Thermal Energy on Water and Oil placed Squeezed Carreau Nanofluids Flow

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:19 No:03 79
190803-4242-IJMME-IJENS © June 2019 IJENS
I J E N S

Abstract— this research work is focused on the numerical study
regarding Carreau nanofluids’ squeezed flow via a permeable
sensor surface. The nanofluids’ thermal conductivity is
considered to be dependent on temperature. A convenient
transformation is employed to reorganize governing equations
into ordinary differential equations. The Runge–Kutta method
and shooting technique are employed to accurately solve the
boundary layer momentum as well as heat equations. Graphical
and tabular aids are used to evaluate the solutions of applicable
parameter with regards to temperature as well as the rate of
heat transfer. In this work, a comparison is done from three
nanofluids, i.e. copper, oxide aluminum and SWCNTs
(nanoparticles) based fluids (water, crude oil and ethylene
glycol) to improve heat transfer. It is found that the
temperature dimensionless was dropped and dominated with the
squeezed flow parameter and nanoparticle volume fraction
parameter. That is for all nanomaterials. When compared with
water and ethylene glycol, crude oil is cooler and a thinner
thermal boundary layer is presented. For the rate of heat
transfer (Nusselt number) was higher in: Ethylene glycol-
SWCNT with high permeable velocity parameter 0.2, Ethylene
glycol- SWCNT with low squeeze flow parameter 0.1 and
Ethylene glycol- oxide aluminum with low nanoparticle volume
fraction 0.05
Index Term— heat transfer, squeezed flow, Carreau
nanofluids flow, permeable sensor surface
I. INTRODUCTION
Regular fluids have slow heat transfer boost. The wide
applications of heat transfer have garnered interests in
various science and engineering fields. Nanofluids are a new
class of fluids that are employed to enhance heat transfer
affectivity. In nanofluids, base liquid containing stably
suspended nanoparticles and handling less than 100nm in
size, which normally include kerosene oil, water, glycol, etc.
Earlier work on this type of fluids was conducted by Choi [1]
and later named as nanofluids. Several theories have been put
forward for the thermal conductivity of nanofluids in a bid to
enhance nanofluids’ heat transfer, so as to approximate the
solutions pertaining to the models of nonlinear flow, and
numerous numerical approaches have been presented for the
same (as analytical solutions are very rare for nonlinear flow
models) (Ahmed et al.[2]).
Nanoparticles are mainly employed to facilitate dissipation of
nanoparticles in fluid. Efforts to boost the conductivity of
thermal can be dated back to Maxwell theory in 1873. When
compared with micro-particles (previous approach),
nanoparticles can continuously suspended for an extended
time, and should they be below a threshold level and/or
improved with surface/stabilizers, they can be kept in
suspension almost indefinitely. Moreover, when compared
with micro-particles, the surface is much larger (million
times) on a per unit volume of nanoparticles (the interior of
nanoparticle has a very large number of surface molecular per
unit area). These characteristics can be excised to enhance
stable suspensions along with heat-transfer, boost flow and
other properties (Rizwan et al. [3]). When mechanical
components pass, it triggers unsteady squeezing as well as
pushing of viscous fluid between two parallel plates – for
instance, the squeezed films in power transformation systems.
In squeeze flows, the material between two parallel plate is
carried out due to compressing plates to squeeze out radially.
An electrical signal is sent by the sensor element into a
mechanical wave, which can be freely encouraged by physical
development (R. Kandasamy et al. [4]).
Most of the biological and chemical sensors employ
stretching surfaces as their sensing elements – for example,
micro cantilever. This element can strictly sense different
diseases or can be employed to identify numerous serious or
bio-warfare agents. On binding to the target molecules, the
micro cantilever bends as it attaches with the receptor on one
of its surfaces. Normally, the micro cantilever is positioned in
thin film fluidic cells, which in the presence of external
disturbances could face relatively large levels of external
squeezing. Modelling of the flow over the micro cantilever
can be carried out as flow over a horizontal surface (R.
Khaled [5]).
Recently, many authors [6][7][8][9][10] have studied the
impacts cast by magnetic hydrodynamic on oscillatory
squeezed discharges within thin films. They demonstrated
that flow change abilities inside thin films can be decreased
by magnetic strength, which could be correlated with the
immense squeezing problems. Numerous investigations
focused on unsteady flow between two parallel plates that are
withdrawing or approaching from each other in a
Thermal Energy on Water and Oil placed
Squeezed Carreau Nanofluids Flow
Mohammed M. Fayyadh1
, R. Roslan1
, R. Kandasamy2
and Inas R. Ali1
1
Research Centre for Computational Fluid Dynamics, FAST, University Tun Hussein Onn Malaysia, Malaysia,
84600, Pagoh, Johor, Malaysia.
2
Knowledge Institute of Technology India, Kalapalayan 637505, Tamilnadu, India
Email: abuzeen@gmail.com

