In this study, convective heat transfer around and through a porous circular cylinder together with internal heat generation has been investigated numerically. Governing equations containing continuity, momentum, and energy equations have been developed in polar coordinate system in both porous and nonporous media based on single-domain approach. However, governing equations in porous medium are derived using intrinsic volume averaging method. The equations are solved numerically based on finite volume method over staggered grid arrangement. Also, pressure correction-based iterative algorithm, SIMPLE, is applied for solving the pressure linked equations. Reynolds and Peclet numbers (based on cylinder diameter and velocity of free stream) are from 1 to 40. Also, Darcy number (Da) varies within the range of $10-6≤Da≤10-2$ and porosity is considered 0.9 for all calculations. The influence of Da and Re numbers on local and average Nu numbers has been investigated. It is found that the local and average Nu numbers increase with any increase in Da number. Two correlations of average Nu number are presented for high and low Da numbers.

## References

1.
Joshi
,
N. D.
, and
Sukhatme
,
S. P.
, 1971, “
An Analysis of Combined Free and Forced Convection Heat Transfer From a Horizontal Circular Cylinder to a Transverse Flow
,”
ASME J. Heat Transfer
,
93
, pp.
441
448
.
2.
Sparrow
,
E. M.
, and
Lee
,
L.
, 1976,
“Analysis of Mixed Convection About a Horizontal Cylinder,”
Int. J. Heat Mass Transfer
,
19
, pp.
229
232
.
3.
Merkin
,
J. H.
, 1976,
“Mixed Convection From Horizontal Circular Cylinder,”
Int. J. Heat Mass Transfer
,
20
, pp.
73
77
.
4.
,
H. M.
, 1984,
“Laminar Combined Convection From a Horizontal Cylinder-Parallel and Contra Flow Regime
,”
Int. J. Heat Mass Transfer
,
27
, pp.
15
27
.
5.
Bharti
,
R. P.
,
Chhabra
,
R. P.
, and
Eswaran
,
V.
, 2007,
“A Numerical Study of the Steady Forced Convection Heat Transfer From an Unconfined Circular Cylinder,”
Heat Mass Transfer
,
43
, pp.
639
648
.
6.
Zhang
,
N.
,
Zheng
,
Z. C.
, and
Eckels
,
S.
, 2008, “
Study of Heat-Transfer on the Surface of a Circular Cylinder in Flow Using an Immersed-Boundary Method
,”
Int. J. Heat Fluid Flow
,
29
, pp.
1558
1566
.
7.
Cheng
,
P.
, 1982, “
Mixed Convection About a Horizontal Cylinder and a Sphere in a Fluid Saturated Porous Medium
,”
Int. J. Heat Mass Transfer
,
25
, pp.
1245
1247
.
8.
Thevenin
,
J.
, and
,
D.
, 1995, “
About Enhancement of Heat Transfer Over a Circular Cylinder Embedded in Porous Medium
,”
Int. Commun. Heat Mass Transfer
,
20
, pp.
295
304
.
9.
Layeghi
,
M.
, and
Nouri-Borujerdi
,
A.
, 2006, “
Darcy Model for the Study of Fluid Flow and Heat Transfer Around a Cylinder Embedded in Porous Media
,”
Int. J. Comput. Methods Eng. Sci. Mech.
,
7
(
5
), pp.
323
329
.
10.
Beavers
,
G. S.
, and
Joseph
,
D. D.
, 1967, “
Boundary Condition at a Naturally Permeable Wall
,”
J. Fluid Mech.
,
30
, pp.
197
207
.
11.
Saffman
,
P.
, 1971, “
On the Boundary Condition at the Interface of a Porous Medium,”
Stud. Appl. Math.
,
50
, pp.
93
101
.
12.
Valipour
,
M. S.
, and
,
A. Z.
, 2011, “
Numerical Investigation of Fluid Flow and Heat Transfer Around a Solid Circular Cylinder Utilizing Nanofluid
,”
Int. Commun. Heat Mass Transfer
,
38
, pp.
1296
1304
.
13.
Nield
,
A.
, and
Bejan
,
A.
, 1998,
Convective Heat Transfer in Porous Media
,
Springer
,
New York
.
14.
Beckermann
,
C.
, and
Viskanta
,
R.
, 1988, “
Double‐Diffusive Convection during Dendritic Solidification of a Binary Mixture
,”
PhysicoChemical Hydrodynamics.
,
10
, pp.
195
213
.
15.
Vafai
,
K.
, and
Kim
,
S.
, 1989, “
Forced Convection in a Channel Filled With Porous Medium: An Exact Solution
,”
ASME J. Heat Transfer
,
111
(
4
), pp.
1103
1106
.
16.
Basu
,
A. J.
, and
Khalili
,
A.
, 1999, “
Computation of Flow Through a Fluid-Sediment Interface in a Benthic Chamber
,”
Phys. Fluids
,
11
(
6
), pp.
1395
1405
.
17.
Braza
,
M.
,
Chassaing
,
P.
, and
Minh
,
H. H.
, 1986, “
Numerical Study and Physical Analysis of the Pressure and Velocity Fields in the Near Wake of a Circular Cylinder
,”
J. Fluid Mech.
,
165
, pp.
79
130
.
18.
Rajani
,
B. N.
,
Kandasamy
,
A.
, and
Majumdar
,
S.
, 2008, “
Numerical Simulation of Laminar Flow Past a Circular Cylinder
,”
Appl. Math. Model.
,
33
, pp.
1228
1247
.
19.
Patankar
,
S. V.
, 1980,
Numerical Heat Transfer and Fluid Flow
,
Hemisphere
,
New York
.
20.
Versteeg
,
H. K.
, and
Malalasekera
,
W.
, 1995,
An Introduction to Computational Fluid Dynamics: The Finite Volume Method
,
John Wiley & Sons, Inc.
,
New York.