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Chemical and Process Engineering Research www.iiste.org
ISSN 2224-7467 (Paper) ISSN 2225-0913 (Online)
Vol.27, 2014
37
Aligned Magnetic Field, Radiation and Chemical Reaction Effects
on Unsteady Dusty Viscous Flow with Heat
Generation/Absorption
J.V. Ramana Reddy1 Dr.V.Sugunamma
2* P.Mohan Krishna
3 Dr.N.Sandeep
4
1,3Research Scholars, Dept.of Mathematics, S.V.University, Tirupati, India.
2Associate Professor, Dept.of Mathematics, S.V.University, Tirupati, India.
4Assistant Professor, Fluid Dynamics Division, VIT University, India.
Abstract
We analysed the laminar convective flow of a dusty viscous fluid of non conducting walls in
presence of aligned magnetic field with volume fraction, radiation, heat absorption along with
chemical reaction. The governing equations of the flow are solved by Perturbation
Technique. Further, the effects of all physical parameters on the velocities of fluid phase and
dust phase, temperature and concentration are analysed and discussed through graphs.
Key Words: Dusty Fluid, Laminar flow, MHD, Chemical Reaction, Viscous flow.
1. Introduction
The Dusty fluid is a mixture of fluid and fine dust particles .The influence of dust
particles on convective flow of dusty viscous fluids in presence of magnetic field and
chemical reaction has its importance in many areas like environmental pollution, cooling
effects of air conditioners, magneto hydrodynamic generators, pumps, accelerators and flow
meters .This type of flow has uses in nuclear reactors, geothermal systems and filtration. The
possible presence of dust particles in combustion MHD generators and their effect on
performance of such devices leads to study of volume fraction of dust particles in non
conducting walls in the presence of aligned magnetic field.
The study of convective flow of dusty viscous fluid under the influence of different
physical conditions has been carried out by many researchers. Saffman [1] has discussed the
stability of laminar flow of a dusty gas. Ezzat et al. [2] studied space approach to the hydro
magnetic flow of a dusty fluid through a porous medium by using Laplace transformation
technique. Sandeep and Sugunamma [3] discussed the effect of inclined magnetic field on
unsteady free convection flow of a dusty viscous fluid between two infinite flat plates filled
by a porous medium. Chakrabarti [4] analysed the boundary layer in a dusty gas. Datta and
Mishra [5] have investigated the boundary layer flow of a dust fluid over a semi infinite flat
plate .Mohan Krishna et al. [6] studied the Magnetic field and chemical reaction effects on
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convective flow of a dusty viscous fluid. In this study they used transverse magnetic field.
Anurag Dubey and Singh [7] discussed effect of dusty viscous fluid on unsteady laminar free
convective flow through porous media with thermal diffusion. Sandeep et al. [8] analysed the
effect of radiation and chemical reaction on transient MHD free convective flow over a
vertical plate through porous media .Mishra et al [9] have studied the two-dimensional
transient conduction and radiation heat transfer with temperature dependent thermal
conductivity. Attia [10] studied the unsteady couettee flow with heat transfer on dusty fluid
with variable physical properties.
Some researchers like Anjali Devi and Jothimani [11] have discussed the heat transfer
in unsteady MHD oscillatory flow. Further, Malashetty et al. [12] have investigated the
convective magnetohydrodynamic two phase flow and heat transfer of a fluid in an inclined
channel. Palani and Ganesan [13] have discussed the heat transfer effects on dusty gas flow past
a semi infinite inclined plate. Ibrahimsaidu at al. [14] analysed the MHD effects on convective
flow of dusty viscous fluid with volume fraction of dust particles in the absence of aligned
magnetic field, radiation, heat absorption and chemical reactions. In continuation of this
study and with the help of above cited papers we have studied the laminar convective flow of
a dusty viscous fluid with non conducting walls in the presence of aligned magnetic field
with volume fraction, radiation, heat absorption along with chemical reaction. The governing
equations of the flow are solved by Perturbation Technique. Further we analysed effects of all
physical parameters on the fluid phase and dust particles phase.
