ArticlePDF Available

Abstract and Figures

An extensive numerical study is conducted to determine cross flow of air (Pr=0.71) around isothermal cylinders of circular cross section in arrangements such as single cylinder, inline arrays and staggered arrays. Commercial software package FLUENT is used to solve the fluid flow and energy equations assuming the flow over the cylinder is two dimensional, steady, viscous and incompressible bounded in a duct, as low Reynolds number is being investigated. The width of the duct is kept 20 times the diameter of the cylinder so that the effects of channel blockage can be avoided. The effects of radiation are also neglected in this study. Variations in properties such as local Nusselt number, average Nusselt number, local pressure coefficient and local skin friction coefficient are presented around the cylinders at Reynolds number ranging from 40 to 10,000. The results are compared with analytical, experimental and numerical data from previous literature and are found to be in excellent agreement. It has been found that heat transfer from a staggered array of cylinders is slightly higher than an inline array of cylinders.
Content may be subject to copyright.
1
HEAT TRANSFER AND FLUID FLOW OVER CIRCULAR
CYLINDERS IN CROSS FLOW
M. JIBRAN HAIDER, S. NOMAN DANISH, W. A. KHAN, S.
UZAIR MEHDI & BILAL AHMED ABBASI
Department of Engineering Sciences
National University of Sciences and Technology (NUST)
Pakistan Navy Engineering College (PNEC)
Karachi
Abstract:
An extensive numerical study is conducted to determine cross flow of air (Pr=0.71)
around isothermal cylinders of circular cross-section in arrangements such as single
cylinder, inline arrays and staggered arrays. Commercial software package FLUENT
is used to solve the fluid flow and energy equations assuming the flow over the
cylinder is two dimensional, steady, viscous and incompressible bounded in a duct, as
low Reynolds number is being investigated. The width of the duct is kept 20 times the
diameter of the cylinder so that the effects of channel blockage can be avoided. The
effects of radiation are also neglected in this study. Variations in properties such as
local Nusselt number, average Nusselt number, local pressure coefficient and local
skin friction coefficient are presented around the cylinders at Reynolds number
ranging from 40 to 10,000. The results are compared with analytical, experimental
and numerical data from previous literature and are found to be in excellent
agreement. It has been found that heat transfer from a staggered array of cylinders is
slightly higher than an inline array of cylinders.
Keywords: Heat Transfer; Computational Fluid Dynamics; FLUENT; Reynolds
Number; Nusselt Number; Circular Cylinder
Corresponding Author:
M. Jibran Haider
jibranhaider@hotmail.com
9221-34812186
92-300-2508252
2
NOMENCLATURE
B.C Boundary condition
CFD Computational Fluid Dynamics
cp Specific heat at constant pressure [J/kg.K]
Cp (θ) Local pressure coefficient,
2
5.0)()()(
UppCp
D Diameter of the cylinder [m]
h (θ) Local heat transfer coefficient [W/m2.K]
k Thermal conductivity [W/m.K]
L Characteristic length = Diameter of cylinder [m]
NuL Average Nusselt number based on characteristic length,
khLNu
NuL (θ) Local Nusselt number,
kLhNuL)()(
p (θ) Local static pressure at the surface of cylinder [N/m2]
P Free stream pressure [N/m2]
Pr Prandtl number,
kcp
Pr
ReL Reynolds number based on characteristic length,
LU
Re
T Temperature [K]
Tw Wall temperature [K]
T Free stream temperature [K]
u x component of velocity [m/s]
U Free stream velocity [m/s]
v y component of velocity [m/s]
W Width of duct [m]
Greek Symbols
θ Angular displacement measured clockwise from front stagnation point [o]
μ Dynamic viscosity [kg/m.s]
ρ Density [kg/m3]
3
1. Introduction
Investigation of heat transfer and fluid flow around cylinders has been a
popular subject because of its importance in variety of applications such as heat
exchangers, nuclear reactors, overhead cables, power generators, thermal apparatus
etc. Many researchers have analytically, experimentally and numerically determined
heat transfer and flow structures around circular cylinders placed in a bank and as
well as in isolation. A brief summary is provided below.
An extensive analytical study has been carried out by Van Der Hegge [1] to
produce a new correlation formula to determine heat transfer by natural and forced
convection from horizontal cylinders. Similarly, Refai Ahmed & Yovanovich [2] have
developed a method to determine heat transfer by forced convection from isothermal
bodies such as infinite circular cylinders, flat plates and spheres. The solution is valid
for a wide range of Reynolds and Prandtl numbers. More recently Khan et al. [3] [4]
have investigated fluid flow and heat transfer from a single circular cylinder and an
infinite circular cylinder analytically by the Von Karman Pohlhausen method.
