Abstract
Fluid flow in saturated porous media imbedded with a solid inclusion may be described by the Darcy–Brinkman equation. When the Darcy number is small, a boundary-layer theory, similar to Prandtl's theory for viscous flow, is established. The pressure and shear forces are predicted for Darcy–Brinkman flows over a variety of solid inclusions.
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References
1.
Ingham
,
D. B.
, and
Pop
,
I.
, 2002
, Transport in Porous Media
,
Pergamon
,
Oxford, UK
.2.
Nield
,
D. A.
, and
Bejan
,
A.
, 2006
, Convection in Porous Media
, 3rd ed.,
Springer
,
New York
.3.
Vafai
,
K.
, and
Tien
,
C. L.
, 1981
, “
Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media
,” Int. J. Heat Mass Transfer
,
24
(2
), pp. 195
–203
.10.1016/0017-9310(81)90027-24.
Beckermann
,
C.
, and
Viskanta
,
R.
, 1987
, “
Forced Convection Boundary Layer Flow and Heat Transfer Along a Flat Plate Embedded in a Porous Medium
,” Int. J. Heat Mass Transfer
,
30
(7
), pp. 1547
–1551
.10.1016/0017-9310(87)90188-85.
Kaviany
,
M.
, 1987
, “
Boundary-Layer Treatment of Forced Convection Heat Transfer From a Semi-Infinite Flat Plate Embedded in Porous Media
,” ASME J. Heat Transfer
,
109
(2
), pp. 345
–349
.10.1115/1.32480866.
Nakayama
,
A.
,
Kokudai
,
T.
, and
Koyama
,
H.
, 1990
, “
Non-Darcian Boundary Layer Flow and Forced Convection Heat Transfer Over a Flat Plate in a Fluid-Saturated Porous Medium
,” ASME J. Heat Transfer
,
112
(1
), pp. 157
–162
.10.1115/1.29103387.
Spielman
,
L.
, and
Goren
,
S. L.
, 1968
, “
Model for Predicting Pressure Drop and Filtration Efficiency in Fibrous Media
,” Envir. Sci. Technol.
,
2
(4
), pp. 279
–287
.10.1021/es60016a0038.
Pop
,
I.
, and
Ingham
,
D. B.
, 1996
, “
Flow Past a Sphere Embedded in a Porous Medium Based on the Brinkman Model
,” Int. Comm. Heat Mass Transfer
,
23
(6
), pp. 865
–874
.10.1016/0735-1933(96)00069-39.
Barman
,
B.
, 1996
, “
Flow of a Newtonian Fluid Past an Impervious Sphere Embedded in a Porous Medium
,” Ind. J. Pure Appl. Math.
,
27
, pp. 1249
–1256
.10.
Ganapathy
,
R.
, 1997
, “
Creeping Flow Past a Solid Sphere in a Porous Medium
,” Z. Angew. Math. Mech.
,
77
(11
), pp. 871
–875
.10.1002/zamm.1997077111311.
Wang
,
C. Y.
, 2009
, “
Darcy-Brinkman Flow With Solid Inclusions
,” Chem. Eng. Commun.
,
197
(3
), pp. 261
–274
.10.1080/0098644090308860312.
Schlichting
,
H.
, and
Gersten
,
K.
, 2000
, Boundary Layer Theory
, 8th ed.,
Springer
,
Berlin
.13.
Milne-Thomson
,
L. M.
, 1996
, Theoretical Hydrodynamics
, 5th ed.,
Dover
,
New York
.14.
Wu
,
Q.
,
Weinbaum
,
S.
, and
Andreopoulos
,
Y.
, 2005
, “
Stagnation-Point Flows in a Porous Medium
,” Chem. Eng. Sci.
,
60
(1
), pp. 123
–134
.10.1016/j.ces.2004.07.06215.
Howarth
,
L.
, 1951
, “
The Boundary Layer in Three Dimensional Flow—Part II: The Flow Near a Stagnation Point
,” Philos. Mag. Ser. 7
,
42
(335
), pp. 1433
–1440
.10.1080/1478644510856096216.
Van Dyke
,
M.
, 1975
, Perturbation Methods in Fluid Mechanics
,
Parabolic Press
,
Stanford, CA
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