In the present study, the effects of radiation and chemical reaction on unsteady free convection flow and mass transfer of a viscous, electrically conducting incompressible fluid near an impulsively moving vertical flat plate with ramped wall temperature is studied. The primary purpose of this study is to characterize the effects of ramped wall temperature, radiation parameter, chemical reaction parameter, Schmidt number etc., on the flow properties. Exact solutions of the present problem are obtained in closed form by Laplace transform technique. The variations in fluid velocity, temperature and concentration are shown graphically whereas numerical values of skin friction, rate of heat and mass transfer are presented in tabular form to observe the effects of various parameters.

References

References
1.
Martynenko
,
O. G.
,
Berezovsky
,
A. A.
, and
Sokovishin
,
Yu. A.
, 1984, “
Laminar Free Convection Flow From a Vertical Plate
Int. J. Heat Mass Transfer
,
27
, pp.
869
881
.
2.
Kolar
,
A. K.
, and
Sastri
,
V. M.
, 1988, “
Free Convective Transpiration Over a Vertical Plate: A Numerical Study
,”
Heat Mass Transfer
,
23
(
6
), pp.
327
336
.
3.
Ramanaiah
,
G.
, and
Malarvizhi
,
G.
, 1992, “
Unified Treatment of Free Convection Adjacent to a Vertical Plate With Three Thermal Boundary Conditions
,”
Heat Mass Transfer
,
27
(
6
), pp.
393
396
.
4.
Camargo
,
R.
,
Luna
,
E.
, and
Trevino
,
C.
, 1996, “
Numerical Study of the Natural Convective Cooling of a Vertical Plate
,”
Heat Mass Transfer
,
32
, pp.
89
95
.
5.
Das
,
U. N.
,
Rar
,
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
,
31
, pp.
163
167
.
6.
Revankar
,
S. T.
, 2000, “
Free Convection Effect on the Flow Past an Impulsively Started or Oscillating Infinite Vertical Plate
,”
Mech. Res. Commun.
,
27
, pp.
241
246
.
7.
Muthukumaraswamy
,
R.
, 2003, “
Effects of Chemical Reaction on Moving Isothermal Plate With Variable Mass Diffusion
,”
Theor. Appl. Mech.
,
30
(
3
), pp.
209
220
.
8.
Panda
,
J. P.
,
Dash
,
G. C.
, and
Dash
,
S. S.
, 2003, “
Unsteady Free Convection Flow and Mass Transfer Past a Vertical Porous Plate
,”
ASME Modelling B
,
72
(
3
), pp.
47
58
.
9.
Israel-Cookey
,
C.
, and
Sigalo
,
F. B.
, 2003, “
Unsteady MHD Free Convection and Mass Transfer Flow Past an Infinite Heated Porous Vertical Plate With Time Suction
,”
ASME Modelling B
,
73
(
3
), pp.
25
32
.
10.
Sahoo
,
P. K.
,
Datta
,
N.
, and
Biswal
,
S.
, 2003, “
Magnetohydrodynamic Unsteady Free Convection Flow Past an Infinite Vertical Plate With Constant Suction and Heat Sink
,”
Indian J. Pure Appl. Math
,
34
(
1
), pp.
145
155
.
11.
Takhar
,
H. S.
,
Ray
,
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 Current
,”
Heat Mass Transfer
,
39
, pp.
825
834
.
12.
Chaudhary
,
R. C.
, and
Jain
,
A.
, 2007, “
Combined Heat and Mass Transfer Effects on MHD Free Convection Flow Past an Oscillating Plate Embedded in Porous Medium
,”
Rom. J. Phys.
,
52
(
5–7
), pp.
505
524
.
13.
Makinde
,
O. D.
, 2010, “
On MHD Heat and Mass Transfer Over a Moving Vertical Plate With a Convective Surface Boundary Condition
,”
Can. J. Chem. Eng.
,
88
, pp.
983
990
.
14.
Cogley
,
A. C.
,
Vincenty
,
W. E.
, and
Gilles
,
S. E.
, 1968, “
Differential Approximation for Radiation in a Non-Gray Gas Near Equilibrium
,”
AIAA J.
,
6
, pp.
551
553
.
15.
Gupta
,
P. S.
, and
Gupta
,
A. S.
, 1974, “
Radiation Effect on Hydrodynamic Convection in a Vertical Channel
,”
Int. J. Heat Mass Transfer
,
17
, pp.
