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INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.4 NO.1 JANUARY 2014
www.ijitce.co.uk
INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.4 NO.1 JANUARY 2014
www.ijitce.co.uk
UK: Managing Editor
International Journal of Innovative Technology and Creative Engineering 1a park lane, Cranford London TW59WA UK E-Mail: editor@ijitce.co.uk Phone: +44-773-043-0249
USA: Editor
International Journal of Innovative Technology and Creative Engineering Dr. Arumugam Department of Chemistry University of Georgia GA-30602, USA. Phone: 001-706-206-0812 Fax:001-706-542-2626
India: Editor
International Journal of Innovative Technology & Creative Engineering Dr. Arthanariee. A. M Finance Tracking Center India 17/14 Ganapathy Nagar 2nd Street Ekkattuthangal Chennai -600032 Mobile: 91-7598208700
INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.4 NO.1 JANUARY 2014
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IJITCE PUBLICATION
International Journal of Innovative Technology & Creative Engineering
Vol.4 No.1
January 2014
www.ijitce.co.uk
INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.4 NO.1 JANUARY 2014
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From Editor's Desk
Dear Researcher, Greetings! Research article in this issue discusses about Pulsatile flow of a Jeffrey fluid. Let us review research around the world this month; Green Drive, is showing off the free app this week at the Consumer Electronics Show in Las Vegas. EnLighten feeds off real-time traffic data supplied by cities, then uses a phone's GPS and accelerometer to determine its user's location and velocity. Ginsberg aims to sell his patented technology to car-makers, so that it can be built into cars. That would avoid draining smartphone batteries and allow for integration into other car systems. It's hardly Chopin. But a soft robot can bend and change the shape of its four rubbery fingers fast enough to hit keys and play a simple tune on a piano. The fingers, which are secured to the edges of the keys, change shape in just 50 milliseconds when air is pumped into them. A computer-controlled valve regulates the pressure of each finger, or actuator, with the appropriate timing. The new actuators have already been used in a pneumatic glove developed for the rehabilitation of stroke sufferers. The system could also be used in robotic surgery, to create soft tools for handling fragile internal organs.The team is now looking at increasing the force that can be applied with the fingers. The next generation of soft robots may not only move faster – they may be more powerful as well. The plant racks in a vertical farm can be fed nutrients by water-conserving, soil-free hydroponic systems and lit by LEDs that mimic sunlight. And they need not be difficult to manage: control software can choreograph rotating racks of plants so each gets the same amount of light, and direct water pumps to ensure nutrients are evenly distributed. Advances in vertical farms could trickle through from other sources, too. The US Defense Advanced Research Projects Agency is using an 18-storey vertical farm in College Station, Texas, to produce genetically modified plants that make proteins useful in vaccines. Adversity also plays its part: the tsunami-sparked nuclear accident in Fukushima, Japan, in 2011 is leading to innovation in vertical farming because much of the region's irradiated farmland can no longer be used. It has been an absolute pleasure to present you articles that you wish to read. We look forward to many more new technologies related research articles from you and your friends. We are anxiously awaiting the rich and thorough research papers that have been prepared by our authors for the next issue. Thanks, Editorial Team IJITCE
INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.4 NO.1 JANUARY 2014
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Editorial Members
Dr. Chee Kyun Ng Ph.D Department of Computer and Communication Systems, Faculty of Engineering, Universiti Putra Malaysia,UPM Serdang, 43400 Selangor,Malaysia. Dr. Simon SEE Ph.D Chief Technologist and Technical Director at Oracle Corporation, Associate Professor (Adjunct) at Nanyang Technological University Professor (Adjunct) at Shangai Jiaotong University, 27 West Coast Rise #08-12,Singapore 127470 Dr. sc.agr. Horst Juergen SCHWARTZ Ph.D, Humboldt-University of Berlin, Faculty of Agriculture and Horticulture, Asternplatz 2a, D-12203 Berlin, Germany Dr. Marco L. Bianchini Ph.D Italian National Research Council; IBAF-CNR, Via Salaria km 29.300, 00015 Monterotondo Scalo (RM), Italy Dr. Nijad Kabbara Ph.D Marine Research Centre / Remote Sensing Centre/ National Council for Scientific Research, P. O. Box: 189 Jounieh, Lebanon Dr. Aaron Solomon Ph.D Department of Computer Science, National Chi Nan University, No. 303, University Road, Puli Town, Nantou County 54561, Taiwan Dr. Arthanariee. A. M M.Sc.,M.Phil.,M.S.,Ph.D Director - Bharathidasan School of Computer Applications, Ellispettai, Erode, Tamil Nadu,India Dr. Takaharu KAMEOKA, Ph.D Professor, Laboratory of Food, Environmental & Cultural Informatics Division of Sustainable Resource Sciences, Graduate School of Bioresources, Mie University, 1577 Kurimamachiya-cho, Tsu, Mie, 514-8507, Japan Mr. M. Sivakumar M.C.A.,ITIL.,PRINCE2.,ISTQB.,OCP.,ICP Project Manager - Software, Applied Materials, 1a park lane, cranford, UK Dr. Bulent Acma Ph.D Anadolu University, Department of Economics, Unit of Southeastern Anatolia Project(GAP), 26470 Eskisehir, TURKEY Dr. Selvanathan Arumugam Ph.D Research Scientist, Department of Chemistry, University of Georgia, GA-30602, USA.
