This paper presents a study of the laminar flow in a channel with longitudinal moving bars arrayed along the channel width. The governing equations describing the fluid, which flows along the direction of the bar’s length, are expressed with double Poisson equations and are solved by eigenfunction-expansion and point-match method. The result shows that when the solid bars move forward, the fluid flow will move in the same direction, and the $f Re$ decreases as the positive velocity of bars increases. However, when the bars move backward, a reverse flow will occur in the channel, and the $f Re$ is higher at larger negative velocity of bars. For a channel flow with moving bars, the $f Re$ value is not a constant, such as a classical one without moving bars, in which the $f Re$ value is a constant. Furthermore, when the area of the cross section of the bar is fixed, both the mean velocities and the $f Re$ values of the fluid can be obtained under different velocities and aspect ratios of the bars.

1.
Sparrow
,
E. M.
, and
Loeffler
,
A. L.
, 1959, “
Longitudinal Laminar Flow Between Cylinders Arranged in Regular Array
,”
AIChE J.
0001-1541,
5
, pp.
325
330
.
2.
Cheng
,
K. C.
, 1966, “
Analog Solution of Laminar Heat Transfer in Noncircular Ducts by Moiré Method and Point-Matching
,”
ASME J. Heat Transfer
0022-1481,
88
, pp.
175
182
.
3.
Trogdon
,
S. A.
, and
Joseph
,
D. D.
, 1982, “
Matched Eigenfunction Expansions for a Slow Flow Over a Slot
,”
J. Non-Newtonian Fluid Mech.
0377-0257,
10
, pp.
185
213
.
4.
Zarling
,
J. P.
, 1976, “
An Analysis of Laminar Flow and Pressure Drop in Complex Shaped Ducts
,”
ASME J. Fluids Eng.
0098-2202,
21
, pp.
702
706
.
5.
Wang
,
C. Y.
, 1994, “
Flow in a Channel With Longitudinal Ribs
,”
ASME J. Fluids Eng.
0098-2202,
116
, pp.
233
237
.
6.
Wang
,
C. Y.
, 1976, “
Parallel Flow Between Corrugated Plates
,”
J. Engrg. Mech. Div.
0044-7951,
102
, pp.
1088
1090
.
7.
Achiq
,
A.
, and
Naciri
,
J. K.
, 2001, “
Asymptotic Solutions of the Wake Induced by a Streamwise Moving Flat Plate in a Channel
,”
Int. J. Eng. Sci.
0020-7225,
39
, pp.
1499
1507
.
8.
Fu
,
W. S.
,
Ke
,
W. W.
, and
Wang
,
K. N.
, 2001, “
Laminar Forced Convection in a Channel With a Moving Block
,”
Int. J. Heat Mass Transfer
0017-9310,
44
, pp.
2385
2394
.
9.
Fu
,
W. S.
,
Tseng
,
C. C.
,
Huang
,
C. P.
, and
Wang
,
K. N.
, 2007, “
An Experimental Investigation of a Block Moving Back and Forth on a Heat Plate Under a Slot Jet
,”
Int. J. Heat Mass Transfer
0017-9310,
50
, pp.
3224
3233
.
10.
Luo
,
X. Y.
, and
Pedley
,
T. J.
, 1995, “
A Numerical Simulation of Steady Flow in a 2-D Collapsible Channel
,”
J. Fluids Struct.
0889-9746,
9
, pp.
149
174
.
11.
Bahrami
,
M.
,
Yovanovich
,
M. M.
, and
Culham
,
J. R.
, 2006, “
Pressure Drop of Fully-Developed, Laminar Flow in Microchannels of Arbitrary Cross-Section
,”
ASME J. Fluids Eng.
0098-2202,
128
, pp.
1036
1044
.