2. Mathematical Formulation
Consider an unsteady laminar flow of a dusty, incompressible, Newtonian, electrically
conducting, viscous fluid of uniform cross section h , when one wall of the channel is fixed
and the other is oscillating with time about a constant non-zero mean. Initially at 0t , the
channel wall as well as the fluid is assumed to be at the same temperature 0T and
concentration0C . When t>0 , the temperature of the channel wall is instantaneously raised to
wT and concentration raised to wC which oscillates with time and is thereafter maintained
constant. Let the fluid flow is along the x- axis at the fixed wall and y- axis is perpendicular
to it. The aligned magnetic field is applied to the flow along y>0direction with the first order
chemical reaction. Here the dust particles are solid, spherical, non-conducting, and equal in
size and uniformly distributed in the flow region. The density of dust particles is constant and
the temperature between the particles is uniform throughout the motion. The interaction
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between the particles, chemical reaction between the particles and liquid has been considered.
The volume occupied by the particles per unit volume of the mixture, (i.e., volume fraction of
dust particles) and mass concentration have been taken into consideration.
The governing equations of the flow are given by
2*
0 02
1(1 ) (1 ) ( ) (C )
u p ug T T g C
t x y
2 2
20 0 0( ) sincKN KN Hv u u
(1)
2*
0 0 0 02( ) (C ) ( )
v p uN m g T T g C KN u v
t x y
(2)
2
02
1(T )r
p p p
qT k T QT
t C y C y C
(3)
2
02(C )l
C CD K C
t y
(4)
The boundary conditions of the problem are given by
int int
0; ( , ) v(y, t) 0, T(y, t) C(y, t) 0 for 0 y 1
0; ( , ) v(y, t) 0, T(y, t) C(y, t) 0 0
( , ) v(y, t) 1 , T(y, t) C(y, t) 1 1
t u y t
t u y t at y
u y t e e at y
(5)
Where u(y,t) is the velocity of the fluid and v(y,t) is velocity of the dust particles, m is the
mass of each dust particle, 0N is the number density of the dust particle, T is the
temperature, 0T is the initial temperature,
wT is the raised temperature, C is the
concentration, 0C is the initial concentration,
wC is the raised concentration, is the volume
fraction of the dust particle, f is mass concentration of dust particle, is the volumetric
coefficient of the thermal expansion, K is the Stoke’s resistance coefficient, is the
electrical conductivity of the fluid, C is the magnetic permeability,
0H is the magnetic field
induction, is the aligned magnetic field angle, pC is the specific heat at constant pressure,
k is the thermal conductivity, K l is chemical reaction parameter,
1K is dimensionless
chemical reaction parameter.
The Problem is simplified by writing the equations in the following non dimensional form.
Here the characteristic length is taken to be h and characteristic velocity is v .
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2* * * * * * * *0 0
2 2
0 0
, , , , , , ,w w
T T C Cx y h p t uh vhx y p t u v T C
h h h T T C C
(6)
Substituting the above non dimensional parameters of equation (6) in the governing equations
(1) – (4) then we get (after removing asterisks)
2
1 22( )
u p uGrT GcC v u Mu
t x y
(7)
2
2( )
v p uf GrT GcC u v
t x y
(8)
2
2
1(1 )
PrH
T TR Q T
t y
(9)
2
12
1C CK C
t Sc y
(10)
Where
3 * 3 2
0 0 01 2 12 2 2
1
23 *2 2 2 2 0
0 1*
1
( ) ( ), , , , , ,
(1 ) 1
16sin , ,Pr , , .
