Effects of Velocity Slip and Temperature Jump on...
Transcript of Effects of Velocity Slip and Temperature Jump on...
JOURNAL OF MECHANICAL ENGINEERING ISSN 2165 - 8145 VOL. 1, NO. 3 NOVEMBER 2012
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Abstract—The present study concerns the first and second law
analyses of an electrically conducting fluid past a porous rotating
disk in the presence of velocity slip and temperature jump
conditions. A semi numerical-analytical technique, combination
of differential transforms method (DTM) and padé approximant,
named DTM-Padé is employed to solve system of ordinary
differential equations that is convert form of the partial
differential equations governing the heat and flow motion.
Entropy generation equation is derived as a function of velocity
and temperature gradients and non-dimensionalized using
geometrical and flow physical field-dependent parameters. The
velocity profiles in radial, tangential and axial directions,
temperature distribution and averaged entropy generation
number are obtained. The effects of flow physical parameters
such as magnetic interaction parameter, suction parameter,
Reynolds number, Knudsen number, Prandtl number, and
Brinkman number on the all fluid velocity components,
temperature distribution, and averaged entropy generation
number are checked and discussed and the path for minimizing
the entropy is also proposed.
Index Terms—velocity slip, temperature jump, entropy
generation, MHD flow, rotating disk, DTM-Padé
I. INTRODUCTION
N most of the investigations no-slip boundary condition (the
assumption that a liquid adheres to a solid boundary) is
established and 0Kn , but in some situations such as
emulsions, suspensions, foams and polymer solution [1], the
no-slip condition is not adequate. For the range of
0.01 0.1Kn (slip flow) the standard Navier–Stokes and
energy equations can still be used by taking into account
velocity slip and temperature jump. In recent years, the slip-
flow regime has been widely studied and researchers have
been concentrating on the analysis of micro-scale in micro-
electro-mechanical systems (MEMS) associated with the
Manuscript received November 13, 2012. Mohammad Mehdi Rashidi is with the Mechanical Engineering
Department, Engineering Faculty of Bu-Ali Sina University, Hamedan, Iran,
(corresponding author to provide phone: +98 811 8257409; fax: +98 811 8257400; e-mail: [email protected], [email protected]).
Navid Freidooni Mehr is with the Mechanical Engineering Department,
Engineering Faculty of Bu-Ali Sina University, Hamedan, Iran (e-mail: [email protected]).
embodiment of velocity slip and temperature jump. Because of
the micro-scale dimensions, the slip flow greatly differs from
the traditional no-slip flow [2]–[4]. Sparrow et al [5]
considered the fluid flow due to the rotation of a porous
surfaced disk and employed a set of linear slip flow
conditions. A substantial reduction in torque occurred as a
result of surface slip. Turkyilmazoglu and Senel [6]
investigated the effects of roughness on the heat and mass
transfer for the flow over a rotating disk subjected to a wall
suction or injection. Arikoglu et al [7] presented the effect of
slip on entropy generation over a rotating disk in MHD flow
by semi-numerical analytical solution technique. Sahoo [8]
studied the effects of partial slip, viscous dissipation, and
Joule heating on the flow and heat transfer of an electrically
conducting non-Newtonian fluid due to a rotating disk.
Entropy generation minimization should be taken into
account in thermal systems in some different situations, for
example when we have thermodynamics irreversibility, heat
transfer through finite temperature gradient, convective heat
transfer characteristics and, viscous effects. The equipment
performance degrades because of irreversibility and it should
be noted that the entropy generation is a scale of process
irreversibility [9], [10]. In order to increase the efficiency in
all types of manufacturing systems and to minimize the
entropy generation, the researchers have been focusing on the
second law of thermodynamics in design of thermal
engineering systems. The system efficiency calculations using
the second law of thermodynamics based on the entropy
generation is much more reliable and suitable than the
calculations by the first law of thermodynamics. Accurate
calculation of the entropy generation plays an important role
in the development of thermal system components and the
entropy generation is a criterion of work demolition in the
systems. Optimal system design will result in reduction of
entropy generation [11], [12]. Many researchers have been
motivated to conduct the second law analysis applications in
the design of thermal engineering systems, in recent years.