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Contents
Pulsatile flow of a Jeffrey fluid in a channel bounded by porous lined plates with suction and injection by S.Sreenadh, P.Govardhan and Y.V.K.Ravi Kumar.............................................................................................[172]
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Pulsatile flow of a Jeffrey fluid in a channel bounded by porous lined plates with suction
and injection S.Sreenadh
1 P.Govardhan
1 Y.V.K.Ravi Kumar
2
1 Department of Mathematics, S. V. University, Tirupati – 517502, INDIA
2 Practice School Division, Birla Institute of Technology and Science (BITS) – Pilani, INDIA (yvkravi@gmail.com ,
corresponding author)
Abstract— Pulsatile flow of a Jeffrey fluid in a channel bounded by porous lined plates with suction and injection is studied in this paper. The steady and unsteady velocities are obtained. The effect of various parameters on the flow phenomenon is discussed through graphs..
Key words — pulsatile flow, Jeffrey fluid, suction, injection.
I. INTRODUCTION
Viscous fluid flow through and past porous media is
attracting the attention of scientists and engineers
because of its wider applications in various branches of
science and technology. The movement of ground water
in soil, the seepage of water through earth fills and
concrete dams, the movement of oil fields can described
using the knowledge of flow through porous media. The
petroleum industry has been showing a lot of interest in
these problems in connection with the crude oil
production from the under ground reservoirs. These
reservoirs consists of porous materials like lime stone
and dolomite where oil is preserved. Oil can be obtained
by drilling wells down into the reservoir. In order to have
a better oil production, it is necessary to use the
knowledge of flow through porous media.
The oil available in the porous reservoir is a complex
fluid. The properties of such fluid have impact on the oil
production. The behavior of the oil may be Newtonian or
non-Newtonian. In view of this, it is interesting to study
non- Newtonian fluid flow through and past porous
media. Further there are many important applications in
biomechanics also (vide Fung and Tang, [1,2].
Muakat [3] made theoretical and experimental studies
on porous flow using Darcy law. Darcy law is observed
to be valid for low speed flows and agrees with several
experiments modeled in one dimensional motion. Yih [4]
suggested the modified Darcy law for describing
unsteady flow through porous media. Following this law,
Rudraiah et al. [5], analyzed several time dependent
flows through and past permeable beds.
Radhakrishnamacharya [6] investigated the pulsatile
flow of a dusty fluid containing small solid particles
uniformly, through a two-dimensional constricted
channel. The effect of non-Newtonion nature of blood
and pulsatality on flow through a stenosed tube is
analyzed by Chaturani and Samy [7].
The pulsatile flow in a porous channel is important in
understanding the process of dialysis of blood in an
artificial kidney. Recently, Chandra and Prasad [8]
discussed the pulsatile flow problems with periodic
acceleration and varying cross section of tubes.
Wang [9] studied the interesting problem of pulsatile flow
in a porous channel bounded by rigid walls. The
pulsatile flow between permeable walls is important in
understanding the blood flow in the circulatory system
where the nutrients are supplied to tissues of various
organs and waste products are removed. Vajravelu et
al.,[10]made a detailed study on pulsatile flow between
permeable beds. Avinash et.al [11] studied the pulsatile
flow of a viscous stratified fluid of variable viscosity
between permeable beds is studied. The interaction of
peristaltic flow with pulsatile flow through a porous
medium is discussed by Afifi and Gad [12].
