This paper reports a new analytical solution for 2D Darcy-Brinkman equations in porous channels filled with porous media subjected to various boundary conditions at walls. The governing equations of fluid flow through porous medium are reduced to a nonlinear ordinary differential equation (ODE) based on physics of fluid flow. The obtained ODE is solved analytically using homotopy perturbation method (HPM). The analytical models for velocity profile and pressure distribution along the length of channel are validated with data available in the open literature and an independent numerical study using finite volume method (FVM). It was shown that there is an excellent agreement between the presented models and the results of the CFD and previous works. Finally, the effects of Reynolds (Re) and Darcy ($Da$), numbers suction or injection parameters ($α,β$) and wall axial velocity coefficients ($λ$ and $γ$) on velocity profiles and pressure drop in different cases are investigated. The models are applicable to analyze flow in channels filled with and without porous media for both moving and stationary walls and can be used to predict flow in micro and macro channels and over stretching sheets in porous medium as well as study of vapor flow in evaporator section of flat plate heat pipes.

## References

References
1.
Vafai
,
K.
, and
Tien
,
C. L.
, 1980, “
Boundary and Inertia Effects on Convection Mass Transfer In Porous Media
,”
Int. J. Heat Mass Transfer
,
25
(
8
), pp.
1183
1190
.
2.
Amiri
,
A.
, and
Vafai
,
K.
, 1994, “
Analysis of Dispersion Effects and Non-thermal Equilibrium, Non-Darcian, Variable Porosity Incompressible Flow Through Porous Media
,”
Int. J. Heat Mass Transfer
,
37
(
6
), pp.
939
954
.
3.
Iyer
,
S. V.
, and
Vafai
,
K.
, 1999, “
Passive Heat Transfer Augmentation in a Cylindrical Annual Utilizing a Porous Perturbation
,”
Numer. Heat Transfer, Part A
,
36
, pp.
115
128
.
4.
Alazmi
,
B.
, and
Vafai
,
K.
, 1999, “
Analysis of Variants within the Porous Media Transport Models
,”
ASME J. Heat Transfer
,
122
, pp.
303
326
.
5.
Kuznestov
,
A. V.
, and
Xiong
,
M.
, 2000, “
Numerical Simulation of the Effect of Thermal Dispersion on Forced Convection in a Circular Duct Partly Filled With a Brinkman-Forchheimer Porous Medium
,”
Int. J. Heat Fluid Flow
,
10
(
5
), pp.
488
501
.
6.
Kuznetsov
,
A. V.
, and
Raleigh
, 2000, “
Investigation of the Effect of Transverse Thermal Dispersion on Forced Convection in Porous Media
,”
Acta Mech. Solida Sinica
,
145
, pp.
35
43
.
7.
Marafie
,
A.
, and
Vafai
,
K.
, 2001, “
Analysis of non-Darcian effects on Temperature Differentials in Porous Media
,”
Int. J. Heat Mass Transfer
,
44
, pp.
4401
4411
.
8.
Haji-Sheikh
,
A.
, and
Vafai
,
K.
, 2004, “
Analysis of Flow and Heat Transfer in Porous Media Imbedded Inside Various-Shaped Ducts
,”
Int. J. Heat Mass Transfer
,
47
, pp.
1889
1905
.
9.
Hooman
,
K.
, 2008, “
A Perturbation Solution for Forced Convection in a Porous Saturated Duct
,”
Comput. Appl. Math.
,
211
, pp.
57
66
.
10.
Hooman
,
K.
, and
Gurgenci
,
H.
, 2008, “
Effects of Temperature-Dependent Viscosity on Forced Convection Inside a Porous Medium
,”
Transp. Porous Media
75
(
2
), pp.
249
267
.
11.
Hooman
,
K.
,
Haji-Sheikh
,
A.
, and
Nield
,
D. A.
, 2007, “
Thermally Developing Brinkman-Brinkman Forced Convection in Rectangular Ducts With Isothermal Walls
,”
Int. J. Heat Mass Transfer
,
50
(
17-18
), pp.
3521
3533
.
12.
Hooman
,
K.
, and
Haji-Sheikh
,
A.
, 2007, “
Analysis of Heat Transfer and Entropy Generation for a Thermally Developing Brinkman-Brinkman Forced Convection Problem in a Rectangular Duct With Isoflux Walls
,”
Int. J. Heat and Transfer
50
(
21
), pp.
4180
4194
.
13.
Jankowski
,
T. A.
, and
Majdalani
,
J.