3
w wH
lc
p
g T T h g C C h KNf m QhGr Gc Q
Kh k
mN K hT f kR M h H f Sc K
kk C D
Here Gr is Thermal Garshof number and Gc is Mass Garshof number, M is Magnetic
parameter, f is Mass concentration of dust particles, is Concentration resistance ratio, Pr
is Prandtal number, Sc is (Schmidt number), K l is Chemical reaction parameter.
The Corresponding non-dimensional boundary conditions are:
int int
0; ( , ) v(y, t) 0, T(y, t) C(y, t) 0 for 0 y 1
0; ( , ) v(y, t) 0, T(y, t) C(y, t) 0 0
( , ) v(y, t) 1 , T(y, t) C(y, t) 1 1
t u y t
t u y t at y
u y t e e at y
(11)
3. Solution of the Problem
To solve the equations (7-10) we use the below equations introduced by Soundalgekar and
Bhat
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.
int
0 1
int
0 1
int
0 1
int
0 1
( , ) ( ) ( )
( , ) ( ) ( )
( , ) ( ) ( )
( , ) ( ) ( )
u y t u y e u y
v y t v y e v y
T y t T y e T y
C y t C y e C y
(12)
pp
x
is constant
After substituting equations (12) in equations (7) – (10), we obtain
0 1 2 0 1 0 0 0( ) ( ) ( ) ( ) ( ) ( )u y M u y v y p GrT y GcC y (13)
1 1 2 1 1 1 1 1( ) ( ) ( ) ( ) ( ) ( )u y M in u y v y GrT y GcC y (14)
0 0 0 0 0( ) ( ) ( ) ( ) ( )v y u y u y p GrT y GcC y
(15)
1 1 1 1 1( inf) ( ) ( ) ( ) ( ) ( )v y u y u y GrT y GcC y
(16)
0 0(1 ) ( ) ( ) 0HR T y Q T y (17)
1 1(1 ) ( ) Pr ( ) 0HR T y Q in T y (18)
0 1 0( ) K ( ) 0C y Sc C y (19)
1 1 1( ) ( ) 0C y Sc K in C y (20)
The corresponding boundary conditions becomes
0 1 0 1 0 1 0 1
0 1 0 1 0 1 0 1
( ) ( ) ( ) ( ) 0, ( ) ( ) ( ) ( ) 0 0
( ) ( ) ( ) ( ) 1, ( ) ( ) ( ) ( ) 1 1
u y u y v y v y T y T y C y C y at y
u y u y v y v y T y T y C y C y at y
(21)
On solving equation (17) and (19) with the help of boundary conditions (21), we get
20
2
sin L( )
sin L
yT y (22)
00
0
sin( )
sin
h L yC y
h L (23)
Substituting the equations (22) and (23) in equations (13) and (15), we get
020 1 2 0 1 0
2 0
sinsin L( ) ( ) ( ) ( )
sin L sin
h L yyu y M u y v y p Gr Gc
h L (24)
020 0 0
2 0
sinsin L( ) ( ) ( )
sin L sin
h L yyv y u y u y p Gr Gc
h L
(25)
Substituting equation (25) in (24), we obtain
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2 020 0
2 0
sinsin L( ) ( )
sin L sin
h L yyu y A u y p Gr Gc
h L (26)
Where
2 2
1
MA
By solving equation (26) with the help of boundary conditions (21), we get
020 12 2 2 2 2
2 2 0 0
sinsin Lsin( ) (cos 1)
sin sin L sin
h L yyp hAy Gr Gcu y hAy B
A hA L A L A h L
(27)
The first and second order partial derivatives of 0 ( )u y are given by
020 12 2 2 2 2
2 2 0 0
coscos Lcos( ) (sin )
sin sin L sin
h L yyp hAy Gr Gcu y hAy B
A hA L A L A h L
(28)
020 12 2 2 2 2
2 2 0 0
sinsin Lsin( ) (cos )
sin sin L sin
h L yyp hAy Gr Gcu y hAy B
A hA L A L A h L
(29)
Substituting the above equations (27) and (29) in equation (25), we obtain
0 20 2 1 32 2 2 2 2
0 0 2 2
024 5
2 0
sin sin Lsin( ) (cos )