In this paper an exact solution for the pulsatile flow of
Jeffrey fluid in porous lined plates is obtained. The flow
between the permeable layers is governed by Jeffrey
model where as the flow in the lower and upper beds
are governed by Darcy law. The velocity distributions in
the porous and non-porous regions are determined.
II. MATHEMATICAL FORMULATION OF THE PROBLEM
Consider the pulsatile flow of a Jeffrey fluid in a
channel bounded by porous lined plates (Fig.1).
The thickness of the porous lining on each of the
plates is . The fluid is injected into the channel
from the lower porous layer with a velocity V and is
sucked out into the upper porous layer with the
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same velocity. The permeabilities of lower and
upper beds are k1 and k2 . The flow between the
permeable beds is governed by the Jeffrey model
whereas the flow in the porous medium is
described by modified Darcy’s law
Fig.1. Physical Model
The following assumptions are made in the analysis of the problem
The flow is laminar and fully developed
The permeable beds are homogeneous
The flow is driven by unsteady pressure gradient. We assume that tiBeA
x
p
1
where A and B are constants and ‘ ’ is the frequency. In view of the above assumptions, the basic equations and boundary conditions of the flow take the following form.
Basic equations
0
y
v
x
u (1)
2
2
11
1
y
u
x
p
y
uV
t
u
(2)
0
y
p (3)
Boundary conditions
1Buu at y = (4)
)( 11
1
Quky
uB
at y = (5)
2Buu at y = h - (6)
)( 22
2
Quky
uB
at y = h - (7)
u, v are velocities of the fluid, is the coefficient of viscosity
p is the pressure, is the slip parameter,k1,k2a are permeabilities of the lower and upper permeable
beds, 21, BB uu are slip velocities in lower and upper
permeable beds and 1 is the Jeffrey parameter.
Separating equations (1) – (7) into steady part denoted by a bar (-) and unsteady part denoted by a tilde ( we get
Steady part:
0
x
u (8)
2
2
11 y
uA
y
uV
(9)
1Buu at y =
(10)
)( 11
1
Qukdy
udB
at y =
(11)
2Buu at y = h - (12)
)( 22
2
Qukdy
udB
at y = h - (13)
where )1( 1
1
1
AkQ , )1( 1
2
2
AkQ
Unsteady part:
0~
x
u (14)
2
2
1
~
1
~~
y
uBe
y
uV
t
u ti
(15)
1~~
Buu at y = ε (16)
)~~(
~
11
1
Qukdy
udB
at y = ε (17)
2~~
Buu at y = h - ε (18)
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)~~(
~
22
2
Qukdy
udB
at y = h – ε (19)
where tieBk
Q
)1(~ 11
1
, tie
BkQ
)1(~ 12
2
Non – Dimensionalization of flow quantities
The following non – dimensional quantities are introduced to make the basic equations and the boundary conditions dimensionless
Steady part:
)( 1
*
v
hA
uu ,
)( 1
1*1
v
hA
uu
BB ,
)( 1
2*2
v
hA
uu
BB
h
xx * ,
h
yy * ,
)( 1
1*
1
v
hA
,
)( 1
2*
2
v
hA
,
h
* where AA 1
.
Unsteady part:
)(
~~
1
2
*
Bh
uu
)(
~~
1
2
1*
1
Bh
uu B
B
)(
~~
1
2
2*
2
Bh
uu B
B ,
)(
~2
*
h
tt ,
)(
~~
2
*
h
,
)(
~~
1
2
1*
1
Bh
)(
~~
1
2
2*
2
Bh
QQ ,
h
yy *
,h
*
where BB 1 .
In view of the above dimensionless quantities Eqs.(8) to (19) take the following form, neglecting the asterisks (*), we get,
Steady part
0dx
ud (20)
Rdy
udR
dy
ud)1()1( 112
2
(21)
1Buu at y = (22)
)1
(2
1
111 Ru
dy
udB
at y = (23)
2Buu at y = 1 - (24)
)1
(2
2
122 Ru
dy
udB
at y = 1- (25)
where
VhR is the Reynolds number,
1
1k
h ,
2
2k
h ( 21, are dimensionless parameters).
