An approximate solution to the Navier–Stokes equations was found for the case describing two-dimensional steady-state laminar flow over an array of porous pipes with high wall Reynolds number. The Navier–Stokes equations in cylindrical coordinates reduced to a fourth-order nonlinear differential equation, which was solved for high wall Reynolds number flows through the porous wall using a zeroth- and first-order singular perturbation method. Our analytic solution for the high wall Reynolds number case is consistent with solutions found from the low Reynolds number case and that found using finite element analysis.

1.
Moussy
,
Y.
, and
Snider
,
A. D.
, 2009, “
Laminar Flow Over Pipes With Injection and Suction Through the Porous Wall at Low Wall Reynolds Numbers
,”
J. Membr. Sci.
0376-7388,
327
, pp.
104
107
.
2.
Berman
,
A. S.
, 1958, “
Laminar Flow in an Annulus With Porous Walls
,”
J. Appl. Phys.
0021-8979,
29
, pp.
71
75
.
3.
Terrill
,
R. M.
, 1967, “
Flow Through a Porous Annulus
,”
Appl. Sci. Res.
0003-6994,
17
, pp.
204
222
.
4.
Huang
,
C. -L.
, 1974, “
Applying Quasilinearization to the Problem of Flow Through an Annulus With Porous Walls of Different Permeability
,”
Appl. Sci. Res.
0003-6994,
29
, pp.
145
158
.
5.
Devanathan
,
R.
, and
Raju
,
K. K.
, 1971, “
Flow of a Power Law Fluid in an Annulus With Porous Walls
,”
Rheol. Acta
0035-4511,
10
, pp.
371
377
.
6.
Jankowski
,
T. A.
, and
Majdalani
,
J.
, 2005, “
Vortical and Acoustical Mode Coupling Inside a Porous Tube With Uniform Wall Suction
,”
J. Acoust. Soc. Am.
0001-4966,
117
(
6
), pp.
3448
3458
.
7.
Yuan
,
S. W.
, and
Finkelstein
,
A. B.
, 1956, “
Laminar Pipe Flow With Injection and Suction Through a Porous Wall
,”
Trans. ASME
0097-6822,
78
, pp.
719
724
.
8.
Baker
,
R. W.
, 2002, “
Future Directions of Membrane Gas Separation Technology
,”
Ind. Eng. Chem. Res.
0888-5885,
41
, pp.
1393
1411
.
9.
Haas
,
P.
, 2007, “
Simulation d’un Generateur d’Hydrogene par Dissociation de Vapeur d’Eau a 2500 K—Project ‘Clean Hydrogen’
,”
Activities de Recherché 2005–2007
, EIG, Geneva.
10.
Cerri
,
G.
,
Giovannelli
,
A.
,
Battisti
,
L.
, and
Fedrizzi
,
R.
, 2007, “
Advances in Effusive Cooling Techniques of Gas Turbines
,”
Appl. Therm. Eng.
1359-4311,
27
, pp.
692
698
.
11.
Hazen
,
D. C.
, 1980, “
Boundary Layer Control
,”
Illustrated Experiments in Fluid Mechanics: The NCFMF Book of Film Notes
,
Encyclopaedia Britannica Education Corp.
,
Chicago, IL
, pp.
89
96
.
12.
Moussy
,
Y.
, 2000, “
Bioartificial Kidney. I. Theoretical Analysis of Convective Flow in Hollow Fiber Modules: Application to a Bioartificial Hemofilter
,”
Biotechnol. Bioeng.
0006-3592,
68
(
2
), pp.
142
152
.
13.
Waterland
,
L. R.
,
Robertson
,
C. R.
, and
Michaels
,
A. S.
, 1975, “
Enzymatic Catalysis Using Asymmetric Hollow Fiber Membranes
,”
Chem. Eng. Commun.
0098-6445,
2
, pp.
37
47
.
14.
Moussy
,
Y.
, 2003, “
Convective Flow Through a Hollow Fiber Bioartificial Liver
,”
Artif. Organs
0160-564X,
27
(
11
), pp.
1041
1049
.
15.
Berman
,
A. S.
, 1953, “
Laminar Flow in Channels With Porous Walls
,”
J. Appl. Phys.
0021-8979,
24
(
9
), pp.
1232
1235
.
16.
Robertson
,
J. A.
, and
Crowe
,
C. T.
, 1985,
Engineering Fluid Mechanics
,
3rd ed.
,
Houghton Mifflin Company
,
Boston, MA
, Chap. 12.
17.
Ma
,
R. P.
,
Gooding
,
C. H.
, and
Alexander
,
W. K.
, 1985, “
A Dynamic Model for Low-Pressure Hollow-Fiber Ultrafiltration
,”
AIChE J.
0001-1541,
31
(
10
), pp.
1728
1732
.
You do not currently have access to this content.