sin sin sin L
sinsin L
sin L sin
h L y yp hAy Gc Grv y B hAy B B
A hA L A h L L A
h L yyB p B Gr Gc
h L
(30)
By solving equations (18) and (20) with the boundary conditions (21), we obtain
31
3
sin( )
sin
L yT y
L (31)
11
1
sin( )
sin
hL yC y
hL (32)
Substituting equations (31) and (32) in equations (14) and (16), we obtain
3 11 1 2 1 1 1
3 1
sin sin( ) ( ) ( ) ( )
sin sin
L y hL yu y M in u y v y Gr Gc
L hL (33)
3 11 1 1
3 1
sin sin( inf) ( ) ( ) ( )
sin sin
L y hL yv y u y u y Gr Gc
L hL
(34)
Substituting equation (34) in equation (33), we obtain
2 3 11 1 1 1
3 1
sin sin( ) ( ) ( )
sin sin
L y hL yu y B u y v y Gr Gc
L hL (35)
On solving equation (35), with the help of boundary conditions (21), we get
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3 11 6 2 2 2 2
3 3 1 1
sin sinsin( )
sin sin sin
L y hL yhBy Gr Gcu y B
hB L B L L B hL
(36)
The first and second order partial derivatives of 1( )u y are
3 11 6 2 2 2 2
3 3 1 1
cos coscos( )
sin sin sin
L y hL yhBy Gr Gcu y B
hB L B L L B hL
(37)
3 11 6 2 2 2 2
3 3 1 1
sin sinsin( )
sin sin sin
L y hL yhBy Gr Gcu y B
hB L B L L B hL
(38)
Substituting the above equations (36) and (38) in equation (34), we obtain
311 7 6 82 2 2 2
1 1 3 3
3 19
3 1
sinsinsin( )
sin sin sin
sin sin
sin sin
L yhL yhBy Gc Grv y B B B
hB L B hL L B L
L y hL yB Gr Gc
L hL
(39)
Substituting the equations (27) and (36) in equation (12), we obtain the expression for
velocity of the fluid phase as
0212 2 2 2 2
2 2 0 0
int3 16 2 2 2 2
3 3 1 1
sinsin Lsin( , ) (cos 1)
sin sin L sin
sin sinsin
sin sin sin
h L yyp hAy Gr Gcu y t hAy B
A hA L A L A h L
L y hL yhBy Gr GcB e
hB L B L L B hL
(40)
Substituting the equations (30) and (39) in equation (12), we obtain expression for the
dust phase as
02 12 2 2
0 0
02 23 4 52 2
2 2 2 0
317 6 82 2 2 2
1 1 3 3
9
sinsin( , ) (cos )
sin sin
sinsin L sin L
sin L sin L sin
sinsinsin
sin sin sin
si
h L yp hAy Gcv y t B hAy B
A hA L A h L
h L yy yGrB B p B Gr Gc
L A h L
L yhL yhBy Gc GrB B B
hB L B hL L B L
B Gr
int
3 1
3 1
n sin
sin sin
eL y hL y
GcL hL
(41)
Substituting the equations (22) and (31) in equation (12), we obtain the expression for
temperature as
int32
2 3
sinsin L( , )
sin L sin
L yyT y t e
L (42)
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Substituting the equations (23) and (32) in equation (12), we get we obtain the expression
for concentration as
int0 1
0 1
sin sin( , )
sin sin
h L y hL yC y t e
h L hL (43)
4. Results and Discussion
In order to study the behavior of fluid velocity ( )u ,dusty velocity ( )v , temperature
( )T and concentration ( )C fields, a comprehensive numerical computation is carried out for
various values of the parameters that describe the flow characteristics, and the results are
reported in terms of graphs as shown in Figures (1) – (15).