Aïboud and Saouli [13] displayed the application of the
second law analysis of thermodynamics to viscoelastic MHD
flow over a stretching surface. The effect of slip and joule
dissipation on entropy generation in MHD flow over a single
rotating disk was studied by Arikoglu et al [7] via semi-
Effects of Velocity Slip and Temperature Jump
on the Entropy Generation in
Magnetohydrodynamic Flow over a Porous
Rotating Disk
M.M. Rashidi, and N. Freidooni Mehr
I
JOURNAL OF MECHANICAL ENGINEERING ISSN 2165 - 8145 VOL. 1, NO. 3 NOVEMBER 2012
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numerical analytical solution method, named differential
transform method. Their work is most similar work to the
present study. Mahian et al [14] analyzed the first and second
laws of thermodynamics to demonstrate the effects of MHD
flow on the distributions of velocity, temperature and entropy
generation between two concentric rotating cylinders. San et
al [15] presented the entropy generation analysis for combined
forced convection heat and mass transfer in a two dimensional
channel.
The use of an external magnetic field is a very important
issue in many industrial applications, especially as a
mechanism to control the material construction [16]. In
addition, study the heat transfer and flow in a closed cavity or
a channel in the presence of a magnetic field due to many
engineering applications such as nuclear cooling reactors,
MHD marine propulsion, MHD micro pumps, electronic
packages and microelectronic devices are very important. The
first studies on the effects of MHD were carried out in 1907.
In that year, Northrup built an MHD pump [17]. Studying the
effects of rotation and magnetic field factors on the fluid flow
was one of the most important research topics for many
researchers in recent years.
Some of strongly nonlinear equations used to describe
physical systems in the form of mathematical modeling, do
not have exact solutions. The numerical or analytical methods
can be applied to solve these nonlinear equations. Despite all
the benefits, there are many disadvantages for the numerical
methods in comparison with the analytical methods.
Therefore, we use one of the semi numerical-analytic
techniques named differential transform method (DTM) [18],
[19] to solve the system of nonlinear differential equations. In
some especial cases with high order of nonlinearity, applying
DTM cannot satisfy the infinity boundary conditions. To
overcome this problem, the padé approximant is applied to the
DTM results to enlarge convergence radius of them. In recent
years, DTM and DTM-Padé were employed to solve for many
kind of high nonlinear problems [20]–[23].
The current article is mainly motivated by the need to
understand the entropy generation in the MHD flow over a
porous rotating disk in the presence of the velocity slip and
temperature jump conditions. We examine the entropy
generation analysis in this perusal, because of more reliability
of second law of thermodynamics analysis than the first one.
The combination of the DTM and Padé approximant, DTM-
Padé, is employed to investigate the effect of flow physical
parameters such as magnetic interaction parameter, suction
parameter, Reynolds number, Knudsen number, and Brinkman
number on the all fluid velocity components, temperature
distribution, and averaged entropy generation number. The
obtained results of present study can be applied to design
thermal systems with reduced sources of irreversibility’s.
