NUMERICAL INVESTIGATION OF NATURAL CONVECTION HEAT TRANSFER FROM CIRCULAR CYLINDER INSIDE AN ENCLOSURE USING DIFFERENT TYPES OF NANOFLUIDS

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 5, May (2014), pp. 214-236 © IAEME
214
NUMERICAL INVESTIGATION OF NATURAL CONVECTION HEAT
TRANSFER FROM CIRCULAR CYLINDER INSIDE AN ENCLOSURE
USING DIFFERENT TYPES OF NANOFLUIDS
1
Omar Mohammed Ali, 2
Ghalib Younis Kahwaji
1
Department of Refrigeration and Air Conditioning, Zakho Technical Institute, Zakho, Iraq
2
Mechanical Department, RIT Institute, Dubai, UAE
ABSTRACT
In the present work, the enhancement of natural convection heat transfer utilizing nanofluids
as working fluid from horizontal circular cylinder situated in a square enclosure is investigated
numerically. Different types of nanoparticles were tested. The types of the nanofluids are Cu, Al2O3
and TiO3 with water as base fluid. A model is developed to analyze heat transfer performance of
nanofluids inside an enclosure taking into account the solid particle dispersionrs on the flow and heat
transfer characteristics. The study uses different Raylieh numbers (104
, 105
, and 106
), the enclosure
width to cylinder diameter ratio W/D is 2.5 and volume fraction of nanofluids is between 0 to 0.2.
The work included the solution of the governing equations in the vorticity-stream function
formulation which were transformed into body fitted coordinate system. The transformations are
based initially on algebraic grid generation, then using elliptic grid generation to map the physical
domain between the heated horizontal cylinder and the enclosure into a computational domain. The
disecritization equation system are solved by using finite difference method. The code build using
Fortran 90 to execute the numerical algorithm.
The results display the comparisons between different types of the nanofluids based on the
effect of Raylieh number, and volume fractions on the thermal and hydrodynamic characteristics.
The results were compared with previous numerical results, which showed good agreement. For all
types of the nanofluids, the Nusselt number increases with increasing the volume fraction of the
nanofluids. The results show that the streamlines change with changing the type of the nanofluid,
while the isotherms remain unchanged. The Nusselt number of Cu nanofluids is more than the those
for other types of the nanofluids.
KEYWORDS: Circular Cylinder, Heat Transfer, Nanofluids, Numerical, Square Enclosure.
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING
AND TECHNOLOGY (IJMET)
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 5, Issue 5, May (2014), pp. 214-236
© IAEME: www.iaeme.com/ijmet.asp
Journal Impact Factor (2014): 7.5377 (Calculated by GISI)
www.jifactor.com
IJMET
© I A E M E

215
NOMENCLATURE
Symbol Definition Unit
Nu Average Nusselt number, (h.D/k).
D Cylinder diameter. m
di,j Source term in the general equation, eqn. (18).
H Convective heat transfer coefficient. W/m2
.°C
J Jacobian.
K Thermal conductivity of the air. W/m.°C
P Pressure. N/m2
P Coordinate control function.
Pr Prandtl number, (ν/α).
Q Coordinate control function.
R maximum absolute residual value.
Ra Raylieh number, (gβ∆TD3
/να).
T Time. Seconds
T Temperature. °C
u Velocity in x-direction. m/s
v Velocity in y-direction. m/s
W Enclosure Width. Cm
W Relaxation factor.
x Horizontal direction in physical domain. m
X
Dimensionless horizontal direction in physical
domain.
Y Vertical direction in physical domain. m
Y Dimensionless vertical direction in physical domain.
Greek Symbols
∆T
Difference between cylinder surface temperature and
environmental temperature.
°C
µ Viscosity of the air. kg/m.s
β Coefficient of thermal expansion. 1/°C
η Vertical direction in computational domain.
ξ Horizontal direction in computational domain.
α Fluid thermal diffusivity m2
/s
Ψ Dimensionless stream function.
ω Vorticity. 1/s
ϖ Dimensionless vorticity.
υ Kinematic viscosity. m2
/s
θ Dimensionless temperature.
φ Dependent variable.
ϕ Volume fraction of nanofluid
ψ Stream Function. 1/sec.
Subscript
nf Nanofluid
p Particle
S Cylinder surface.
∞ Environment.
X Derivative in x-direction.