The variation of fluid velocity for different values of aligned magnetic field angle ( )
is shown in Figure 1. It is observed that the velocity profiles of fluid phase and dust phase
decreases with an increase in aligned magnetic field angle. In general increase in magnetic
field causes the decrease in fluid velocity, because of induced forces acting opposite to flow.
In present case an increase in aligned angle causes the increase in magnetic field .Therefore
our results are exactly coincident with transverse magnetic field case at π/2 which is
clearly shown in Fig. 2. Fig 3 depicts the increase in radiation parameter causes the decrease
in fluid and dust phase velocities. Fig.4 shows the effect of heat generation/absorption
parameter on velocity profiles of fluid and dust phase. It is observed that an increase in heat
generation/absorption parameter causes the increase in velocities of the fluid and dust phase.
From Fig.5 it is interesting to note that an increase in chemical reaction parameter causes the
increase in velocity of fluid phase but due to chemical reaction with dust particles the dust
phase velocity decreases initially and then follows the fluid phase.
Velocity profiles for different values of mass Grashof number ( )Gc and thermal
Grashof number ( )Gr are shown in figures 6 and 7 respectively. It is evident that an increase
in mass Grashof number decreases the velocity of the fluid phase, but it is reversed in dust
phase. But in case of thermal Grashof number the above results are completely differs. The
effect on velocity profiles for different values of Prandtl number (Pr) are shown in figure 8.It
is evident that an increase in Prandtl number causes decrease in fluid phase velocity. But it
helps to the dust phase velocity. Figure 9 represents velocity profiles for different values of
Schmidt number ( )Sc . It is clear that the velocity of fluid and dust phases increases with an
increase in Schmidt number. From fig.10 it is clear that the increase in volume fraction of the
dust particles increases the velocity of the fluid and dust phase.
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The effect of radiation parameter ( )R on temperature profiles is shown in fig.11 and it
is clear that an increase in radiation parameter causes the decrease in dusty fluid
temperature.Fig.12 depicts the variation in temperature for different values of heat
generation/absorption parameter and it is observed that increase in heat generation/absorption
parameter causes the increase in fluid temperature. From figure 13 it is evident that fluid
temperature decreases with an increase in time.
The variations of concentration profiles for different values of the Schmidt
number ( )Sc and chemical reaction parameter1( )K are shown in Figs. 14 and 15 respectively.
It is observed that the concentration decreases gradually with increase in Schmidt number
( )Sc as well as chemical reaction parameter1( )K .
0 0.5 10
0.5
1
1.5
2
2.5
3
3.5
4
4.5
y
u
=pi/6
=pi/4
=pi/3
=pi/2
0 0.5 1-2
0
2
4
6
8
10
12
y
v
=pi/6
=pi/4
=pi/3
=pi/2
Figure 1: velocity profiles for different values of
When Pr =0.71,Gr =5,Gc =5, R =2,1M =8, Sc =2,Q =2,
1K =0.5, t =0.1.
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0 0.5 10
0.5
1
1.5
2
2.5
3
3.5
4
4.5
y
u
M=2
M=4
M=6
M=8
0 0.5 1-2
0
2
4
6
8
10
12
y
v
M=2
M=4
M=6
M=8
Figure 2: velocity profiles for different values of M
When Pr =0.71,Gr =5,Gc =5, R =2, Sc =2,Q =2,1K =0.5, t =0.1.