II. GOVERNING EQUATIONS AND MATHEMATICAL
FORMULATION
Consider the axially symmetric laminar flow of an
incompressible Newtonian fluid past a porous rotating disk
that has a constant angular velocity, in the presence of
externally applied uniform vertical magnetic field. The
coordinate system and geometry of the problem are shown in
Fig. 1. The three dimensional governing equations for the
continuity, momentum and energy in laminar MHD
incompressible boundary layer flow in cylindrical coordinates
can be presented, respectively, as follows
1
0,w
rur r z
(1)
2
22 2
0
2 2 2
1
1,
u u v pu w
r z r r
Bu u u uu
r rr z r
(2)
22 2
0
2 2 2
1,
v v uvu w
r z r
Bv v v vv
r rr z r
(3)
2 2
2 2
1 1,
w w p w w wu w
r z z r rr z
(4)
2 2
2 2
1,
p
T T k T T Tu w
r z C r rr z
(5)
where is the fluid density, p is the fluid pressure, is the
kinematic viscosity, is the electrical conductivity, k is the
thermal conductivity and pC is the specific heat at constant
pressure. The flow velocity components are in the directions
of increasing cylindrical polar coordinates , ,r z . An
external uniform magnetic field B is applied normal to the
disk surface that has a constant magnetic flux density 0B ,
which is assumed constant by taking small magnetic Reynolds
number much smaller than the fluid Reynolds number. The
surface of the rotating disk is maintained at a uniform
temperature wT , while the temperature and pressure of the
ambient fluid are T and p , respectively. Assuming the
effect of velocity slip is very important and should be included
in the modeling of flow field for the more accurate prediction.
In the base of slip flow theory, one can declare that the fluid
velocity at the surface is different from the wall velocity
compared to the local velocity gradient in normal direction.
According to Karniadakis and Beskok [24], the following
form for the slip flow equation has been proposed:
22 3 1
,2
vs w
v
u Kn Re TU U
z Ec r
(6)
where sU is the velocity of the fluid near to the disk surface,
wU is the wall velocity, and v is the tangential momentum
accommodation coefficient, which is usually determined
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empirically [25] and depends on fluid and surface finish and
is the ratio of specific heats. Thermal creep effect is shown
in the second term of right-hide side of (6). This effect induces
velocity slip along the wall due to the temperature gradient
near to the wall along the surface. It can be illustrated that this
term is of second-order in terms of Knudsen number. Thus, it
is negligible comparing to the first term that is of first-order in
the slip-flow regime [25]–[27]. For thermal boundary
condition, we have considered temperature jump effect that
was derived by von Smoluchowski [24]. The temperature
jump condition can be given by [24]:
2 2,
1
t ss w
t
TT T
Pr z
(7)
where sT is the temperature of the fluid near to the disk
surface, wT is the disk wall temperature, and t is the energy
accommodation coefficient that is usually determined
experimentally and depends on the surface finish, the fluid
temperature, and the pressure. Thus, following above
description about boundary conditions, the appropriate
boundary conditions, subjected to uniform suction 0w through
the disk, become:
0
2,
2,
at 0,
,
2 2,
1
0, 0, , at .
v
v
v
v
t sw
t
uu
z
vv r
z z
w w
TT T
Pr z
u v T T z
(8)
The non-dimensional forms of the mean flow velocities and
temperature distributions of (1)-(5) are given by Von
Karman’s exact self-similar solution of the Navier-Stokes
equations:
1 2
1 2
,
, , ,
, .w
z
u r F v r G w H
p p P T T T T
(9)
Substituting (9) in (1)-(5), we obtain the following system
of ordinary differential equations:
F HF F G MF (10)
G HG FG MG (11)
H F (12)
,Pr H (13)
where , , F G H and are the non-dimensionless functions
of modified dimensionless vertical coordinate ,
2
0M B is the magnetic interaction parameter,
pPr C k is the Prandtl number and primes denote
differentiation with respect to . The transformed boundary
conditions can be written as follows:
0 0 , 0 1 0 ,
0 , 0 1 0 ,
0, 0, 0, as ,
s
F F G G
H W
F G
(14)
where 2 2v v v v Kn Re
is
the slip factor,
1 2
0sW w is the suction parameter that
0sW shows a uniform suction at the disk surface,
2 2 1t t Kn Pr Re is the temperature
jump factor, and Re is the rotational Reynolds number. The
values of tangential momentum accommodation number,
energy accommodation coefficient and the specific heat ratio
for air are considered as 0.9, 0.9, and 1.4, respectively [24].