Unsteady Part:
0~
dx
ud (26)
tiedt
ud
dy
udR
dy
ud )1(~
)1(~
)1(~
1112
2
(27)
Letting tieyfu )(
~~
)1()(~
)1()(~
)1()(~
111 yfiyfRyf (28)
Using ti
B efu 11
~~ , ti
B efu 22
~~
The boundary conditions become
1
~~ff at y = (29)
)1~
(
~
2
1
111
f
dy
fd at y = (30)
2
~~ff at y = 1 - (31)
)1~
(
~
2
2
122
f
dy
fd at y = 1 - (32)
III. SOLUTION OF THE PROBLEM
Steady part:
Solving Eq.(21) subject to boundary conditions (22)-(25) we get the velocity field as
We get the velocity field as
yeCCuy
)1(
211 (33)
The slip velocities are 1Bu and 2Bu are given by
)(
)(
2341
14221
DDDD
EDEDuB
,
)(
)(
2341
21132
DDDD
EDEDuB
(34)
Unsteady part:
Solving equation (28) subject to boundary conditions (10) –(13), we get
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iBeAeyf
ymym 21)(
~ (35)
The unsteady part of the velocity is given by
iwteyfu )(~~
Separating real and imaginary parts, we get
)()(~12121212 tSinAtCosBitSinBtCosAu
The slip velocities are given by
timm
ti
B eeBmeAm
efu
)
1(
~~2
1
1
2
2
1
111
21
ti
mm
ti
B eeBmeAm
efu
)
1(
~~
2
)1(
2
2
)1(
1
2
2
122
21
5. Deductions
(i) Taking k1 = k2 = k (i.e. in equation (33 )
and (35) we obtain the velocity field for pulsatile flow of Jeffrey fluid between porous lined plates with equal permeability as follows: Steady state velocity
= c1 + c2 ( + y
(36) Unsteady part:
(
)
(37)
(ii) When the permeabilities k1 and k2 tend to zero in equations (36) and (37) we obtain the velocity field for the pulsatile flow of the Jeffrey fluid in a channel bounded by rigid walls as follows
Steady part
(38)
The slip velocities and are zero. Unsteady part
(
) (39)
The slip velocities and are zero.
Further with , the results (38) and (39) reduce the
corresponding ones of Wang [9].
RESULTS AND DISCUSSION
From equation (33) we have calculated the steady part of the velocity as a function of y for different values of permeability parameter with fixed 0.5, 2, 0.5,R
0.02 and is shown in Fig.2. We observe that the
velocity decreases with the increase in h
k . This
may be due to the increase in the permeability ‘k’ of the upper and lower beds. Also, as the
increases, the gap between the velocity profiles becomes smaller i.e. there is not much change in the velocity due to variation for large values of .
The variation of steady part of the velocity with y is calculated from equation (33) for different values of permeability parameter with
fixed 0.1, 2, 0.5R , 0.02 and is shown
in Fig.3. It is noticed that the velocity decreases with the increase in . From Fig.2 and Fig.3 it is
noticed that the magnitude of the velocity increases with decrease in the slip parameter . Also, as the
increases, the gap between the velocity profiles
becomes smaller.
The variation of u with y is
calculated from equation (33) for different values of the Reynolds number R and for fixed
2, 25, 0.5, 0.02 and is shown in
Fig.4. We observe that the velocity increases with the increase in R.
From equation (33) we have calculated the steady part of the velocity as a function of y for different values of Jeffrey parameter with fixed
2, 25, 2R , 0.02 and is shown in
Fig.5. It is noticed that the velocity increases with the increase in the Jeffrey parameter . Similar
behavior due to is noticed by Srinivas et al.
(2008) and Hayat et al. (2008) for the peristaltic transport of viscous fluid in a flexible channel.
From equation (33) we have calculated the steady part of the velocity as a function of y for different values of the thickness of porous lined plate with fixed 2, 25, 2R , 0.5 and is
shown in Fig.6. We observe that the velocity decreases with the increase in .
We have calculated the unsteady part of the velocity as the function of y from equation (35) for different values of wt with fixed 5, 5, 0R
, 0.02 , M=1, 1 and is shown in Fig.7.We
observe the velocity decreases with the increase in wt .
We have calculated the unsteady part of the velocity ( u ) as the function of y from equation (35)
for different values of wt with fixed
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0.5, 25, 10R , 0.02 , M = 1, 1 and is
shown in Fig.8.We observe the velocity decreases with the increase in wt . From Fig.7. and Fig.8. for
fixed wt and , as R increases the maximum
velocity moves closure to the upper permeable bed.
We have calculated the unsteady part of the velocity ( u ) as the function of y from equation (35)
and are shown in Figs.9 and 10. For fixed wt , the
velocity decreases with the increment in . As R
increases the maximum velocity moves closure to the upper permeable bed.