0 0.5 1-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
y
u
R=0.5
R=2
R=4
R=8
0 0.5 10
1
2
3
4
5
6
y
v
R=0.5
R=2
R=4
R=8
Figure 3: velocity profiles for different values of R
When Pr =0.71,Gr =5,Gc =5, Sc =2,Q =2,1M =3,
1K =0.5, t =0.1, =π/6
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0 0.5 1-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
y
u
Q=2
Q=4
Q=6
Q=8
0 0.5 10
1
2
3
4
5
6
7
y
v
Q=2
Q=4
Q=6
Q=8
Figure 4: velocity profiles for different values of Q
When Pr =0.71,Gr =5,Gc =5, Sc =2, R =2,1M =3,
1K =0.5, t =0.1, =π/6
0 0.5 1-0.2
0
0.2
0.4
0.6
0.8
1
1.2
y
u
K1=1
K1=2
K1=3
K1=4
0 0.5 10
1
2
3
4
5
6
y
v
K1=1
K1=2
K1=3
K1=4
Figure 5: velocity profiles for different values of 1K
When Pr =0.71,Gr =5,Gc =5, Sc =2, R =2,1M =3,Q =2, t =0.1, =π/6
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0 0.5 1-1
-0.5
0
0.5
1
1.5
y
u
Gc=2
Gc=4
Gc=6
Gc=8
0 0.5 10
1
2
3
4
5
6
7
8
y
v
Gc=2
Gc=4
Gc=6
Gc=8
Figure 6: velocity profiles for different values of Gc
When Pr =0.71,Gr =5,1K =0.5, Sc =2, R =2,
1M =3,Q =2, t =0.1, =π/6
0 0.5 1-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
y
u
Gr=4
Gr=8
Gr=12
Gr=16
0 0.5 10
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
y
v
Gr=4
Gr=8
Gr=12
Gr=16
Figure 7: velocity profiles for different values of Gr
When Pr =0.71,Gc =5,1K =0.5, Sc =2, R =2,
1M =3,Q =2, t =0.1, =π/6
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0 0.5 1-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
y
u
Pr=0.71
Pr=1.0
Pr=7.0
Pr=11.4
0 0.5 10
1
2
3
4
5
6
7
y
v
Pr=0.71
Pr=1.0
Pr=7.0
Pr=11.4
Figure 8: velocity profiles for different values of Pr
When Gr =5,Gc =5,1K =0.5, Sc =2, R =2,
1M =3,Q =2, t =0.1, =π/6
0 0.5 1-0.2
0
0.2
0.4
0.6
0.8
1
1.2
y
u
Sc=2
Sc=2.5
Sc=3
Sc=4
0 0.5 10
1
2
3
4
5
6
y
v
Sc=2
Sc=2.5
Sc=3
Sc=4
Figure 9: velocity profiles for different values of Sc
When Pr =0.71,Gr =5,Gc =5,1K =0.5, R =2,
1M =3,Q =2, t =0.1, =π/6
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0 0.5 1-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
y
u
=0.2
=0.4
=0.6
=0.8
0 0.5 1-1
0
1
2
3
4
5
6
7
8
9
y
v
=0.2
=0.4
=0.6
=0.8
Figure 10: velocity profiles for different values of
When Pr =0.71,Gr =5,Gc =5,1K =0.5, R =2,
1M =3,Q =2, t =0.1, =π/6, Sc =2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
y
T
R=0.5
R=2
R=4
R=6
Figure 11: Temperature profiles
for different values of R .When
Pr =0.71,Q =2, t =0.1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
y
T
Q=2
Q=4
Q=6
Q=8
Figure 12: Temperature profiles for
different values of Q .When
Pr =0.71, R =2, t =0.1
Chemical and Process Engineering Research www.iiste.org
ISSN 2224-7467 (Paper) ISSN 2225-0913 (Online)
Vol.27, 2014
51
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
y
T
t=0.4
t=0.8
t=1.2
t=1.6
Figure 13: Temperature profiles for
different values of t .When
Pr =0.71,Q =2, R =2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
y
C
Sc=2
Sc=2.5
Sc=3
Sc=4
Figure 14: Concentration profiles for different
values of Sc .When K =2,1K =0.5, t =0.1.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
y
C
K1=1
K1=2
K1=3
K1=4
Figure 15: Concentration profiles for
different values of 1K .When
K =2, Sc =2, t =0.1.