1437
1442
.
16.
Soundalgekar
,
V. M.
, and
Takhar
,
H. S.
, 1992, “
Radiative Convective Flow Past a Semi Infinite Vertical Plate
,”
Modeling Measure and Cont.
,
51
, pp.
31
40
.
17.
Hossain
,
M. A.
, and
Takhar
,
H. S.
, 1996, “
Radiation Effect on Mixed Convection Along a Vertical Plate With Uniform Surface Temperature
,”
Heat Mass Transfer
,
31
, pp.
243
248
.
18.
Raptis
,
A.
, 1998, “
Radiation and Free Convection Flow Through a Porous Medium
,”
Int. Commun. Heat Mass Transfer
,
25
, pp.
289
295
.
19.
Muthcuumaraswamy
,
R.
, and
Senthil
,
G. K.
, 2004, “
Heat and Mass Transfer Effects on Moving Vertical Plate in the Presence of Thermal Radiation
,”
Theor. Appl. Mech.
,
31
(
1
), pp.
35
46
.
20.
Makinde
,
O. D.
, 2005, “
Free Convection Flow With Thermal Radiation and Mass Transfer Past Amoving Vertical Porous Plate
,”
Int. Commun. Heat Mass Transfer
,
32
, pp.
1411
1419
.
21.
Majumder
,
M. K.
, and
Deka
,
R. K.
, 2007, “
MHD Flow Past an Impulsively Started Infinite Vertical Plate in Presence of Thermal Radiation
,”
Rom. J. Phys.
,
52
(
5–7
), pp.
565
573
.
22.
Shateyi
,
S.
,
Sibanda
,
P.
, and
Motsa
,
S. S.
, 2007, “
Magnetohydrodyanamic Flow Past a Vertical Plate With Radiative Heat Transfer
,”
ASME J. Heat Transfer
,
129
, pp.
1708
1713
.
23.
Ogulu
,
A.
, and
Makinde
,
O. D.
, 2009, “
Unsteady Hydromagnetic Free Convection Flow of a Dissipative and Radiating Fluid Past a Vertical Plate With Constant Heat Flux
,”
Chem. Eng. Commun.
,
196
(
4
), pp.
454
462
.
24.
Toki
,
C. J.
, 2008, “
Free Convection and Mass Transfer Flow Near a Moving Vertical Porous Plate: An Analytical Soluton
,”
ASME J. Appl. Mech.
,
75
(
1
), p.
011014
.
25.
Das
,
K.
, and
Das
,
R.
, 2009, “
MHD Free Convection Flow Near a Moving Vertical Plate in Presence of Thermal Radiation: An Analytical Soluton
,”
Moldavian J. Phys. Sci.
,
8
, pp.
358
365
.
26.
Das
,
K.
, 2010, “
Exect Solution of MHD Free Convection Flow and Mass Transfer Near a Moving Vertical Plate in Presence of Thermal Radiation
,”
African J. Math. Phys.
,
8
, pp.
29
41
.
27.
Apelblat
,
A.
, 1982, “
Mass Transfer With a Chemical Reaction of the First Order. Effects of Axial Diffusion
,”
Chem. Eng. J.
,
23
, pp.
193
199
.
28.
Jensen
,
K. F.
,
Einset
,
E. Q.
, and
Fotiadis
,
D. I.
, 1991, “
Flow Phenomena in Chemical Vapor Deposition of Thin Films
,”
Ann. Rev. Fluid. Mech.
,
23
, pp.
197
232
.
29.
Cheng
,
W. T.
, and
Lin
,
H. T.
, 2002, “
Non Similarity Solution and Correlation of Transient Heat Transfer in Laminar Boundary Layer Flow Over a Wedge
,”
Int. J. Eng. Sci.
,
40
, pp.
531
538
.
30.
Bor
,
K. L.
, 2005, “
Heat Transfer Analysis for the Falkner Skan Wedge Flow by the Differential Transformation Method
,”
Int. J. Heat Mass Transfer
,
48
, pp.
5036
5045
.
31.
Makinde
,
O. D.
, and
Olanrewaju
,
P. O.
, 2011, “
Unsteady Mixed Convection With Soret and Dufour Effects Past a Porous Plate Moving Through a Binary Mixture of Chemically Reacting Fluid
,”
Chem. Eng. Commun.