216
Y Derivative in y-direction.
ξ Derivative in ξ-direction.
D Circular cylinder diameter.
ψ Stream function.
T Temperature.
ω Vorticity
I. INTRODUCTION
Laminar buoyancy-driven convection in enclosed cylinders has long been a subject of interest
due to their wide applications such as in solar collector-receivers, cooling of electronic equipment,
aircraft cabin insulation, thermal storage system, and cooling systems in nuclear reactors, etc, Ali,
[1].
Nanofluids are relatively new class of fluids which consist of a base fluid with nano-sized
particles (1–100 nm) suspended within them. In order to improve the performance of engineered heat
transfer fluids, dispersion of highly-conductive nano-sized particles (e.g., metal, metal oxide, and
carbon materials) into the base liquids has become a promising approach since the pioneering
investigation by Choi [2]. Laminar steady-state natural convection of nanofluids in confined regions,
such as square/rectangular cavities, horizontal annuli and triangular enclosures, has been studied for
a variety of combinations of base liquids and nanoparticles [3]. It is noted that in most of the
numerical efforts the nanofluids were considered as a single phase such that the presence of
nanoparticles only plays a role in modifying the macroscopic thermophysical properties of the base
liquids. Therefore, a large number of studies have been dedicated to reveal the mechanisms of
thermophysical properties modification of nanofluids. Most of cooling or heating devices have low
efficiency because the working fluids have the low thermal conductivity. Many experiments have
been carried out in the past which showed tremendous increase in thermal conductivity with addition
of small amount of nanoparticles. However, very few mathematical and computational models have
been proposed to predict the natural convection heat transfer.
Ternik et., al. [4], performed numerical analysis to investigate the natural convection heat
transfer enhancement of Au, Al2O3, Cu and TiO3 water based nanofluids in an enclosure. The
Raylieh number range 103
≤Ra≤105
, and the nanofluid's volume fraction range is 0≤ϕ≤0.1. The
results indicate that the average Nusselt number is an increasing function of Raylieh number and
volume fraction of nanoparticles. The results display that low Raylieh numbers show more
enhancement compared to high Raylieh numbers.
Hakan, et. al. [6], studied heat transfer and fluid flow due to buoyancy forces in a partially
heated enclosure using different types of nanoparticles. They used a flush mounted heater. The
temperature of the right vertical wall is lower than that of heater while other walls are insulated. The
finite volume technique is used to solve the governing equations. Calculations were performed for
Rayleigh number(103 ≤ Ra ≤ 5×105), height of heater (0.1 ≤ h ≤ 0.75), location of heater (0.25 ≤ yp
≤ 0.75), aspect ratio (0.5 ≤ A ≤ 2) and volume fraction of nanoparticles (0 ≤ ϕ ≤ 0.2). Different types
of nanoparticles were tested (water as base fluid with nanoparticles Cu, Al2O3, and TiO3). An
increase in mean Nusselt number was found with the volume fraction of nanoparticles for the whole
range of Rayleigh number. It was found that the heat transfer enhancement, using nanofluids, is more
pronounced at low aspect ratio than at high aspect ratio. The increase in Nusselt number for Cu is
more than other nanofluids.
The present work deals with numerical investigation natural convection heat transfer using
different types of nanofluids from circular horizontal cylinder situated in an enclosed square
enclosure. The study uses different Raylieh numbers and different volume fraction of nanoparticles.

217
The work performed the comparison between three types of the nanofluids based on the flow and
heat transfer characteristics of the nanofluids.
II. MATHEMATICAL FORMLATION
The schematic diagram in figure (1), display the flow between the heated horizontal cylinder
and the enclosure. The different types of the nanofluids in the enclosure is a water based nanofluid
containing either Cu, Al2O3 or TiO3. The governing equations of the flow based on the assumptions
that the nanofluid is incompressible, and the flow is laminar no internal heat sources, and two-
dimensional. It is assumed that the base fluid (water) and the nanoparticles are in thermal equilibrium
and no slip occurs between them. The thermophysical properties are given in table (1).The
thermophysical properties of the nanofluids are assumed to be constant and the flow is Boussinesq,
Hakan et. al. [6].
Figure 1: Configuration of cylinder-enclosure combination
Table 1: Thermophysical properties of fluid and nanoparticles, Hakan, et. al.[6]
Physical Properties
Fluid phase
(water)
Cu
Al2O3 TiO3
Cp (J/kg.°K) 4197 385 765 686.2
ρ (kg/m3
) 997.1 8933 3970 4250
k (W/m.°K) 0.613 400 40 8.9538
α×107
(m2
/sec) 1.47 1163.1 131.7 30.7
β×10-5
(m2
/sec) 21 1.67 0.85 0.9
W
T∞
Te
W
Ts

218
The governing equations include the equation of continuity, momentum and the energy
equation, Hakan, et. al. [6]. These equations are presented below:
0=
∂
∂
+
∂
∂
y
v
x
u
(1)
The x –momentum equation is:
( )
Tgg
y
u
x
u
x
p
y
u
v
x
u
u
t
u
nf
nf
nf
nf
∆+








∂
∂
+
∂
∂
+
∂
∂
−=
∂
∂
+
∂
∂
+
∂
∂
ρ
βρ
ν
ρ
&
2
2
2
2
1
(2)
The y –momentum equation is:
( )
Tgg
y
v
x
v
x
p
y
v
v
x
v
u
t
v
nf
nf
nf
nf
∆+








∂
∂
+
∂
∂
+
∂
∂
−=
∂
∂
+
∂
∂
+
∂
∂
ρ
βρ
ν
ρ
&
2
2
2
2
1
(3)
The energy equation is:








∂
∂
+
∂
∂
=
∂
∂
+
∂
∂
+
∂
∂
2
2
2
2
y
T
x
T
y
T
v
x
T
u
t
T
nfα (4)
With Boussinesq approximations, the density is constant for all terms in the governing
equations except for the buoyancy force term that the density is a linear function of the temperature.
( )To ∆−= βρρ &1 (5)
Where β is the coefficient of thermal expansion.
The stream function (ψ) and vorticity (ω) in the governing equations are defined as follows,
Anderson [7], and Petrovic [8]:
x
v
y
u
∂
∂
−=
∂
∂
=
ψψ
, (6)
y
u
x
v
∂
∂
−
∂
∂
=ω (7)
Or V
r
×∇=ω
The governing equations for laminar flow become:

219
Energy Equation:






∂
∂
∂
∂
+





∂
∂
∂
∂
=
∂
∂
∂
Ψ∂
−
∂
∂
∂
Ψ∂
+
∂
∂
yyxxyxxyt
θ
λ
θ
λ
θθθ
(8)
Momentum Equation:
( ) ( )
( )
( )
x
Ra
yx
yxxyt
s
f
f
s
s
f
f
s
∂
∂


















+
−
+
+
−
+







∂
∂
+
∂
∂






















+−−
=
∂
∂
∂
Ψ∂
−
∂
∂
∂
Ψ∂
+
∂
∂
θ
ρ
ρ
ϕ
ϕ
β
β
ρ
ρ
ϕ
ϕ
ϖϖ
ρ
ρ
ϕϕϕ
ϖϖϖ
1
1
1
1
1
1
Pr
11
Pr
2
2
2
2
25.0
(9)
Continuity Equation:
ϖ−=
∂
Ψ∂
+
∂
Ψ∂
2
2
2
2
yx
(10)
Where
λ ൌ
ೖ೙೑
ೖ೑
ሺଵିఝሻାఝ
൫ഐ಴ು൯ೞ
൫ഐ಴ು൯೑
(11)
ߙ௡௙ ൌ
௞೐೑೑
ሺఘ஼ುሻ೙೑
(12)
The effective density of the nanofluid is given as
ߩ௡௙ ൌ ሺ1 െ ߮ሻߩ௙ ൅ ߮ߩ௦ (13)
The heat capacitance of the nanofluid is expressed as:
ሺߩ‫ܥ‬௉ሻ௡௙ ൌ ሺ1 െ ߮ሻሺߩ‫ܥ‬௉ሻ௙ ൅ ߮ሺߩ‫ܥ‬௉ሻ௦ (14)
It is assumed the shape of the nanofluids is spherical, therefore, the effective thermal
conductivity of the nanofluid is approximated by the Maxwell–Garnetts model:
௞೙೑
௞೑
ൌ
௞ೞାଶ௞೑ିଶఝ൫௞೑ି௞ೞ൯
௞ೞାଶ௞೑ାఝ൫௞೑ି௞ೞ൯
(15)
The viscosity of the nanofluid can be approximated as viscosity of a base fluid lf containing
dilute suspension of fine spherical particles and is given by Brinkman [9]:

220
ߤ௡௙ ൌ
ఓ೑
ሺଵିఝሻమ.ఱ (16)
In the stream function-vorticity formulation, there is a reduction in the number of equations
to be solved in the ψ-ω formulation, and the troublesome pressure terms are eliminated in the ψ-ω
approach.
The dimensionless variables in the above equations are defined as:
D
x
X = ,
D
y
Y = ,
f
uD
U
α
= ,
f
vD
V
α
= ,
2
D
t fα
τ = ,
fα
ψ
=Ψ ,
f
D
α
ω
ϖ
2
= ,
∞
∞
Τ−Τ
Τ−Τ
=
c
θ (17)
The cylinder diameter D is the characteristic length in the problem. By using the above
parameters, the governing equations (8)-(10) transformed to the following general form in the
computational space:
(18)
Where φ is any dependent variable.
The governing equations represented by interchanging the dependent variable φ for three
governing equations as follow
φ
bφ dφ
1 ω
( ) ( ) 







+−−
f
s
ρ
ρ
ϕϕϕ 11
Pr
25.0 ( )
( )
( ) ( )[ ]ηξξη θθ
ρ
ρ
ϕ
ϕβ
β
ρ
ρ
ϕ
ϕ
yyRa
s
ff
s
s
f
−












+
−
+
+
−
1
1
1
1
1
1
Pr
λ 0
t∂
∂φ
represents the unsteady term.