Appendix:
0 1 1 1
2 3
2 2
1
2 11 2
1
1 2 2 2 2 2
2 0
2 3 4 2
5 6 2
3
, ,
Pr,
1 1
inB
in in
1 (1 cos hA)
11 , 1 ,
, 1
H H
L K Sc L K in Sc
Q Q inL L
R R
MA
fM in
f f
p Gr GcB
A L A L A
B B BA
GrB B
L
2 2 2
1
7 8 9, ,
Gc
B L B
B B Bin f in f in f
Chemical and Process Engineering Research www.iiste.org
ISSN 2224-7467 (Paper) ISSN 2225-0913 (Online)
Vol.27, 2014
52
References
[1] Saffman P .G, 1962. On the stability of laminar flow of a dusty gas. Journal of Fluid
dynamics, 13,120-128.
[2] Ezzat M. A, A .A El-Bary, M. M Morsey,20120. Space approach to the hydro magnetic
flow of a dusty fluid through a porous medium. Computers and Mathematics with
Applications. 59, 2868-2879.
[3] Sandeep N, V .Sugunamma. 2013. Effect of inclined magnetic field on unsteady free
convection flow of a dusty viscous fluid between two infinite flat plates filled by a porous
medium.Journal of Applied Mathematics and modelling.1, 1-9.
[4] Chakrabarti K .M,1974. Note on boundary layer in a dusty gas.AAIA Journal. 12, 1136-
1137.
[5] Datta N and S. K Mishra, 1982. Boundary layer flow of a dust fluid over a semi infinite
flat plate. Acta-Mechanica. 42, 71-83.
[6] Mohan Krishna P, V. Sugunamma and N. Sandeep,2013 . Magnetic field and chemical
reaction effects on convective flow of a dusty viscous fluid. Communications in Applied
Sciences. 1,161-187.
[7] Anurag Dubey and U. R Singh,2012. Effect of dusty viscous fluid on unsteady laminar
free convective flow through porous medium along a moving porous hot vertical with
thermal diffusion. Applied Mathematical Sciences. 6, 6109-6124.
[8] Sandeep N, A. V .B Reddy, V. Sugunamma,2012. Effect of radiation and chemical
reaction on transient MHD free convective flow over a vertical plate through porous media.
Chemical and process engineering Research.,2,1-9.
[9] Mishra S.C, P. T Alukdhar, D. Trimas and F.Drust,2005.Two-dimensional transient
conduction and radiation heat transfer with temperature dependent thermal conductivity.
Int.com Heat and Mass transfer. 32,305-314.
[10] Attia H.A,2006.Unsteady MHD couettee flow and heat transfer of dusty fluid with
variable physical properties. Applied Mathematics and computation. 177,308-318.
[11]. Anjali Devi S.P and S. Jothimani,1996. Heat transfer in unsteady MHD oscillatory
flow, Czechoslovak Journal of Physics. 46, 825–838.
[12]. Malashetty M.S, J.C. Umavathi and Prathap Kumar,2001. Convective
magnetohydrodynamic two fluidflow and heat transfer in an inclined channel. Heat and Mass
Transfer/Waerme- und Stoffuebertragung.37, 259–264.
Chemical and Process Engineering Research www.iiste.org
ISSN 2224-7467 (Paper) ISSN 2225-0913 (Online)
Vol.27, 2014
53
[13]. Palani G and P .Ganesan,2007. Heat transfer effects on dusty gas flow past a semi-
infinite inclined plate. Forschung im Ingenieurwesen.71, 223–230.
[14] Ibrahim Saidu, M .M Waziri, Abubakar Roko and Hamisu Musa,2010. MHD effects on
convective flow of dusty viscous fluid with volume fraction of dust particles, ARPN J Eng
and applied sciences. 5, 86-91.
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