,
198
(
7
), pp.
920
938
.
32.
Das
,
K.
, and
Jana
,
S.
, 2009, “
MHD Free Convection Flow of a Radiating and Chemically Reacting Fluid
,”
Int. J. Eng. Inter. Discipline Maths
,
1
, pp.
23
33
.
33.
Muhaimin
,
I.
,
Kandasamy
,
R.
, and
Hashim
,
I.
, 2010, “
Effect of Chemical Reaction, Heat and Mass Transfer on Nonlinear Boundary Layer Past a Porous Shrinking Sheet in the Presence of Suction
,”
Nucl. Eng. Des.
,
240
, pp.
933
939
.
34.
Das
,
K.
, and
Das
,
R.
, 2010, “
Effects of Radiation and Transpiration on Free Convection and Mass Transfer Flow Through a Porous Medium of a Chemically Reacting Fluid
,”
J. Indian Acad. Math
,
32
, pp.
405
419
.
35.
Das
,
K.
, 2011, “
Effects of Heat and Mass Transfer on MHD Free Convection Flow Near a Moving Vertical Plate of a Radiating and Chemically Reacting Fluid
,”
J. Siberian Fed. Univ. Maths. Phys.
,
4
, pp.
18
31
.
36.
Das
,
K.
, 2011, “
Effect of Chemical Reaction and Thermal Radiation on Heat and Mass Transfer Flow of MHD Micropolar Fluid in a Rotating Frame of Reference
,”
Int. J. Heat Mass Transfer
,”
54
, pp.
3505
3513
.
37.
Hayday
,
A. A.
,
Bowlus
,
D. A.
, and
McGraw
,
R. A.
, 1967, “
Free Convection From a Vertical Plate With Step Discontinuities in Surface Temperature
,”
ASME J. Heat Trans.
,
89
, pp.
244
250
.
38.
Kelleher
,
M.
, 1971, “
Free Convection From a Vertical Plate With Discontinuous Wall Temperature
,”
ASME J. Heat Trans.
,
93
, pp.
349
356
.
39.
Kao
,
T. T.
, 1975, “
Laminar Free Convective Heat Transfer Response Along a Vertical Flat Plate With Step Jump in Surface Temperature
,”
Lett. Heat Mass Transfer
,
2
, pp.
419
428
.
40.
Lee
,
S.
, and
Yovanovich
,
M. M.
, 1991, “
Laminar Natural Convection From a Vertical Plate With a Step Change in Wall Temperature
,”
ASME J. Heat Transfer
,
113
, pp.
501
504
.
41.
Chandran
,
P.
,
Sacheti
,
N. C.
, and
Singh
,
A. K.
, 2005, “
Natural Convection Near a Vertical Plate With Ramped Wall Temperature
,”
Heat Mass Transfer
,
41
, pp.
459
464
.
42.
Seth
,
G. S.
, and
Ansari
,
Md. S.
, 2010, “
MHD Natural Convection Flow Past an Impulsively Moving Vertical Plate With Ramped Wall Temperature in the Presence of Thermal Diffusion With Heat Absorption
,”
Int. J. Appl. Mech.
,
15
, pp.
199
215
.
43.
Seth
,
G. S.
,
Ansari
,
Md. S.
, and
Nandkeolyar
,
R.
, 2011, “
MHD Natural Convection Flow With Radiative Heat Transfer Past an Impulsively Moving Plate With Ramped Wall Temperature
,”
Heat Mass Transfer
,
47
, pp.
551
561
.
44.
Bestman
,
A. R.
, 1985, “
Free Convection Heat Transfer to Steady Radiating Non-Newtonian MHD Flow Past a Vertical Porous Plate
,”
Int. J. Numer. Methods Eng.
,
21
, pp.
899
908
.
45.
Azzam
,
G. E. A.
, 2002, “
Radiation Effects on the MHD Mixed Free Forced Convective Flow Past a Semi-Infinite Moving Vertical Plate for High Temperature Differences
,”
Phys. Scr.
,
66
, pp.
71
76
.
46.
Gebhart
,
B.
,
Jaluria
,
Y.
,
Mahajan
,
R. L.
, and
Sammakia
,
B.
, 1988,
Buoyancy Induced Flows and Transport
,
Hemisphere Publishing
,
New York
, Chaps. 3, 6, 7, 8, 10 and 12.
You do not currently have access to this content.