∂
∂
−





∂
∂
ηξ
φ
ξ
ψ
φ
η
ψ
J
1
is the convective term.
( )φφ∇∇ b is the diffusion term.
In addition, φd is the source term.
( ) φφ
ηξ
φ φφ
ξ
ψ
φ
η
ψφ
db
Jt
a +∇∇=






















∂
∂
−





∂
∂
+
∂
∂ 1

221
2.1 Grid Generation
The algebraic grid generation method is used to generate an initial computational grid points.
The elliptic partial differential equations that used are Poisson equations:
( )ηξξξ ,Pyyxx =+ (19a)
( )ηξηη ,Qyyxx =+ (19b)
Interchanging dependent and independent variables for equations (19a, and b), gives:
( ) 0
2
2
=+
++−
ηξ
ηηξηξξ γβα
xQxPJ
xxx
(20a)
( ) 0
2
2
=+
++−
ηξ
ηηξηξξ γβα
yQyPJ
yyy
(20b)
Where 22
ηηα yx += ; ηξηξβ yyxx += ;
22
ξξγ yx +=
The coordinate control functions P and Q may be chosen to influence the structure of the grid,
Thomas et. al. [10]. The solution of Poisson equation and Laplace equation are obtained using
Successive over Relaxation (SOR) method with relaxation factor value equal to 1.4, Hoffman [11]
and Thompson [12].
The transformation of the physical domain into computational domain using elliptic grid
generation is shown in figure (2).
Figure (2) Transformations of the physical domains into computational domains using elliptic grid
generation
2.2 Method Of Solution
In the present study, the conversion of the governing integro-differential equations into
algebraic equations, amenable to solution by a digital computer, is achieved by the use of a Finite
Volume based Finite Difference method, Ferziger [13].

222
To avoid the instability of the central differencing scheme (second order for convective term) at
high Peclet number (Cell Reynolds Number) and an inaccuracy of the upwind differencing scheme
(first order for convective term) the hybrid scheme is used. The method is hybrid of the central
differencing scheme and the upwind differencing scheme.
( ) jijijijijiM
o
P
o
PSSNNWWEEPP
da
aaaaaa
,1,11,11,11,1 ++−−
+++++=
+−−+−−++ φφφφ
φφφφφφ
(21)
o
PSNWEP aaaaaa ++++= (22)
The resulting algebraic equation is solved using alternating direction method ADI in two
sweeps; the first sweep, the equations are solved implicitly in ξ-direction and explicitly in η-
direction. The second sweep, the equations are solved implicitly in η-direction and explicit in ξ-
direction. In first sweep, the implicit discretization equation in ξ-direction is solved by using Cyclic
TriDiagonal Matrix Algorithm (CTDMA) because of its cyclic boundary conditions. In second
sweep, the implicit discretization equation in η-direction is solved by using TriDiagonal Matrix
Algorithm (TDMA).
The solution of the stream function equation was obtained using Successive Over-Relaxation
method (SOR).
The initial conditions of the flow between heated cylinder and vented enclosure are:
Ψ=0, θ = 0, ω = 0 For t = 0 (23)
The temperature boundary condition of the cylinder surface assumed as constant.
0=
∂
∂
m
η
θ
at enclosure wall (24a)
Using 2nd
order difference equation, the temperature at the enclosure surface becomes:
2,1,,
3
1
3
4
−− −= mimimi θθθ (24b)
Vorticity boundary conditions, Roache [14], are
( )1,,2
2
−−= mimi
J
ψψ
γ
ϖ at enclosure wall (25a)
( )2,1,2
2
ii
J
ψψ
γ
ϖ −= at cylinder surface (25b)
The stream function of the cylinder is assumed as zero because the cylinder is a continuous
solid surface and no matter enters into it or leaves from it. The stream function of the enclosure is
assumed as constant.

223
The Nusselt number Nu is a nondimensional heat transfer coefficient that calculated in the
following manner:
fk
hD
Nu =
(27)
The heat transfer coefficient is expressed as
h ൌ
୯౭
୘ౄି୘ై
(28)
The thermal conductivity is expressed as
k୬୤ ൌ െ
୯౭
பθ ப୬⁄
(29)
By substituting Eqs. (24), (25), and (7) into Eq. (23), and using the dimensionless quantities, the
Nusselt number on the left wall is written as:
ζ
θπ
∂
∂
∂
−= ∫
2
0
nk
k
Nu
f
nf
(30a)
The derivative of the nondimensional temperature is calculated using the following formula,
Fletcher [15] :
( ) η
θγ
γθβθ
γ
θ
ηξ
η ∂
∂
=+−=
∂
∂
= JJn const
1
.
(30b)
θξ = 0 at cylinder surface
A computer program in (Fortran 90) was built to execute the numerical algorithm which is
mentioned above; it is general for a natural convection from heated cylinder situated in an enclosure.
III. RESULTS AND DISCUSSION
In the present study, the numerical work deals with natural convection heat transfer utilizing
nanofluids as working fluid from circular horizontal cylinder when housed in an enclosed square
enclosure. The Prandtl number is taken as 6.2. The cases for three different enclosure width to
cylinder diameter ratios W/D =1.67, 2.5 and 5, Rayleigh numbers of 104
, 105
, and 106
, and volume
fractions of nanofluid ϕ are 0, 0.05, 0.1, 0.15 and 0.2 were studied.
After numerical discretization by the Hybrid method, the resultant algebraic equations are
solved by the ADI method. The convergence criteria are chosen as RT<10-6
, Rψ<10-6
and Rω<10-6
for
T, ψ and ω respectively. When all the three criteria are satisfied, the convergent results are
subsequently obtained.
Stability and Grid Independency Study
The stability of the numerical method is investigated for the case Ra=105
, W/D=2.5, Pr=0.7.
Three time steps are chosen with values 1×10-4
, 5×10-4
, 5×10-6
. The maximum difference between
the values of Nu with different time steps is 2%. The grid-independence of numerical results is