From equation (35) we have calculated the unsteady part of the velocity as a function of y for different values of Reynolds number R and Jeffrey
parameter with fixed 5, M=1, 0.02,4
wt
, 10 and are shown in Fig.11. and Fig.12. It is
noticed that the velocity increases with the increase in . As R increases the maximum velocity moves
closure to the upper permeable bed.
The variation of u with y is calculated from
equation (35) for different values of the Reynolds number R and for fixed 2, 25 , M=1,
0.02,4
wt
, 0.5 and is shown in Fig.13. We
observe that the velocity decreases with the increase in R.
From equation (35) we have calculated the unsteady part of the velocity as a function of y for different values of the thickness of porous lined
plate with fixed 2, 10 , M = 1, 2,4
R wt
, 0.5 and is shown in Fig.14. We
observe that the velocity decreases with the increase in .
Fig. 2. Steady state velocity profiles for
0.5, 2, 0.5R and 0.02
Fig. 3. Steady state velocity profiles for with
fixed 0.1, 2, 0.5R and 0.02
Fig..4. Steady state velocity profiles for R with fixed
2, 25, 0.5 and 0.02
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Fig..5. Steady state velocity profiles for with fixed
2, 25, 2R and 0.02
Fig. 6. Steady state velocity profiles for with
fixed 2, 25, 2R and 0.5
Fig.7. Unsteady state velocity profiles for t with
fixed 5, 5, 0R , 0.02 , M=1 and 1
Fig.8. Unsteady state velocity profiles for t with
fixed 0.5, 25, 10R , 0.02 , M=1 and
0.5
Fig.9. Unsteady state velocity profiles for with
0.5
Fig. 10. Unsteady state velocity profiles for with
1
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Fig. 11. Unsteady state velocity profiles for with
fixed 5, 2R ,M=1, 0.02,4
wt
and
10 .
Fig. 12. Unsteady state velocity profiles for with
fixed 5, 10R , M=1, 0.02,4
wt
and
10
Fig. 13. Unsteady state velocity profiles for R with
fixed 2, 25 ,M=1, 0.02,4
wt
and
0.5 .
Fig. 14. Unsteady state velocity profiles for with
fixed 2, 10 , M=1, 2,4
R wt
and
0.5 .
Acknowledgements: Authors thank DST, Govt. of India for providing financial support under major research project to carry this work.
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References
[1].Fung.Y. C. and Tang H.T, “Longitudinal discersion of Trater
particles in the blood flowing in a pulmonary alveonar Sheep”, ASME, J.Appl, Mech.42 (1975b) 546.
[2].Fung,Y. C. and Tang, H.T, “Solute distribution in the flow in a channel bounded by a porous layer”, ASME, J.Appl, Mech.42 (1975a) 531.
[3].Muakat, M.,” Flow of homogeneous fluids through porous Media”, Mc Graw Hill book Company. (1937)
[4].Yih,S.W.,”Dynamics of non-homogeneous fluids”, Macmillan Co. (1967).
[5].Rudraiah, N. et al., “Some flow problems in Porous media”PGSAM series, Bangalore University, Bangalore. (1979).
[6].Radhakrishnamacharya, G.,” Pulsatile flow of dusty fluid through a constricted channel” , J. of Applied. Math. Phys. (ZAMP), 29 (1981)
[7].Chaturani.P and Samy, R.P.,”Pulsatile flow of casson’s fluid through stenosed articles with applications to blood flow”, Biorheology, 23(5) (1986) 499-511.
[8]Chandra, P., Prasad, J.S.V.R.K,”Pulsatile flow in circular tubes of varying cross-section with suction/injection”, J.Aust. Math. Soc. Ser. B.35 (1994) 366-381.
[9].Wang, Y.C.,”Pulsatile flow in a porous channel”, Transaction of ASME, J. Appl. Mech. 38 (1971) 553-555.
[10].Vajravelu, K..,Ramesh, K.,Sreenadh, S.and Arunachalam, P.V.,” Pulsatile flow between permeable beds”, Int.Jr. of Non-Lin. Mech., 38 (2003) 999-1005.
[11].Avinash .K., Ananda Rao .J., Ravi Kumar. Y.V.K., Sreenadh.S.,” Pulsatile flow of a viscous stratified fluid of variable viscosity between permeable beds”, Jr.of Porous Media,14(12),2011,1115 – 1124,
[12].Afifi, N.A.S and Gad, N.S.,” Interaction of peristaltic Flow with pulsatile fluid through a porous medium”, App. Math. and Comp., 142 (2003) 167-176.
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