III. ENTROPY GENERATION ANALYSIS
Generally, the local volumetric entropy generation rate, in
the presence of axial symmetry and magnetic field, can be
expressed as (for more details, see [7], [10])
2
2
1. ,
gen
ww
w
kS T
TT
J QV E V BT
(15)
where
2
,T T T
r r z
(16)
,
u v w v wu
r z z rr
w u u vr
r z r r r
(17)
,J E V B (18)
where is viscous dissipation, J is electric current, Q is
electric charge density, V is the velocity vector and E is
electric field. It is assumed that the electric force per unit
charge, in compared with V B in (15) is negligible and we
also consider that the electric current is much greater than
.QV Thus, the entropy generation rate reduces in this case to:
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2gen
w
Thermal irreversibility
w
Fluid friction irreversibility
2
0
k TS
zT
u wu
r zr
T v u vr
z z r r
B
T
.w
Joule dissipation irreversibility
u v
(19)
The above equation reveals that the entropy generation is
due to three effects, the first effect, a conductive effect, is the
local entropy generation due to heat transfer irreversibility
HTIN , which contains the entropy generation by heat
transfer due to axial conduction from the rotating disk, the
second one, a viscous effect, is due to fluid friction
irreversibility FFIN and the last effect denotes to the
magnetic effects in the form of joule dissipation irreversibility
JDIN that is caused by the movement of electrically
conducting fluid under the magnetic field inducing electric
currents that circulate in the fluid [7]. The entropy generation
number, dimensionless form of entropy generation rate,
represents the ratio between the actual entropy generation rate
genS and characteristic entropy generation rate 0 .S The
similarity transformation parameters of (9) are employed to
non-dimensionalized the local entropy generation given in
(19), thus the entropy generation number becomes:
2
,G
F HRe Re
N Br F Gr
M F G
(20)
where wT T is the dimensionless temperature
difference, Br R k T is the rotational Brinkman
number, r r R is the dimensionless radial coordinate and
G gen wN S k T T is the dimensionless entropy
generation rate.
The averaged entropy generation number that is an
important measure of total global entropy generation can be
evaluated using the following formula
1
,0 0
12 ,
m
G av GN r N dr d
(21)
where is the considered volume. In order to consider both
the velocity and thermal boundary layers, we calculate the
volumetric entropy generation in a large finite domain. Thus,
integration in (21) is obtained in the domain 0 1r and
0 ,m where m is a sufficiently large number.
IV. ANALYTICAL APPROXIMATIONS BY MEANS OF
DTM-PADÉ
Taking differential transform of (12)‒(13) (for more details
of DTM theory, see [21], [28]), one can obtain
0
1 2 2
1 1
0,
k
r
k k F k
k r H r F k r
F r F k r G r G k r
M F k
(22)
0
1 2 2
1 1
2
0,
k
r
k k G k
k r H r G k r
F r G k r
M G k
(23)
1 1 2 0,k H k F k
(24)
0
1 2 2
1 1 0,k
r
k k k
Pr k r H r k r
(25)
where , , ,F k G k H k and k are the transformed
functions of , , ,F G H and , respectively
and are given by:
,k
k =0
F = F k
(26)
,k
k =0
G = G k
(27)
,k
k =0
H = H k
(28)
.k
k =0
= k
(29)
The transformed boundary conditions become
0 1 , 1 ,
0 1 1 , 1 ,
0 1 1 , 1 ,
0 ,s
F F F a
G G G b
c
H W
(30)
where ,a b and c are constants. Substituting (30) into (22)‒
(25) and with a recursive method, one can calculate the values
of , , ,F k G k H k and .k Therefore, substituting
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all , , ,F k G k H k and k into (26)‒(29), we have
the series solutions as follows
2
22 2
3
22 2
1
2 1
2 1
1,
61
s
s
s
aW a MF a a
a b
a M b b
a W a MW
a b
(31)
2
3
111
2 2 1
2 11
,16
2 1
s
s
s
b W M bG b b
a b
b M a b
b W M bW
a b
(32)
2
23 2 2
2
11 ,
3
s
s
H W a a
a W a M a b
(33)
2
3 2 2
11
2
12 .
