## Abstract

In this study we analyze the combined influence of mass and thermal stratification on non-Darcian double-diffusive natural convection from a wavy vertical wall to a porous media. A finite difference scheme based on the Keller box approach is derived for the boundary layer equations resulting from the use of nonsimilarity transformation on the coupled nonlinear partial differential equations. Extensive numerical simulations are carried out to analyze the influence of wave amplitude $a,$ Grashof number $Gr*,$ thermal stratification parameter $ST,$ concentration stratification parameter $SC,$ buoyancy ratio $B,$ and Lewis number $Le$ on the double-diffusive natural convection process. Increasing $a$ and $Gr*$ or decreasing $B$ is seen to favor the heat and mass transport in the porous region thereby reducing the heat and mass fluxes along the vertical heated surface. Increasing $ST$ or decreasing $Le$ leads to an enhanced mass transfer process. Presence of surface waviness brings in a wavy pattern in the local heat and mass fluxes with decreasing magnitudes in the streamwise direction in the presence of stratification terms.

1.
Nield, D. A., and Bejan, A., 1998, Convection in Porous Media, Springer Verlag, New York.
2.
Bejan
,
A.
, and
Khair
,
K. R.
,
1985
, “
Heat and Mass Transfer by Natural Convection in a Porous Medium
,”
Int. J. Heat Mass Transfer
,
28
(
5
), pp.
909
918
.
3.
Angirasa
,
D.
,
Peterson
,
G. P.
, and
Pop
,
I.
,
1997
, “
Combined Heat and Mass Transfer by Natural Convection With Opposing Buoyancy Effects in a Fluid Saturated Porous Medium
,”
Int. J. Heat Mass Transfer
,
40
(
12
), pp.
2755
2773
.
4.
Singh
,
P.
, and
Queeny
,
O.
,
1997
, “
Free Convection Heat and Mass Transfer Along a Vertical Surface in a Porous Medium
,”
Acta Mech.
,
123
, pp.
69
73
.
5.
Nakayama
,
A.
, and
Hossain
,
M. A.
,
1995
, “
An Integral Treatment for Combined Heat and Mass Transfer by Natural Convection in a Porous Medium
,”
Int. J. Heat Mass Transfer
,
38
(
4
), pp.
761
765
.
6.
Angirasa
,
D.
,
Peterson
,
G. P.
, and
Pop
,
I.
,
1997
, “
Combined Heat and Mass Transfer by Natural Convection in a Saturated Thermally Stratified Porous Medium
,”
Numer. Heat Transfer, Part A
,
31
, pp.
255
272
.
7.
Rathish Kumar
,
B. V.
,
Singh
,
P.
, and
Bansod
,
V. J.
,
2002
, “
Effect of Thermal Stratification on Double-Diffusive Natural Convection in a Vertical Porous Enclosure
,”
Numer. Heat Transfer, Part A
,
41
, pp.
421
447
.
8.
El-Khatib
,
G.
, and
,
V.
,
1987
, “
Effects of Stratification on Thermal Convection in Horizontal Porous Layers With Localized Heating from Below
,”
ASME J. Heat Transfer
,
109
, pp.
683
687
.
9.
Rathish Kumar
,
B. V.
, and
Shalini
,
2004
, “
Double-Diffusive Natural Convection Induced by a Wavy Surface in a Stratified Porous Medium
,”
J. Porous Media
,
7
(
4
), pp.
31
40
.
10.
Takhar
,
H. S.
, and
Pop
,
I.
,
1987
, “
Free Convection From a Vertical Flat Plate to a Thermally Stratified Fluid
,”
Mech. Res. Commun.
,
14
(
2
), pp.
81
86
.
11.
Tewari
,
K.
, and
Singh
,
P.
,
1992
, “
Natural Convection in a Thermally Stratified Fluid Saturated Porous Medium
,”
Int. J. Eng. Sci.
,
8
, pp.
1003
1007
.
12.
Rees
,
D. A. S.
, and
Lage
,
J. L.
,
1997
, “
The Effect of Thermal Stratification on Natural Convection in a Vertical Porous Insulation Layer
,”
Int. J. Heat Mass Transfer
,
40
(
1
), pp.
111
121
.
13.
Rathish Kumar
,
B. V.
, and
Singh
,
P.
,
1998
, “
Effect of Thermal Stratification on Free Convection in a Fluid-Saturated Porous Enclosure
,”
Numer. Heat Transfer, Part A
,
34
, pp.
343
356
.
14.
Yao
,
L. S.
,
1983
, “
Natural Convection Along a Vertical Wavy Surface
,”
ASME J. Heat Transfer
,
105
, pp.
465
468
.
15.
Rees
,
D. A. S
, and
Pop
,
I.
,
1994
, “
A Note on Free Convection Along a Vertical Wavy Surface in a Porous Medium
,”
ASME J. Heat Transfer
,
116
, pp.
505
508
.
16.
Cheng
,
C. Y.
,
2000
, “
Natural Convection Heat and Mass Transfer Near a Vertical Wavy Surface with Constant Wall Temperature and Concentration in a Porous Medium
,”
Int. Commun. Heat Mass Transfer
,
27
(
8
), pp.
1143
1154
.
17.
Bejan
,
A.
, and
Poulikakos
,
D.
,
1984
, “
The Non Darcy Regime for Vertical Boundary Layer Natural Convection in a Porous Medium
,”
Int. J. Heat Mass Transfer
,
27
(
5
), pp.
717
722
.
18.
Plumb
,
O. A.
, and
Huenefeld
,
J. C.
,
1981
, “
Non-Darcy Natural Convection from Heated Surfaces in Saturated Porous Medium
,”
Int. J. Heat Mass Transfer
,
24
(
4
), pp.
765
768
.
19.
Kumari
,
M.
,
Pop
,
I.
, and
Nath
,
G.
,
1985
, “
Non-Darcy Natural Convection from a Heated Vertical Plate in Saturated Porous Media with Mass Transfer
,”
Int. Commun. Heat Mass Transfer
,
12
, pp.
337
346
.
20.
Lai
,
F. C.
, and
Kulacki
,
F. A.
,
1987
, “
Non-Darcy Convection from Horizontal Impermeable Surfaces in Saturated Porous Media
,”
Int. J. Heat Mass Transfer
,
30
(
10
), pp.
2189
2192
.
21.
Angirasa
,
D.
, and
Srinivasan
,
J.
,
1992
, “
Natural Convection Heat Transfer From an Isothermal Vertical Surface to a Stable Thermally Stratified Fluid
,”
ASME J. Heat Transfer
,
114
, pp.
917
923
.
22.
Johnson
,
C. H.
, and
Cheng
,
P.
,
1978
, “