I J E N S
symmetrical manner, which was also analysed by P Singh et
al. [11] and P.S. Gupta et al. [12].
Heat transfer on squeezed fluid flow on a sensor surface
concerning tangent hyperbolic fluid that had changing the
conductivity of thermal was investigated by Ganesh Kumar et
al. [13]. As per the study, it was found that the variation in
squeezed flow index, Weiss Enberg and permeable velocity
parameters had a significant effect on the thermal boundary
layer thickness and momentum. Masood Khan et al. [14]
investigated unsteady Carreau nanofluids’ two-
dimensional flow and included the general mass prevision
and convection heat, along with temperature-dependent
thermal conductivity over a shrinking or stretching
horizontal cylinder. Khan et al. [15], M. Khan, M. Azam
[16] assessed the Carreau fluid model by considering
various surfaces with variable thermal conductivity. N.
Muhammad et al. [10] evaluated the magneto hydrodynamics
squeezed flow concerning nanofluid over a sensor shell,
exposed to temperature-dependent viscosity. The squeezed
flow of water-based CNTs was also studied over a sensor
surface that had variable viscosity.
Various investigations were carried out on squeezed MHD
flow over sensor surface that had variable thermal
conductivity by considering different properties, including
surface, size, shapes and impacts on thermo-physical
characteristics [17][18][19][20][21] .
Naveed Ahmed et.al[22],
[23],
[24],
[25],
[26] Investigated the
effect of thermal radiation from Newtonian fluid on squeezing
porous channel, the impact of viscous flow through
deformable asymmetric porous channel, nonlinear radiation
squeezed flow in a rotating frame and the effect of flow of
Jeffery fluid in stretchable channels. On the other hand Fitnat
Saba et.al [27],
[28], analysed the Hybrid Nanofluid in an
Asymmetric Channel with Squeezing Walls in different
Shapes of Nanoparticles. Furthermore, investigated the
thermal of carbon nanotube nanofluid on stretched surface.
This work is aimed at evaluating the impact of three different
nanoparticles (aluminium oxide, SWCNTs and Cu) that were
suspended in nanofluid (ethylene glycol, water and crude oil),
which was based on unsteady external squeezing flow, by
employing the Carreau nanofluids model on a permeable
horizontal surface. A reduction was made in unsteady partial
differential equations to include nonlinear system of ordinary
differential equations after numerically resolving convenient
similarity transformation.
II.DESCRIPTION OF THE PROBLEM
a. Carreau model
The Carreau rheological model, the modelled Cauchy
stress tensor τ can be presented as:
;
(1)
Where p represents pressure, I signifies Identity tensor, μ
denotes apparent viscosity, μ0 represents viscosity of
essentially shear rate, μ∞ signifies viscosity of infinite
shear rate, Γ denotes constant of material time, n and γ
represents index of power law and the rate of shear . The
shear rate is given by:
(2)
Here, Π signifies the rate of second invariant strain tensor.
(3)
Where A1 denotes the tensor of the Rivlin – Ericksen. In
most of the practical cases, μ0 ≫ μ∞, where μ∞ is given as
zero. Employing Eqs. (1) and (2) gives:
(4)
The index n of power law, range changes between 0 and 1,
i.e. 0 < n < 1, denotes the pseudo plastic fluids or shear
thinning. n > 1 represents the dilatant fluids or shear
thickening, and n = 1 signifies the fluid of Newtonian
material [29],
[16],
[30].
b. Mathematical Analysis
For a horizontal surface consider a flow, which is Carreau
nanofluids flow with incompressible, 2-D boundary layer that
unsteady flow onto a sensor surface that is continuously
permeable. The surface’s length is considered to be L. The x-
axis gets along the surface’s length, which starts from its free
end, while the y-axis gets normal towards the upper surface
as presented in Fig. 1. Furthermore, Fig. 1 show that h(t) the
closed of hight squeezed channel which is much larger when
compared to the boundary layer thickness. The squeezing free
stream is assumed to come from the surface tip. This issue
finds application in flow over micro cantilever sensor due to
an external squeezing near the fluidic cell’s boundaries [31].
Fig. 1. Flow configuration and coordinates system
(5)
(6)
Squeezing