6
s
s
c c c PrW
c Pr W ac Pr
(34)
The Padé approximant is applied to enlarge the convergence
radius of the truncated series solution. In this way, the
polynomial approximation converts into a ratio of two
polynomials. As it is shown in Fig. 2-5, without using the
Padé approximant, the DTM solution, cannot satisfy boundary
conditions at infinity. Therefore, it is important to combine the
DTM with the Padé approximant series solution to provide an
effective tool to handle infinite boundary value problems.
Thus, we apply the Padé approximation to (31)‒(34) and using
the boundary conditions of (14) at , one can obtain ,a b
and c . The number of required terms is characterized by the
convergence of the numerical values to one’s desired
accuracy.
V. RESULTS AND DISCUSSION
For the present investigation, we have considered the value
of the Prandtl number is equal to 1. The default values of other
flow physical parameters are referred in each of the graphs.
Figs. 6-9 display the effect of magnetic interaction parameter
on the all velocity components and temperature distribution. A
drag-like force that named Lorentz force is created by the
infliction of the vertical magnetic field to the electrically
conducting fluid. This force has the tendency to slow down the
flow around the disk at the expense of increasing its
temperature. Indeed, the magnetic field as a body force
increases in effect of friction forces and the great resistances
on the fluid particles, which cause to generate heat in the fluid,
apply as the vertical magnetic field increases. Due to the
above reasons, the velocity profiles in radial, tangential and
magnitude of axial directions reduce and the thermal boundary
layer thickness increases with the increase in magnetic
interaction parameter. It must be pointed that the radial and
axial velocity component distributions decay rapidly along
with increasing the magnetic interaction parameter and also
the magnetic interaction parameter variations has the less
effect on the temperature distribution and the radial velocity
profile experiences a maximum value close to the disk surface
due to the existence of the centrifugal forces.
The effect of suction parameter on the all velocity
component distributions and temperature field is shown in
Figs. 10-13. When the suction applies at the disk surface, the
radial and tangential velocity profiles reduce and the
magnitude of axial velocity increases. In addition, the radial
velocity component becomes very small, for strong values of
the suction parameter. The usual decay of temperature occurs
for the higher values of suction.
The effects of Reynolds number and Knudsen number on
the radial, tangential and axial velocity components and
temperature distribution are demonstrated in Figs. 14-21,
respectively. The effects of these two parameters have been
studied together; because of their similar effects on the slip
boundary condition. The maximum of radial velocity
component decreases, and its location moves toward the disk
in the presence of the slip condition. In addition, the radial
velocity profile caused by the centrifugal forces starts from
zero only in the case of no slip condition 0Kn . The fluid
velocity components in all directions and temperature
distribution decrease with increasing the values of the
Reynolds and Knudsen numbers. In other word, less amount
of flow is drawn and pushed away in the velocity directions,
as the slips get stronger and decreasing in the heat generation
in the vicinity of the disk occurs in the slip condition.
Fig. 22 shows the effect of Prandtl number on the
temperature distribution. As we know, the thermal boundary
layer thickness is inversely proportional to the square root of
Prandtl number. Hence, the thermal boundary layer
thicknesses get decreased with increasing the value of the
Prandtl number. In other word, the flow with large Prandtl
number prevents spreading of heat in the fluid.
Figs. 23-27 depict the results of averaged entropy
generation number as a function of suction parameter,
Reynolds number, Knudsen number, Prandtl number, and
Brinkman number for a wide range of the magnetic interaction
parameter. With applying magnetic effect, the radial and
tangential velocity components decrease and axial velocity
and temperature distribution increase, as it is explained before.
