Int'l Conference on Advanced Computational Technologies & Creative Media (ICACTCM’2014) Aug. 14-15, 2014 Pattaya (Thailand)
Laminar Natural Convection in Partially
Heated and Cooled Square Cavity Using
Nanofluid
Alireza Falahat, and Amir Vosough

showed that the maximum heat transfer occurred for the heat
source positioned at the middle of the hot wall. Khanafer et
al.[7] numerically investigated the natural convection heat
transfer of a copper-water nanofluid in a differentially heated
square cavity. They showed that the heat transfer rate increases
with an increase in the nanoparticle volume fraction at any
given Grashof number.\
Natural convection heat transfer in inclined devices has also
been the subject of many studies in the past since rarely is the
earth’s surface aligned with geo-potential lines. Abu-Nada et
al. [8] employed the finite volume method to study the effects
of inclination angle on natural convection in square cavity
filled with Cu-water nanofluids. They investigated the effects
of the Rayleigh number, inclination angle, and the volume
fraction of the nanoparticles on the heat transfer inside the
enclosures. They found that Inclination angle can be a control
parameter for nanofluid filled enclosure and Percentage of heat
transfer enhancement using nanoparticles decreases for higher
Rayleigh numbers. Aminossadati et al. [9] numerically
investigated the flow and temperature fields in an inclined
enclosure simulating an inclined electronic device. They
showed that placing the enclosure at different orientations
significantly affected the heat transfer rate.
The main aim of the this study is to examine the natural
convection heat transfer in a square cavity with constant partial
heating at left vertical wall and partial cooling at the right
vertical wall along with the adiabatic top and bottom walls
filled with the Cu–water nanofluid. A parametric study is
performed and the effects of pertinent parameters, such as
Rayleigh number and the volume fraction of nanoparticles on
the fluid flow and heat transfer inside the cavity investigated.
Abstract— Natural convection flow and heat transfer in partially
heated cavity is studied numerically. A control volume based Finite
volume method is applied to discretize the governing equations while
the SIMPLE algorithm is employed to couple velocity and pressure
fields. The constant partial heating at left vertical wall and partial
cooling at the right vertical wall along with the adiabatic top and
bottom walls of cavity filled with the Cu-water nanofluid. The effects
of volume fraction of nanoparticles and Rayleigh number are
investigated. Results have clearly indicated Heat transfer enhances
with increasing of Rayleigh number and volume fraction of
nanoparticles. Also the rate of increase of the average Nusselt
number with increase in the volume fraction of nanoparticles is
higher for lower Rayleigh number.
Keywords— Natural convection, Finite volume method,
Nanofluid, Cavity.
I. INTRODUCTION
N
convection is found in many engineering
applications such as electronics cooling, heat exchangers,
and energy systems [1,2]. A major limitation against
enhancing the heat transfer in such engineering systems is the
inherently low thermal conductivity of the commonly used
fluids, such as, air, water, and oil. Nanofluids were introduced
in order to circumvent the above limitation [3].
Nanotechnology has been widely used in industry since
materials with sizes of nanometers possess unique physical and
chemical properties. Nano-scale particle added fluids are
called as nanofluid which is firstly utilized by Choi [3]. Some
numerical and experimental studies on nanofluids include
thermal conductivity [4] and convective heat transfer [5].
Studies on natural convection using nanofluids are very
limited and they are related with differentially heated
enclosures. The buoyancy-driven heat transfer in square
cavities filled with air with partially active vertical walls was
studied numerically by Valencia and Frederick [6]. They
considered different relative positions of the active parts of the
walls for the Rayleigh numbers of 103–107. Their results
ATURAL
II. MATHEMATICAL MODELING
Fig.1 displays the schematic diagram and boundary
condition of the two-dimensional square cavity considered in
this study. The cavity with constant partial heating at left
vertical wall and partial cooling at the right vertical wall along
with the adiabatic top and bottom walls is filled with a waterCu nanofluid. The nanofluid is Newtonian, incompressible,
and laminar. The base fluid (water) and the spherical
nanoparticles (Cu) are in thermal equilibrium. The properties
are taken from [7]. The thermophysical properties of the
nanofluid are assumed constant except for the density
Alireza Falahat Department of Mechanics, Mahshahr branch, Islamic
Azad university, Mahshahr, Iran (corresponding author’s phone:
+98 6522358994 ; e-mail: [email protected] ).
Amir Vosough, Department of Mechanics, Mahshahr branch, Islamic
Azad university,Mahshahr,Iran(e-mail:[email protected]).
http://dx.doi.org/10.15242/IIE.E0814514
63
Int'l Conference on Advanced Computational Technologies & Creative Media (ICACTCM’2014) Aug. 14-15, 2014 Pattaya (Thailand)
variation, which is determined based on the Boussinesq
approximation.
(5)
1
2

