
, pp. 803
–811
.11.
Chang
, M.-H.
, 2003, “Hydrodynamic Stability of Taylor–Dean Flow Between Rotating Porous Cylinders With Radial Flow
,” Phys. Fluids
1070-6631, 15
, pp. 1178
–1188
.12.
Beavers
, G. S.
, and Joseph
, D. D.
, 1967, “Boundary Conditions at a Naturally Permeable Wall
,” J. Fluid Mech.
0022-1120, 30
, pp. 197
–207
.13.
Neale
, G.
, and Nader
, W.
, 1974, “Practical Significance of Brinkman Extension of Darcy’s Law. Coupled Parallel Flow Within a Channel and a Bounding Porous Medium
,” Can. J. Chem. Eng.
0008-4034, 52
, pp. 475
–478
.14.
Ochoa-Tapia
, J. A.
, and Whitaker
, S.
, 1995, “Momentum Transfer at the Boundary Between a Porous Medium and a Homogeneous Fluid—I. Theoretical Development
,” Int. J. Heat Mass Transfer
0017-9310, 38
, pp. 2635
–2646
.15.
Ochoa-Tapia
, J. A.
, and Whitaker
, S.
, 1995, “Momentum Transfer at the Boundary Between a Porous Medium and a Homogeneous Fluid—II. Comparison With Experiment
,” Int. J. Heat Mass Transfer
0017-9310, 38
, pp. 2647
–2655
.16.
Kuznetsov
, A. V.
, 1997, “Influence of the Stress Jump Condition at the Porous-Medium∕Clear-Fluid Interface on a Flow at a Porous Wall
,” Int. Commun. Heat Mass Transfer
0735-1933, 24
, pp. 401
–410
.17.
Kuznetsov
, A. V.
, 1998, “Analytical Investigation of Coette Flow in a Composite Channel Partially Filled With a Porous Medium and Partially Filled With a Clear Fluid
,” Int. J. Heat Mass Transfer
0017-9310, 41
, pp. 2556
–2560
.18.
Kuznetsov
, A. V.
, 1999, “Fluid Mechanics and Heat Transfer in the Interface Region Between a Porous Medium and a Fluid Layer: A Boundary Layer Solution
,” J. Porous Media
1091-028X, 2
, 309
–321
.19.
Alazmi
, B.
, and Vafai
, K.
, 2001, “Analysis of Fluid Flow and Heat Transfer Interfacial Conditions Between a Porous Medium and a Fluid Layer
,” Int. J. Heat Mass Transfer
0017-9310, 44
, pp. 1735
–1749
.20.
Nield
, D. A.
, 2000, “Resolution of a Paradox Involving Viscous Dissipation and Nonlinear Drag in a Porous Medium
,” Transp. Porous Media
0169-3913, 41
, pp. 349
–357
.21.
Al-Hadhrami
, A. K.
, Elliott
, L.
, and Ingham
, D. B.
, 2003, “A New Model for Viscous Dissipation in Porous Media Across a Range of Permeability Values
,” Transp. Porous Media
0169-3913, 53
, pp. 117
–122
.Copyright © 2008
by American Society of Mechanical Engineers
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