An exact solution of the problem of the unsteady free convection and mass transfer flow near an infinite vertical porous plate, which moves with time-dependent velocity in a viscous and incompressible fluid, is presented here by the Laplace transform technique. All expressions of the new solutions of the present problem were obtained in closed forms with arbitrary Prandtl number $(Pr)$, Schmidt number $(Sc)$, thermal Grashof number $(Gr)$, and mass Grashof number $(Gm)$. Two applications of physical interest for porous or nonporous plate are discussed. Applying numerical values into the expressions of analytical solution, we was also discussed the vertical air flows—the usual phenomenon at plumes into the atmosphere.

1.
Gebhart
,
B.
,
Jaluria
,
Y.
,
Mahajan
,
R. L.
, and
Sammakia
,
B.
, 1988,
Buoyancy-Induced Flows and Transport, Hemisphere
,
New York
, Chaps. 3, 6, 7, 8, 10, 12.
2.
Jaluria
,
Y.
, 1980,
Natural Convection Heat and Mass Transfer
,
Pergamon
,
Oxford, UK
.
3.
Soundalgekar
,
V. M.
, 1979, “
Effects of Mass Transfer and Free Convection Currents on the Flow Past an Impulsively Started Vertical Plate
,”
J. Appl. Mech.
0021-8936,
46
, pp.
757
760
.
4.
Hossain
,
M. A.
, and
Mandal
,
A. C.
, 1985, “
Mass Transfer Effects on the Unsteady Free Convection Flow Past an Accelerated Vertical Porous Plate
,”
J. Phys. D
0022-3727,
18
, pp.
L63
L69
.
5.
Tokis
,
J. N.
, 1988, “
Free Convection and Mass Transfer Effects on the Magnetohydrodynamic Flows Near a Moving Plate in a Rotating Medium
,”
Astrophys. Space Sci.
0004-640X,
98
, pp.
291
301
.
6.
Das
,
U. N.
,
Ray
,
S. N.
, and
Soundalgekar
,
V. M.
, 1996, “
Mass Transfer Effects on Flow Past an Impulsively Started Infinite Vertical Plate With Constant Mass Flux—An Exact Solution
,”
Heat Mass Transfer
0947-7411,
31
, pp.
163
167
.
7.
Muthucumaraswamy
,
R.
, 2003, “
Effects of Chemical Reaction on Moving Isothermal Plate With Variable Mass Diffusion
,”
Theor Appl. Mech.
0285-6042,
30
(
3
), pp.
209
220
.
8.
Ganesan
,
P.
, and
Palani
,
G.
, 2003, “
Natural Convection Effects on Impulsively Started Inclined Plate With Heat and Mass Transfer
,”
Heat Mass Transfer
0947-7411,
39
, pp.
277
283
.
9.
Takhar
,
H. S.
,
Roy
,
S.
, and
Nath
,
G.
, 2003, “
Unsteady Free Convection Flow Over an Infinite Vertical Porous Plate Due to the Combined Effects of Thermal and Mass Diffusion, Magnetic Field and Hall Currents
,”
Heat Mass Transfer
0947-7411,
39
, pp.
825
834
.
10.
Sivasankaran
,
S.
,
Bhuvaneswari
,
M.
,
Kandaswamy
,
P.
, and
Ramasami
,
E. K.
, 2006, “
Lie Group Analysis of Natural Convection and Mass Transfer in an Inclined Porous Surface with Heat Generation
,”
J. Appl. Math. Mech.
0021-8928,
2
(
1
), pp.
34
40
.
11.
Alan
,
M. S.
,
Rahman
,
M. M.
, and
,
M. A.
, 2006, “
Dufour and Soret Effects on Unsteady MHD Free Convection and Mass Transfer Flow Past a Vertical Porous Plate in a Porous Medium
,”
Nonlinear Analysis: Modelling and Control
,
11
(
3
), pp.
217
226
.
12.
Eskinazi
,
S.
, 1975,
Fluid Mechanics and Thermodynamics of Our Environment
,
,
New York
, Chap. 10.
13.
Holman
,
J. P.
, 1972,
Heat Transfer
,
McGraw-Hill
,
New York
.
14.
Toki
,
C. J.
, and
Tokis
,
J. N.
, 2007, “
Exact Solutions for the Unsteady Free Convection Flows on a Porous Plate with Time-dependent Heating
,”
Z. Angew. Math. Mech.
0044-2267,
87
(
1
), pp.
4
13
.