Nu  Nu(Y ) dY
0
Nu, a 
Nu( )
Nu(  0)
(6)
The validation of the adopted results has already conducted
by authors which is available in Table I.
TABLE I
VALIDATION OF THE PRESENT WORK AGAINST WITH FUSESEGI ET AL [2]
Rayleigh
number
1000
Fig. 1 Schematic diagram of cavity
III. GOVERNING EQUATIONS
The continuity, momentum, and energy equations for the
laminar and steady state natural convection in the twodimensional inclined cavity can be written in dimensional form
as follows.
(1)
u v

0
x y
(2)
  2 u  2 u 
u
u
1  p


u
v







nf 
2
x
y  nf  x
y 2 
 x
(3)
 p
  2v  2v  
  nf  2  2   
v
v
1 
u v 
y  
 y
 x
x
y  nf 

(  ) nf g (T  Tc )

(4)
  2T  2 T 
T
T
u
v
  nf  2  2 
x
y
y 
 x
FUSESEGI ET AL [2]
1.103
1.105
10000
2.242
2.302
100000
4.721
4.646
1000000
9.345
9.012
IV. RESULTS
Fig. 2 shows the variation of average Nusselt number
volume fraction of nanofluid and Rayleigh number. Average
Nusselt number is increased with increasing of volume fraction
of nanofluid Rayleigh number. Fig. 3 shows the influence of
the Rayleigh number and the nanoparticles volume fraction on
the augmentation average Nusselt number along the heated
surface of the cavity. It is clearly observed that the addition of
nanoparticles causes the values of augmentation average
Nusselt number to increase and the rate of increment depends
on the value of the Rayleigh number. Also, the percentage of
heat transfer enhancement decreases with increasing of
Rayleigh number for all nanoparticles volume fraction. For
example, at Ra  105 , the addition of 5% nanoparticles by
volume, augmentation average Nusselt number enhance about
59% but for Ra  103 enhance about 69% .
Fig. 4 and Fig. 5 present the horizontal and vertical velocity
profiles along the mid-section of the square cavity at different
Rayleigh number. The velocity shows a parabolic variation
near the isothermal walls and near the adiabatic walls. The
horizontal and vertical velocity is sensitive to the Rayleigh
number. With increasing of Rayleigh number, the horizontal
and vertical velocity increase. Also by adding the
nanoparticles into the fluid is associated with random motion
through the fluid which in turn results in higher velocity for the
nanofluid. The velocity profile gives idea on flow rotation
direction.
where u and v are the velocity components in the x and y
directions,
respectively. p is the pressure, T is the
temperature,  is the volume fraction of the nanoparticles and
β is the thermal expansion coefficient. The thermo-physical
properties of the nanofluid are taken from relations in [7].
The governing equations, Eqs.(1)-(4), and the associated
boundary conditions are solved numerically using the finite
volume method on uniform grid system [10]. The SIMPLE
algorithm is used to couple the pressure and velocity terms.
Discretization of the momentum and energy equations is
performed by a second order upwind scheme and pressure
interpolation is provided by PRESTO scheme [11].
The average Nusselt number (Nu) is determined by
integrating Nu along the hot wall. To estimate the
enhancement of heat transfer between pure fluid and nanofluid,
a augmentation average Nusselt number is defined as the ratio
of Nusselt number at any volume fraction of nanoparticles to
that of pure Water that is:
http://dx.doi.org/10.15242/IIE.E0814514
Present Work
64
Int'l Conference on Advanced Computational Technologies & Creative Media (ICACTCM’2014) Aug. 14-15, 2014 Pattaya (Thailand)
Fig. 5 Variation of of X-velocity at the midsection of for different
Rayleigh number and φ=10%
Fig. 2 Variation of y-velocity at the midsection of cavity for
different Rayleigh number
V. CONCLUSION
In this present paper the influence of volume fraction of nanoparticle and
Rayleigh number for a square cavity filled with the Cu-water nanofluid was
investigated numerically using finite volume method. The results of the
numerical analysis lead to the following conclusions.
Results have clearly indicated Heat transfer enhances with increasing of
Rayleigh number. At all Rayleigh numbers considered, the average Nusselt
number increases when the solid volume fraction of the nanofluid increase.
The rate of increase of the average Nusselt number with increase in the
volume fraction of nanoparticles is higher for cavity with lower Rayleigh
number. This mean that the addition of nanoparticles causes the values of
augmentation average Nusselt number to increase and the rate of increment
depends on the value of the Rayleigh number.
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Fig. 3 Variation of the augmentation averaged Nusselt number
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Fig. 4 Variation of of Y-velocity at the midsection of for different
Rayleigh number and φ=10%
[8]
[9]
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Int'l Conference on Advanced Computational Technologies & Creative Media (ICACTCM’2014) Aug. 14-15, 2014 Pattaya (Thailand)
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