224
studied for the case with Ra=104
, and 105
, W/D =2.5, Pr = 6.2. The three mesh sizes of 96×25,
128×45, and 192×50 are used to do grid-independence study. It is noted that the total number of grid
points for the above three mesh sizes is 2425, 5805, and 9650 respectively. Numerical experiments
showed that when the mesh size is above 96×45, the computed Nu remain the same. The same
accuracy is not obtainable with W/D=5 and high Raylieh numbers, therefore; the mesh size 128×45
is used in the present study for all cases.
Validation Test
The code build using Fortran 90 to execute the numerical algorithm. To test the code
validation, the natural convection problem for a low temperature outer square enclosure and high
temperature inner circular cylinder was tested. The calculations of average Nusselt numbers and
maximum stream function ψmax for the test case are compared with the benchmarks values by
Moukalled and Acharya [16], for Prandtl number Pr=0.7, different values of the enclosure width to
cylinder diameter ratios (W/D=1.667, 2.5, and 5) with Rayleigh numbers Ra=104
and 105
as given in
table (2). From table 2, it can be seen that the present results generally agree well with those of
Moukalled and Acharya [16].
Table 2: Comparisons of Nusselt numbers and maximum stream function
L/D Ra
ψmax ܰ‫ݑ‬തതതത
Present
Moukalled and
Acharya [16]
Present
Moukalled and
Acharya [16]
5.0
104
2.45 2.08 1.7427 1.71
2.5 3.182 3.24 0.9584 0.97
1.67 5.22 5.4 0.4274 0.49
5.0
105
10.10 10.15 3.889 3.825
2.5 8.176 8.38 4.93 5.08
1.67 4.8644 5.10 6.23 6.212
Flow Patterns and Isotherms
The numerical solutions for four volume fraction of nanofluids ϕ were obtained. The volume
fraction values are: ϕ = 0.05, 0.1, 0.15, and 0.2 will be presented herein. Figure (3) shows a
comparison of streamlines and isotherms between Cu-water nanofluid (ϕ=0.1) and pure fluid (ϕ=0)
for W/D=2.5 with Raylieh number values Ra=104
, 105
, and 106
. At Ra=104
and 105
, the isotherms for
two cases are similar. There are some differences in isotherms between two cases for Ra =106
. The
disagreement appear at the upper region of the isotherms above the circular cylinder. The plumes for
pure fluid appear as more flat than those for ϕ=0.1. The streamlines are different between two cases.
The difference becomes more as Raylieh number increases. At Ra=104
, the conduction is the
dominant heat transfer, therefore, the disagreement between the two cases is very small. The flow
circulation for ϕ=0.1 is more than those for pure fluid. The maximum stream function value
ψmax=1.75 for ϕ=0.1 as compared with those for pure fluid ψmax=0.96. As Raylieh number increases
to Ra=105
, the flow circulation becomes more and the disagreement between two cases increases.
The general aspects of the flow patterns are similar except that a single small kernel eddy appears
rather than the dual kernel eddies for Ra=104
for pure fluid. The size of the kernel eddy increases for
ϕ=0.1 and the flow circulation is more than those for pure fluid. The maximum stream function value
ψmax=13.68 for ϕ=0.1, while; the maximum stream function value ψmax=8.05 for pure fluid. As
Raylieh number increases to Ra=106
, the flow becomes stronger and the maximum stream function

225
increases for two cases. The maximum stream function value ψmax=36.94 for ϕ=0.1, while; the
maximum stream function value ψmax=23.34 for pure fluid. The flow are symmetrical about the
vertical center line. As compared with the streamlines of the pure fluid, the streamlines of the ϕ=0.1
trends to the declination at the upper region of the enclosure and the flow region between the
cylinder and the enclosure becomes more than those for pure fluid, that means the stagnant area
decreases. The size of the kernel eddy becomes less and the densely packed becomes more.
Figure (3): Streamlines (on the left) and Isotherms (on the right) for Cu-water nanofluids (- - -),
pure fluid (___
), W/D=2.5, (a) Ra = 104
, (b) Ra = 105
(c) Ra =106
.
Figures (4-11) display the streamlines and isotherms for W/D= 2.5. The Raylieh number
values are Ra=104
, 105
, and 106
, volume fraction of the nanofluids are: ϕ=0.05, 0.1, 0.15, 0.2, and
the nanofluid types are: Cu, Al2O3, and TiO3 nanofluids with water as base fluid.