I J E N S
(7)
(8)
In equations (5-8) we have for x, y-axis’s such that , u and v
represent the components of velocity along x and y directions,
respectively. The velocity of free stream is U, n characterizes
the index of power law, represents the constant of material
time, p denotes the pressure of fluid, implies the
variable thermal diffusivity, symbolizes the viscosity of
kinematic, T denotes temperature and represents the
density. The governing equations (6,7)becomes when
removing the pressure gradient of nanofluids:
(9)
With boundary conditions;
(10)
Where, denotes the velocity of free stream, the
temperature of free stream and the heat flux of the wall.
Here, thermal conductivity takes the
form , in which represents a small quantity
(M.S. Abel and N. Mahesha [32]). The wall is considered to
be a function of heat flux . Reference velocity
denotes the velocity at the sensor surface, which can be
calculated after the surface is made permeable. This velocity
and the vertical velocity are both symmetrical at the
disordered boundary, which increases with increase in the
bulk of the surface pores, or when the surface is in proximity
to the disordered boundary. The following similarity
transformations can be employed to transform Eqs. (8) and
(9) into differential form:
(11)
Here, and . s denotes a constant
b represents the index of squeezed flow, , a signifies the flow
of strength squeezing parameter, indicates the flux of the
heat and k symbolises thermal conductivity.
It needs to be noted that the governing Eq. (5) is identically
satisfied, and then eques. (8, 9) are represented by:
(12)
(13)
, ,
where,
,
Moreover, the physical transformations in the above-
mentioned equations, include which is nanofluid of
the heat effective capacity represents nanofluid of the
dynamic effective viscosity, namely the Brinkman model for
effective viscosity and Hamilton-Crosser’s model is employed
for effective thermal conductivity. These models are as
follows [2]. In these expressions, kf and ks represent the
conductivities pertaining to the fluid and nanoparticles. Also,
the parameter m signifies the solid nanoparticles’ different-
shape factor (sphere 3.0), and represents the nanoparticles’
volume fraction.
Further, the conditions for the corresponding transformed
boundary include:
(14)
Here, denotes Prandtl number, represents
the permeable velocity and signify the
Weissenberg number. By employing the boundary
approximations, at the sensor surface, the wall shear stress
can be presented as:
(15)
The coefficient of skin friction and Nusselt number are
defined as ;
(16)
In the dimensionless form, the skin friction and Nusselt
number are defined as:
(17)
where [33].
III. SOLUTION OF NUMERICAL AND VALIDATION
MODEL
MAPLE 18 is employed to numerically integrate the
equations of non-linear combination of ordinary
differential Eqs. (12) and (13) , Eq. (14), represents the
initial and boundary conditions with the help of mean of
the Shooting technique. Based on this approach, boundary
value issues presented in Eqs (12) and (13) are transformed
into the initial value issue. The far field boundary
conditions are assumed to possess convenient finite values
as η → ∞. Then, rewriting is done for the system of
ordinary differential Eqs. (12) and (13) as following:

I J E N S
… (18)
With initial conditions
…… (19)
Where,
(20)
The values of and ) are needed to integrate Eqs.
(18) and (19) with the initial condition (20). For ) and
, convenient initial guesses are selected before carrying
out the integration. A comparison is done between the
calculated values pertaining to f ′ and θ at , and the given
boundary conditions and . A better approximation
for the solution is obtained by modifying the estimated values
of and . A fifth-forth order of Runge-Kutta
Fehlberg scheme is employed to numerically solve the
resulting initial value problem.
a. Validation model
The current value is compared with that of Rizwan et al. [3].
to validate the put forward numerical scheme. It was seen that
the table 3 significantly resemble each other, which suggests
that there is an excellent agreement with the rate of skin
friction theoretical solution.
IV. RESULTS AND DISCUSSION
This section focuses on the investigation of the impact of
different non-dimensional physical quantities associated with
the Carreau flow model of a nanofluid flowing between two
parallel plates. Numerical computation involves several sets
of relevant parameters like permeable velocity ( ), squeezed
flow index (b) and nanoparticle volume fraction ( ).
Before starting with the process of evaluating heat transfer
and fluid flow properties, it would be helpful to mention here
that the base fluid includes ethylene glycol, water and crude
oil and fixes the numerical values pertaining to the Prandtl
Number (Pr). Moreover, we need to consider the thermos-
physical characteristics of nanoparticles and fluids, which are
listed in table 1. For the details parameter using
water , ethylene
glycol using
and crude oil
using .
Figure 3 shows the effect cast by squeezed flow index b on
temperature profile, which shows that if there is an increase
in the squeezed flow, the temperature parameter for (water,
ethylene glycol and crude oil)-nanoparticles is compelled to
reduce because of increasing phenomena and causes
improvement in the fluid particles’ kinetic energy. This
implies that an inverse correlation exists between the squeeze
flow index and the strength of squeeze flow, which results in
reduced velocity profile. Furthermore, the largest thermal
boundary layer was found for water–ethylene glycol
nanoparticles when compared with crude oil–nanoparticle,
which implies that the crude oil is turning cooler.
Fig. 3 shows increased temperature distribution due to the
effect of permeable velocity parameter . This results in
increased thermal boundary layer thickness as presented in
fig. 3 (a) water–( ) and fig. 4 (b) Ethylene
glycol–( ), which is restricted in fig. 4 (c)
crude oil–( ). At the surface for negative
values, suction conditions make the flow more attached
towards the surface versus in blowing conditions, where
suction conditions are archived should the sensor’s surface
oppose the disturbed boundary. Finally, as the Prandtl number
increases, cooling improvement for the sensor (micro
cantilever) turns bunchy as presented in figures 2(c), 3(c),
4(c), 5(c), 6(c), 7(c) for crude oil.
Fig. 4 displays the impact of nanoparticle volume fraction,
which results in decreased temperature as presented in Fig. 4
(c) crude oil – ( ) and Fig. 4 (a) water –
( ). In in Fig. 4 (a, b, c), Water, Ethylene
glycol, crude oil displays two behaviors, first a decrease and
then increase until convergence. Dominance is maintained by
the nanoparticle volume fraction in the heat transfer rate.
Table 2 showed that the effect of nanoparticle volume fraction
on the rate of skin friction in water – ( ),
oil crude – ( ) and ethylene glycol –
( ).

I J E N S
Fig. 5, Fig. 6, Fig. 7 specifies the impact of squeezed flow,
permeable velocity and nanoparticle volume fraction
parameters respectively on the rate of heat transfer
(Nusselt number). Fig.5 (a, b, c) show reduced the heat
transfer with increase squeezed flow parameter is such that
Water, Ethylene glycol, crude oil with SWCNTs was higher
transfer of heat than others with b = 0.1. Fig. 6 indicates the
effect of permeable velocity parameter on the rate of heat
transfer (Nusselt number). Which shows is increasing
of transfer of heat since permeable velocity increase. Fig. 7 (a,
b, c) showed increased nanoparticle volume fraction that
resulted in decrease in heat transfer temperature for all
material, such that we select various quantities of
nanoparticle with ethylene glycol, water and crude oil.
Fig. 8 shows the effect of nanoparticle volume fraction on the
rate of skin friction . The figure shows that ethylene
glycol-SWCNT was lower skin friction and water-Cu is
higher, is such that . Fig. 9 shows the comparison
effect of squeezed flow impact on temperature dimensionless
between water and water with nanoparticle. Fig. 9 show the
reduced temperature with water include nanoparticle.
Fig.2 (a) Fig.2 (b) Fig.2 (c)
Fig. 2. the impact index of the squeezed flow on temperature profiles (a) water- ( ); (b) Ethylene glycol-( ); (c)
Crude oil – ( ).
Fig. 3 (a) Fig. 3 (b) Fig. 3 (c)
Fig. 3. the effect of the permeable velocity on temperature profile (a) water- ( ); (b) Ethylene glycol-( ); (c) Crude oil
– ( ).

