Numerical solutions are presented for the problem of transient, developing, forced-convection flow in concentric annuli partially filled with porous substrates. The porous substrate is attached either to the inner cylinder (case I), or to the outer cylinder (case O). In both cases, the boundary in contact with the porous substrate is exposed to a sudden change in its temperature while the other boundary is kept adiabatic. Including the macroscopic inertial term, the Brinkman-Forchheimer-extended Darcy model is used to model the flow inside the porous domain. The effects of different parameters regarding the geometry, the solid matrix, and the fluid on the hydrodynamic and thermal behavior are investigated. It is shown that porous substrates may improve Nusselt number by 1200 percent keeping other flow and geometrical parameters fixed. Also, it is found that there is an optimum thickness for the porous substrate beyond which there is no significant improvement in Nusselt number. In the present work, the dimensionless hydrodynamic entrance length Zen varies within the range 2–45 and it has significant effect on the fully developed Nusselt number at steady-state conditions. As a result, the macroscopic inertial term in the porous domain momentum equation should not be neglected.

1.
Beavers
G. S.
, and
Joseph
D. D.
,
1967
, “
Boundary Conditions at a Naturally Permeable Wall
,”
J. Fluid Mech.
, Vol.
13
, pp.
197
207
.
2.
Bodoia
J. R.
, and
Osterle
J. F.
,
1961
, “
Finite-Difference Analysis of Plane Poiseuille and Couette Flow Developments
,”
Apll. Sci. Res.
, Vol.
A10
, pp.
265
276
.
3.
Chikh
S.
,
Boumedien
A.
,
Bouhadef
K.
, and
Lauriat
G.
,
1995
a, “
Analytical Solution of Non-Darcian Forced Convection in an Annular Duct Partially Filled with a Porous Medium
,”
Int. J. Heat and Mass Transfer
, Vol.
38
, pp.
1543
1551
.
4.
Chikh
S.
,
Boumedien
A.
,
Bouhadef
K.
, and
Lauriat
G.
,
1995
b, “
Non-Darcian Forced Convection Analysis in an Annular Partially Filled with a Porous Material
,”
Numerical Heat Transfer A
, Vol.
28
, pp.
707
722
.
5.
El-Shaarawi
M. A.
, and
Alkam
M.
,
1992
, “
Transient Forced Convection in the Entrance Region of Concentric Annuli
,”
Int. J. Heat Mass Transfer
, Vol.
35
, pp.
3335
3344
.
6.
Jang
J. Y.
, and
Chen
J. L.
,
1992
, “
Forced Convection in a Parallel Plate Channel Partially Filled with a High Porosity Medium
,”
Int. Comm. Heat Mass Transfer
, Vol.
19
, pp.
263
273
.
7.
Kakac, S., Kilkis, B., Kulacki, F., and Arinc, F., 1991, Convective Heat and Mass Transfer in Porous Media, Kluwer Academic Publishers, The Netherlands, pp. 563–615.
8.
Poulikakos
D.
, and
Kazmierczak
M.
,
1987
, “
Forced Convection in a Duct Partially Filled with a Porous Material
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
109
, pp.
653
662
.
9.
Rudraiah
N.
,
1985
, “
Forced Convection in a Parallel Plate Channel Partially Filled with a Porous Material
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
107
, pp.
322
331
.
10.
Vafai
K.
, and
Kim
S. J.
,
1990
, “
Fluid Mechanics of the Interface Region Between a Porous Medium and a Fluid Layer-An Exact Solution
,”
Int. J. Heat and Fluid Flow
, Vol.
11
, pp.
254
256
.
11.
Vafai
K.
, and
Kim
S. J.
,
1995
, “
On the Limitations of the Brinkman-Forchheimer-extended Darcy Equation
,”
Int. J. Heat and Fluid Flow
, Vol.
16
, pp.
11
15
.
12.
Vafai
K.
, and
Thiyagaraja
R.
,
1987
, “
Analysis of Flow and Heat Transfer at the Interface Region of a Porous Medium
,”
Int. J. Heat and Mass Transfer
, Vol.
30
, pp.
1391
1405
.
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