226
At ϕ=0.05, the flow patterns for Raylieh numbers Ra=104
, 105
, 106
, and nanofluid types Cu,
Al2O3 and TiO3 are presented in figure (4). The maximum stream function value varies between
Ψmax=1.0744 at Ra=104
and Al2O3 nanofluid type to Ψmax=32.28 at Ra=106
and Cu nanofluid type.
For all Raylieh numbers and types of nanofluids, the flow is symmetrical about the vertical line
through the center of the circular cylinder. For Ra=104
, the maximum stream function value is small
that means the flow circulation is weak. The flow patterns appear as a curved kidney-shaped contain
one kernel eddy. The densely packed of the flow for Cu nanofluid is relatively weak. The densely
package of the flow for Al2O3 and TiO3 nanofluid types becomes more and the flow region area
increases. The flow patterns for those types are nearly similar. Two eddies appear for each side rather
than single eddy for those of Cu nanofluid type. As Raylieh number increases to Ra=105
for Cu
nanofluid type, the flow circulation becomes stronger, it moves upward, the flow region area
becomes less and the densely package of the flow decreases as compared with Ra=104
. A single
large eddy appears. The densely package of the flow for Al2O3 and TiO3 nanofluid types increase, the
flow region area become more and the size of the eddy decreases. The aspects of the flow patterns
for types Al2O3 and TiO3 nanofluid are nearly similar. At Ra=106
, the aspects of the flow patterns
with types Al2O3 and TiO3 nanofluid are nearly similar. The flow circulation becomes stronger and
stronger and the stream function values increase. The flow move upward and the streamlines at the
upper of the enclosure appear as horizontal lines and the size of the eddies increase and appear as
triangular-shaped eddies. The stagnant area enlarges and the flow region area decreases. The flow
patterns of the various types are different. Tiny eddies appear inside the eddies. The single eddy size
for of the Cu nanofluid is larger than those of other types and it appear as longitudinal eddy. The
width of the eddies for Al2O3 nanofluid increase and the length of those decrease.
Figure (4): Effect of volume fraction of nanofluids on streamlines for ϕ=0.05 and (a) Ra = 104
,
(b) Ra = 105
, (c) Ra = 106
Cu Al2O3 TiO3
(c)
(b)
(a)

227
The characteristics of the temperature distributions are presented by means of isotherms in
figures (5, 7, 9, 11). The same arrangements as flow patterns are displayed in the figure with same
volume fraction of nanofluids and Raylieh numbers. The isotherms are symmetrical about the
vertical line through the center of the circular cylinder. The isotherms are similar and independent of
volume fraction of nanofluids and types of the nanofluid for each Raylieh number. At Ra=104
, the
isotherms display as rings around the cylinder. The shape of the isotherms ensure that the mode of
heat transfer is pure conduction and the effect of the convection is very low. At Ra=105
, the
temperature distributions have small distortions around the cylinder due to the effect of the
convection heat transfer. A thermal plume appear on the top of the cylinder. The isotherms appear as
horizontal and flat near the lower enclosure wall with very little distortion in the isotherms at this
region. At Ra=106
, the convection becomes the dominant mode of heat transfer. A thermal plume
impinging on the top of the enclosure. The thermal stratification (horizontal and flat isotherms) are
formed near the bottom region of the enclosure. Two thermal plumes displayed on the top of the
cylinder with about 60° from the vertical center line. It is noted that when the Raylieh number
increases the thermal boundary layer becomes thinner and thinner.
, 105
, 106
Ψmax=1.19 at Ra=104
and Cu nanofluid type. For
Cu Al2O3 TiO3
(c)
(b)
(a)
Figure (5): Effect of volume fraction of nanofluids on isotherms for ϕ=0.05 and (a) Ra = 104
, (b)
Ra = 105
, (c) Ra = 106

228
all Raylieh numbers and types of nanofluids, the flow is symmetrical about the vertical line through
the center of the circular cylinder. For Ra=104
, the flow circulation is weak. The maximum stream
function value is small. The flow patterns appear as a curved kidney-shaped contain two kernel
eddies. The densely packed of the flow for Cu nanofluid type is strong and the flow region area is
large that lead to a decrease in the stagnant area. Two kernel eddies appear for each side for Cu
nanofluids. The aspects of the flow for Al2O3 and TiO3 nanofluid types are similar to Cu nanofluid
type, but the densely package becomes less and the flow region area decreases. The flow patterns for
those types are nearly similar. As Raylieh number increases to Ra=105
for Cu nanofluid type, the
flow moves upward, the flow region area becomes more and the densely package of the flow
decreases as compared with Ra=104
. A single large eddy appears rather than two eddies for those of
Ra=104
. The densely package of the flow for Al2O3 and TiO3 nanofluid types increase, the flow
region area become more and the size of the eddy decreases. The aspects of the flow patterns for
Ra=106
with types Al2O3 and TiO3 nanofluid are nearly similar. The flow circulation becomes
stronger and stronger and the stream function values increase. The flow move upward and the
streamlines at the upper of the enclosure appear as horizontal lines and the eddies extended in the
longitudinal axis. The stagnant area enlarges and the flow region area decreases. The flow patterns of
the various types are different. The single eddy size of the Cu nanofluid is larger than those for other
types and it appear as longitudinal eddy.
,
(b) Ra = 105
, (c) Ra = 106
Cu
Al2O3
TiO3
(c)
(b)
(a)