I J E N S
Fig. 4 (a) Fig. 4 (b) Fig. 4 (c)
Fig. 4. the effect of nanoparticle volume fraction on temperature profiles (a) water- ( ); (b) Ethylene glycol-( ); (c)
crude oil – ( ).
Fig. 5 (a) Fig. 5 (b) Fig. 5 (c)
Fig. 5 the effect of squeezed flow index on Nusselt number (the heat transfer) profiles (a) water- ( ); (b) Ethylene glycol-
( ); (c) Crude oil – ( ).
Fig. 6 (a) Fig. 6 (b) Fig. 6 (c)
Fig. 6. the effect of the permeable velocity on Nusselt number (the heat transfer) profiles (a) water- ( ); (b) Ethylene glycol-
( ); (c) Crude oil – ( ).

I J E N S
Fig. 7 (a) Fig. 7 (b) Fig. 7 (c)
Fig. 7 the effect of the permeable velocity on Nusselt number (the heat transfer) profiles (a) water- ( ); (b) Ethylene glycol-
( ); (c) Crude oil – ( )
Table 1
Thermo-physical properties of base fluid and nanoparticles Rizwan Haq[3], R. Kandasamy[34]
water Ethylene glycol Crude oil Cu SWCNT
997.1 1115 870 8933 3970 2600
4179 2430 1988 385 765 42.5
0.613 0.253 120 401 40 6600
5.5 1.07 0.9 59.6 16.7 1.26
Prantle No. 6.82 203.63 1490.51
Table II
Various nanoparticle volume fraction impact on the rate of skin friction.
0.05 0.1 0.2
Water – Al2O3 1.151639 1.144477 1.097925
Ethylene glycol -
Al2O3
1.141607 1.126756 1.130566
Crude oil - Al2O3 1.143762 1.132945 1.135715
Water – Cu 1.263363 1.333812 1.379892
Ethylene glycol - Cu 1.242998 1.300262 1.331607
Crude oil Cu 1.218846 1.262014 1.285815
Water – SWCNT 1.118519 1.085430 1.003961
Ethylene - SWCNT 1.111738 1.073139 1.003961
Crude oil - SWCNT 1.122060 1.094349 1.045750
Table III
comparison the rate of skin friction between present work and Rizwan et al. [3], for zero nanoparticle volume fraction with squeeze flow, zero
magnetic field M and various permeable velocity parameter .
Rizwan et al. [3] Present work
0.0 - 0.5 1 0.5 1.48113 1.48113 1.48113 1.48117 1.48117 1.48117
0.5 1 0.86652 0.86652 0.86652 0.86677 0.86677 0.86677
0.5 0.0 1.16223 1.16223 1.16223 1.16238 1.16238 1.16238

I J E N S
Fig. 8. the effect of nanoparticle volume fraction with the rate of skin friction on different nanofluids
Fig. 9. Temperature drop comparison between water with and without nanoparticle on various squeezed flow parameter (b)
V. CONCLUSION
We investigate two-dimensional squeezed flow of variable
thermal conductivity in the Carreau flow nanofluids model.
This research work is helpful in various applications,
including science and engineering, to improve the heat
transfer along with comparison of three materials: ethylene
glycol, water and crude oil. And such that using three
nanoparticles oxide aluminum , copper , single
walled carbon nanotubes
 The temperature dimensionless was dropped and
dominated with the squeezed flow parameter and
nanoparticle volume fraction parameter. That is for
all nanomaterials.
 The effect of permeable velocity parameter was
increasing the temperature dimensionless in in all
nonofluids.
 Ethylene glycol-SWCNT was lower skin friction
and water-Cu is higher with high
nanoparticle volume fraction.
 For the rate of heat transfer (Nusselt
number) was higher in:
a) Ethylene glycol- SWCNT with high
permeable velocity parameter 0.2.
b) Ethylene glycol- SWCNT with low squeeze
flow parameter 0.1.
c) Ethylene glycol- oxide aluminium with low
nanoparticle volume fraction 0.05.
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I J E N S
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