Therefore, from (19), some of the entropy generation
irreversibility mechanisms produce greater rate of entropy
with increasing magnetic interaction parameter whiles the
others generate decreasing rate. Fig. 23 shows the effect of
suction parameter on the averaged entropy generation number.
By applying the suction at the disk surface, the averaged
entropy generation number decreases. The effects of Knudsen
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and Reynolds number on the averaged entropy generation
number are presented in Figs. 24 and 25. Both the temperature
and the velocity gradients decrease, as the Knudsen and
Reynolds number increases. This results in a decrease in the
averaged entropy generation. Increasing the velocity slip and
temperature jump at the wall cause to decreasing heat transfer
and momentum transfer from the wall to the fluid and this also
brings about the reduction in the averaged entropy generation.
Fig. 26 represents the effect of Prandtl number on the
averaged entropy generation number. As the Prandtl number
increases, the value of averaged entropy generation increases.
Fig. 27 demonstrates the effect of Brinkman number on the
averaged entropy generation number versus magnetic
interaction parameter. An increase in the entropy generation
produced by fluid friction and joule dissipation brings with
increasing the value of the Brinkman number.
VI. CONCLUSIONS
In the current perusal, the mathematical formulation has
been derived for the entropy generation analysis in MHD flow
over a porous rotating disk in the presence of the velocity slip
and temperature jump. DTM-Padé is applied to solve the
system of ordinary differential equations. An excellent
agreement can be observed between the results of this study
and the numerical results obtained by shooting method, in an
especial case. The effects of physical flow parameters such as
magnetic interaction parameter, suction parameter, Reynolds
number, Knudsen number, and Brinkman number on the fluid
velocity in radial, tangential, and axial directions, temperature
distribution, and averaged entropy generation are illustrated.
The results show that the main goal of second law of
thermodynamics that is minimizing entropy, are reached as the
magnetic interaction parameter, Prandtl number, and
Brinkman number decrease or suction parameter, Reynolds
number, and Knudsen number increase. It can be seen that the
disk surface acts as a strong source of irreversibility.
Fig. 1. Configuration of the flow and geometrical coordinates.
Fig. 2. The profile of F obtained by DTM for different value of n and
different order of DTM-Padé in comparison with the numerical solution when
1M , 1sW , 0.05Kn and Re 100 .
Fig. 3. The profile of G obtained by DTM for different value of n and
different order of DTM-Padé in comparison with the numerical solution when
1M , 1sW , 0.05Kn and Re 100 .
Fig. 4. The profile of H obtained by DTM for different value of n and
different order of DTM-Padé in comparison with the numerical solution when
1M , 1sW , 0.05Kn and Re 100 .
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Fig. 5. The profile of obtained by DTM for different value of n and
different order of DTM-Padé in comparison with the numerical solution when
1M , 1sW , 0.05Kn and Re 100 .
Fig. 6. Effect of magnetic interaction parameter on radial velocity profile
when 1sW , 0.05Kn and Re 100 .
Fig. 7. Effect of magnetic interaction parameter on tangential velocity profile
when 1sW , 0.05Kn and Re 100 .
Fig. 8. Effect of magnetic interaction parameter on axial velocity profile
when 1sW , 0.05Kn and Re 100 .
Fig. 9. Effect of magnetic interaction parameter on temperature distribution
when 1sW , 0.05Kn and Re 100 .
Fig. 10. Effect of suction parameter on radial velocity profile when 1M ,
0.05Kn and Re 100 .
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Fig. 11. Effect of suction parameter on tangential velocity profile when
1M , 0.05Kn and Re 100 .
Fig. 12. Effect of suction parameter on axial velocity profile when 1M ,
0.05Kn and Re 100 .
Fig. 13. Effect of suction parameter on temperature distribution when 1,M
0.05Kn and Re 100 .