229
Cu Al2O3 TiO3
,
(b) Ra = 105
, (c) Ra = 106
, 105
, 106
Ψmax=1.3 at Ra=104
and Cu nanofluid type. For all
Raylieh numbers and types of nanofluids, the flow is symmetrical about the vertical line through the
center of the circular cylinder. For Ra=104
, the flow circulation is weak. The maximum stream
function value is small. The flow patterns show that the densely package of the flow is strong. The
streamlines appear as a curved kidney-shaped contain two kernel eddies. The flow region area is
large that lead to a decrease in the stagnant area. The kernel eddies appear for each side for Cu
nanofluids. The aspects of the flow for Al2O3 nanofluid types are similar to Cu nanofluid type, but
the densely package becomes less and the flow region area decreases. The streamlines of the TiO3
becomes less densely package but the flow region area unchanged. Single longitudinal eddy appears
rather than two eddies for Al2O3 and Cu nanofluid types. At Ra=105
for Cu nanofluid type, the flow
circulation becomes more. The flow moves upward, the flow region area becomes less and the
densely package of the flow decreases as compared with Ra=104
. A single large eddy appears rather
than two eddies for those of Ra=104
. The densely package of the flow for Al2O3 and TiO3 nanofluid
types decrease, the flow region area become less and the size of the eddy decreases. As Raylieh
number increases to Ra=106
, the flow circulation becomes stronger and stronger and the stream
function values increase. For Cu nanofluid type, the flow move upward and the streamlines at the
upper of the enclosure appear as nearly horizontal and flat lines near the upper surface of the
enclosure and the eddies extended in the longitudinal axis. Two tiny eddies appear near the vertical
center line at bottom of the enclosure. The flow patterns of the various types are different. For Al2O3
and TiO3 nanofluid types, the flatness becomes more and the densely package of the flow becomes
less. The two tiny eddies disappear. The single eddy size of the Cu nanofluid is larger than those for
other types and it appear as longitudinal eddy. The width of the eddies for Al2O3 nanofluid increase
and the length of those decrease.
(c)
(b)
(a)

230
Cu Al2O3 TiO3
Figure (8): Effect of volume fraction of nanofluids on streamlines for ϕ=0.15 and
(a) Ra = 104
, (b) Ra = 105
, (c) Ra = 106
Cu Al2O3 TiO3
,
(b) Ra = 105
, (c) Ra = 106
.
(c)
(b)
(a)
(c)
(b)
(a)

231
, 105
, and 106
, and nanofluid types
Cu, Al2O3 and TiO3 are presented in figure (10). The maximum stream function value varies between
Ψmax=1.39 at Ra=104
and Al2O3 nanofluid type to Ψmax=47 at Ra=106
and Cu nanofluid type. For all
Raylieh numbers and types of nanofluids, the flow is symmetrical about the vertical line through the
center of the circular cylinder. As volume fraction of the nanofluids increases, the strength of the
flow becomes more and the stream function increases. For Ra=104
, the flow circulation is weak, the
maximum stream function values are small. The flow patterns appear as a curved kidney-shaped
contain single big kernel eddy. The densely packed of the flow for Cu nanofluid is very weak and the
flow region area is small that means the stagnant area enlarged. The aspects of the flow for Al2O3
and TiO3 nanofluid types are similar to Cu nanofluid type, but the densely package becomes more
and the flow region area increases. Two different sized eddies appear for Al2O3 nanofluid type rather
than single eddy fo Cu nanofluids type. The size of the eddies become same for TiO3 nanofluid type.
At Ra=105
for Cu nanofluid type, the flow region area becomes more and the densely package of the
flow becomes more as compared with Ra=104
. A single tiny eddy appears rather than large eddy for
those of Ra=104
. The densely package of the flow for Al2O3 and TiO3 nanofluid types decrease, the
flow region area become less and the size of the eddy increases. As Raylieh number increases to
Ra=106
, the flow moves upward, the densely package of the flow increases. The flow region area
increase near the sides and upper walls of the enclosure, while; it decreases near the upper of the
enclosure surface. The aspects of the flow patterns for Ra=106
with types Al2O3 and TiO3 nanofluid
are nearly similar. The flow circulation becomes stronger and stronger and the stream function
values increase. The flow move upward and the streamlines at the upper of the enclosure appear as
horizontal and flat and the eddies appear as single triangular-shaped eddy. The densely package of
the flow becomes less.
Cu Al2O3 TiO3
,
(b) Ra = 105
, (c) Ra = 106
(c)
(b)
(a)