, 2002, “
Laminar Flow in a Porous Channel With Large Wall Suction and a Weakly Oscillatory Pressure
,”
Phys. Fluids
,
14
(
3
), pp.
1101
1110
.
14.
Attia
,
H. A.
, 2005,
The Effect of Suction and Injection on the Unsteady Flow Between Two Parallel Plates with Variable Properties,”
Tamkang Journal of Science and Engineering
,
8
(
1
), pp.
17
22
.
15.
Attia
,
H. A.
, 2005, “
Unsteady Couette Flow With Heat Transfer Considering Ion-Slip
,”
Turk. J. Phys.
,
29
, pp.
379
388
.
16.
Sharma
,
P. K.
, and
SAINI
,
B. S.
, 2008, “
The Effect of Injection/Suction on Flow Past Parallel Plates with Transpiration Cooling
,”
Turk. J. Eng. Environ. Sci.
,
32
, pp.
289
294
.
17.
Layeghi
,
M.
, and
Seyf
,
H. R.
, 2008, “
Fluid Flow in an Annular Microchannel Subjected to Uniform Wall Injections
,”
ASME J. of Fluids Eng.
,
130
(
5
), pp.
054502.1
054502.5
.
18.
Biazar
,
J.
,
Ayati
,
Z.
, and
Ebrahimi
,
H.
, 2009, “
Homotopy Perturbation Method for General Form of Porous Medium Equation
,”
J. Porous Media
,
12
, pp.
1121
1127
.
19.
Dehghan
,
M.
, and
Shakeri
,
F.
, 2008, “
Use of He’s Homotopy Perturbation Method for Solving a Partial Differential Equation Arising in Modeling of Flow in Porous Media
,”
J. Porous Media
,
11
, pp.
765
778
.
20.
Tasawar
,
H.
, and
Ahmed
,
G.
, 2008, “
Thin-Film Flow of MHD Third Grade Fluid in a Porous Space
,”
J. Porous Media
,
12
, pp.
65
75
.
21.
Rafei
,
M.
,
Vaseghi
,
J.
, and
Ganji
,
D.
, 2007, “
Application of Homotopy-Perturbation Method for Systems of Nonlinear Momentum and Heat Transfer Equations
,”
Heat Transfer Res.
,
38
, pp.
361
379
.
22.
Jafari
,
H.
,
Zabihi
,
M.
, and
Saidy
,
M.
, 2008, “
Application of Homotopy Perturbation Method for Solving Gas Dynamics Equation
,”
Appl. Math. Sci.
,
2
, pp.
2393
2396
.
23.
Ganj
,
D.
, and
Esmaeilpour
,
M.
, 2008, “
A Study on Generalized Couette Flow by He’s Methods and Comparison With the Numerical Solution
,”
World Applied Sciences Journal
,
4
, pp.
470
478
.
24.
Siddiqui
,
A. M.
,
Mahmood
,
R.
, and
Ghori
,
Q. K.
, 2006, “
Homotopy Perturbation Method for Thin Film Flow of Third Grade Fluid Down an Inclined Plane
,”
Chaos, Solitons Fractals
,
35
, pp.
140
147
.
25.
He
,
J. H.
, 2000, “
A Coupling Method of Homotopy Technique and Perturbation Technique for Nonlinear Problems
,”
Int. J. Non-Linear Mech.
,
351
, pp.
37
43
.
26.
He
,
J. H.
, 1999, “
Homotopy Perturbation Technique
,”
Comput. Math. Appl.
,
178
(
3
), pp.
257
262
.
27.
Patankar
,
S. V.
, 1980,
Numerical Heat Transfer and Fluid Flow
,
Hemisphere
,
New York
.
28.
Ferziger
,
J. H.
, and
Peric
,
M.
,
Computational Methods for Fluid Dynamics
,
2nd ed.
, (
Springer
,
New York
, 1999).
29.
Tamayol
,
A.
,
Hooman
,
K.
, and
Bahrami
,
M.
, 2010,
“Thermal Analysis of Flow in a Porous Medium Over a Permeable Stretching Wall,”
Transp. Porous Media
,
85
(1),
661
676
.
30.
Zhu
,
N.
, and
Vafai
,
K.
, 1998, “
Vapor and Liquid Flow in an Asymmetrical Flat Plate Heat Pipe: a Three-dimensional Analytical and Numerical Investigation
,”
Int. J. Heat Mass Transfer
,
41
(
1
), pp.
159
174
.