Fig. 14. Effect of Reynolds number on radial velocity profile when 1M ,
1sW and 0.05Kn .
Fig. 15. Effect of Reynolds number on tangential velocity profile when
1M , 1sW and 0.05Kn .
Fig. 16. Effect of Reynolds number on axial velocity profile when 1M ,
1sW and 0.05Kn .
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Fig. 17. Effect of Reynolds number on temperature distribution when 1M ,
1sW and 0.05Kn .
Fig. 18. Effect of Knudsen number on radial velocity profile when 1M ,
1sW and Re 100 .
Fig. 19. Effect of Knudsen number on tangential velocity profile when
1M , 1sW and Re 100 .
Fig. 20. Effect of Knudsen number on axial velocity profile when 1M ,
1sW and Re 100 .
Fig. 21. Effect of Knudsen number on temperature distribution when 1M ,
1sW and Re 100 .
Fig. 22. Effect of Prandtl number on temperature distribution when 1M ,
1sW , 0.05Kn and Re 100 .
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Fig. 23. Change of ,G avN with respect to magnetic interaction parameter for
different values of suction parameter when 0.05Kn , Re 100 and
10Br .
Fig. 24. Change of ,G avN with respect to magnetic interaction parameter for
different values of Reynolds number when 1sW , 0.05Kn and 5Br .
Fig. 25. Change of ,G avN with respect to magnetic interaction parameter for
different values of Knudsen number when 1sW , Re 100 and 5Br .
Fig. 26. Change of ,G avN with respect to magnetic interaction parameter for
different values of Prandtl number when 1sW , 0.05Kn , Re 100 and
10Br .
Fig. 27. Change of ,G avN with respect to magnetic interaction parameter for
different values of Brinkman number when 1sW , 0.05Kn and
Re 100 .
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Mohammad Mehdi Rashidi is born in Hamedan,
Iran in 1972. He received his B.Sc. degree in Bu-Ali Sina University, Hamedan, Iran in 1995. He also
received his M.Sc. and Ph.D degrees from Tarbiat
Modares University, Tehran, Iran in 1997 and 2002, respectively. His research (Areas of Specialization)
focuses on heat and mass transfer,
Thermodynamics, computational fluid dynamics (CFD), nonlinear analysis, engineering mathematics
and exergy and second law analysis.
He is an associate professor of Mechanical Engineering at the Bu-Ali Sina University, Hamedan, Iran. His works have
been published in the journal of Energy, Computers and Fluids,
Communications in Nonlinear Science and Numerical Simulation and several other international journals. He has published a book: Mathematical
Modelling of Nonlinear Flows of Micropolar Fluids (Germany, Lambert
Academic Press, 2011). He has published over 100 journal articles. Dr. Rashidi is a reviewer of several journals such as Applied
Mathematical Modelling, Computers and Fluids, Energy, Computers and
Mathematics with Applications, International Journal of Heat and Mass Transfer, International journal of thermal science, Mathematical and
Computer Modelling, etc. He was an invited professor in Génie Mécanique,
Université de Sherbrooke, Sherbrooke, QC, Canada J1K 2R (From Sep 2010-Feb 2012), Universite Paris Ouest, France (For Sep 2011) and University of
the Witwatersrand, Johannesburg, South Africa (For Aug 2012). He also is the
member of Islamic Educational, Scientific and Cultural Organization (ISESCO). He is the editor of the International Journal of Applied
Mathematical Research (IJAMR), Journal of Advanced Computer Science & Technology and Scientific Research and Essays, and Journal of Mechanical
Engineering.
Navid Freidooni Mehr received his B.Sc. degree in
Mechanical Engineering from Bu-Ali Sina University, Hamedan, Iran in 2010. He is currently
a M.Sc. student in Bu-Ali Sina University, Iran.
Born in Hamedan in 1988, his research interests include entropy generation analysis, heat and mass
transfer, nonlinear analysis and thermodynamics
cycle analysis.