232
Cu Al2O3 TiO3
, (b) Ra
= 105
, (c) Ra = 106
Figures (4, 6, 8, and 10) show that the strongest flow occurs for Cu nanofluid type and the
weakest flow occurs for Al2O3 nanofluid type for all volume fractions of the nanofluids. The flow
strength becomes more as volume fractions of the nanofluid increases for all types of the nanofluids.
These figures display that the viscosity and thermal conductivity of the nanofluids have an effect on
the behavior of the thermal and flow characterstics.
Overall heat transfer Coefficient and correlations
The average Nusselt number is chosen as the measure to investigate the heat transfer from the
circular cylinder. Figures (12,13), display the effect of using different nanofluid types (Cu, Al2O3 and
TiO3 nanofluid types) on the Nusselt number, and the effect of volume fraction of the nanofluids on
the average Nusselt numbers with Ra=104
, 105
, and 106
for enclosure width to the cylinder ratio
W/D=2.5, with different types of the nanofluids such as Cu, Al2O3 and TiO3 nanofluid types. The
volume fractions of the nanofluids ϕ in the present study are:0, 0.05, 0.1, 0.15, 0.2. The Nusselt
number increases with increasing the volume fraction of the nanofluids ϕ, for all Raylieh numbers
and nanofluid types. The effect of volume fraction of the nanofluids on the Nusselt number for
W/D=2.5 and different types of the nanofluids are shown in figure (12). The enhancement of the
Nusselt number with changing the nanofluids volume fractions increases with increasing Raylieh
number. The maximum enhancement in the Nusselt number when the volume fraction of
nanoparticles is increased from 0 to 0.2, using Ra=104
, is approximately 43% with type Cu
nanofluid, the maximum enhancement is around 48% for Ra= 105
with type Cu nanofluid, whereas
the maximum enhancement is around 46% for Ra= 106
with type Cu nanofluid. Figure (13) shows
the variation of the Nusselt number with volume fraction of the nanofluids using different nanofluid
types. The enhancement in the Nusselt number when the volume fraction of nanoparticles is
(c)
(b)
(a)

233
increased from 0 to 0.2 with Ra=104
, is approximately 43% for Cu nanofluid type, 41% for Al2O3
nanofluid type, 37% for TiO3 nanofluid type. The maximum increase is around 48% for Ra=105
with
Cu nanofluid type, 37.5% for Al2O3 nanofluid type, 35% for TiO3 nanofluid type. The maximum
enhancement is around 46% with Ra=106
for Cu nanofluid type, 38% for Al2O3 nanofluid type, 35%
for TiO3 nanofluid type. This tells that the enhancement in heat transfer for Cu nanofluid type. The
heat transfer increase for Al2O3 is less than those for Cu nanofluid type, but, it is more those for TiO3
nanofluid type. This phenomena occurs because the thermal conductivity of the Cu nanofluid type
play a role in this behavior.
(a)
(b)
(c)
Figure (12): Effect of volume fraction of Nanofluids on the Nusselt number for each
Raylieh number, (a) Cu, (b) Al2O3, (c) TiO3

234
(a)
(b)
(c)
Figure (13): Effect of volume fraction of Nanofluids on the Nusselt number for each nanofluid type,
(a) Ra=104, (b) Ra=105, (c) Ra=106.
CONCLUSIONS
Effect of the presence of the nanofluids on the natural convection heat transfer from circular
horizontal cylinder in a square enclosure was investigated numerically over a fairly wide range of Ra
with taking the effect of nanofluid types. The main conclusions of the present work can be
summarized as follows:

235
1. The numerical results show that the Nusselt number increases with increasing the Raylieh
number for all cases.
2. The flow patterns and isotherms display the effect of Ra, nanofluid type, and volume
fractions of the nanofluids on the thermal and hydrodynamic characteristics.
3. The Conduction is the dominant of the heat transfer at Ra=104
for all cases. The contribution
of the convective heat transfer increases with increasing the Raylieh number.
4. The results show that the isotherms are nearly similar when the volume fraction of
nanoparticles is increased from 0 to 0.2 for each Raylieh number and nanofluid type.
5. The streamlines are asymmetrical when the volume fraction of nanoparticles is increased
from 0 to 0.2 for each Raylieh number and nanofluid type.
6. The results display that the strongest flow occurs for Cu nanofluid type and the weakest flow
occurs for Al2O3 nanofluid type for all volume fractions of the nanofluids.
7. The flow strength becomes more as volume fractions of the nanofluid increases for all types
of the nanofluids
8. The average Nusselt number enhances gradually when the volume fraction of nanoparticles is
increased from 0 to 0.2 for each Raylieh number and nanofluid type.
9. The enhancement of the heat transfer for Cu nanofluid type is more than other types, the heat
transfer enhancement for Al2O3 nanofluid type is the weakest.
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NUMERICAL INVESTIGATION OF NATURAL CONVECTION HEAT TRANSFER FROM CIRCULAR CYLINDER INSIDE AN ENCLOSURE USING DIFFERENT TYPES OF NANOFLUIDS

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NUMERICAL INVESTIGATION OF NATURAL CONVECTION HEAT TRANSFER FROM CIRCULAR CYLINDER INSIDE AN ENCLOSURE USING DIFFERENT TYPES OF NANOFLUIDS