Correlations are obtained for heat transfer and drag coefficients which are applicable
for a wide range of Reynolds and Prandtl numbers. Effects of both isothermal and
isoflux boundary conditions are analyzed.
Meel [5] experimentally determined the circumferential heat transfer
coefficient by measuring temperature distribution on the outer surface of the cylinder.
A series of experiments were conducted by Igarashi [6] [7] at high Reynolds Numbers
to determine pressure and drag coefficients around two circular cylinders placed in
tandem. The effects of varying the longitudinal distance between the cylinders and
their diameters were also investigated. Igarashi along with Suzuki [8] extended the
study to three circular cylinders arranged inline. An extensive experimental study was
undertaken by Buyruk [9] to determine local Nusselt Number and local pressure
coefficient around a circular cylinder for various Reynolds Numbers and blockage
ratios. This research was also extended to tube banks and the variation of local
Nusselt Number was obtained for every row with changes in longitudinal and
transverse pitches. Similarly Mehrabian [10] attempted to investigate the rate of
cooling of a cylindrical copper element by forced convection. The author has also
analyzed the uncertainty in the measurement of heat transfer characteristics of the
system.
On the other hand Wung and Chen [11] have utilized a finite analytic method
to determine heat transfer at various Reynolds numbers from inline and staggered tube
arrays. Buyruk [12] has numerically investigated heat transfer from cylinders placed
in tandem, inline tube banks and staggered tube banks. He has used a finite element
method to obtain the circumferential variation in Nusselt number for the cylinders. A
steady as well as an unsteady analysis has been undertaken by Szczepanik et al. [13]
to determine heat transfer from a cylinder in cross flow. Unsteady simulations of the
cylinder depict vortex shedding. The numerical study makes use of a k-ω turbulence
model.
4
The present study utilizes a commercial CFD software package, FLUENT
which is based on a control volume based technique to solve the governing equations
such as conservation of mass, momentum, energy and turbulence. Algebraic equations
are generated for discrete dependant variables like pressure, velocity, temperature etc,
for each control volume. Finally the discretized equations are linearized and a solution
is obtained [14].
5
2. Computational Methods
2.1. Methodology
The following methodology has been adopted in order to obtain results
through CFD simulations. It highlights the iterative procedure which must be carried
out in order to obtain an accurate set of results.
Create geometry in GAMBIT
Export mesh to FLUENT
Set solution parameters and
solver settings
Generate mesh
Set boundary conditions
Initialize the solution
Iterate to obtain a solution
Check for convergence
Modify solution
parameters, solver
settings and boundary
conditions or modify
meshing technique or
mesh density
Yes
No
Check for accuracy
Stop
Yes
No
6
2.2. Assumptions
A two dimensional analysis is performed as the length of the cylinder is kept
much greater than its diameter. The assumption that flow is incompressible is
warranted as relatively low Reynolds number is being investigated. The width of the
duct is kept much larger (20 times) than the diameter of the cylinder so that the wall
effects of the duct can be neglected. This means that the effects of boundary layer
formation on the duct boundary will not affect the flow in the vicinity of the cylinder.
2.3. Geometry and Meshing
The geometry is created in GAMBIT, which is the pre-processor for geometric
modeling and mesh generation. The rectangular computational domain is bounded by
the inlet, outlet and duct boundaries. The flow enters the domain from the inlet
boundary on the extreme left and leaves from the outlet boundary on the extreme right
for all simulations. A 2D structured mesh of non uniform grid spacing is created. The
mesh density is kept intense near the cylinder for resolving the boundary layer
accurately. The distinct points of the mesh are called nodes where all the equations
involved in the system are solved. These equations are:
Equation of continuity
0
y
v
x
u
x component of conservation of momentum
2
2
2
2
1yu
xu
x
p
y
u
v
x
u
u
t
u
y component of conservation of momentum
2
2
2
2
1yv
xv
y
p
y
v
v
x
v
u
t
v
Energy equation
Basically two slightly different techniques were utilized for mesh generation.
The first technique was applied to the mesh of a single cylinder. It involves the
generation of a block structured quadrilateral mesh around the cylinder. Figure 1
focuses on the mesh in the vicinity of a circular cylinder. It highlights the block
technique which is used for a smooth transition in mesh. A smooth transition in cell
volumes between adjacent cells is necessary as inability to do so may lead to
truncation errors.
2
2
2
2
yT
xT
y
T
v
x
T
u
t
T
7
Figure 1 Mesh in the Vicinity of the Cylinder
The second technique of mesh generation is applied to inline and staggered
arrangements. The mesh for these arrangements consists of tri meshing. Due to a
relatively complex geometry generating block structured quadrilateral mesh near the
cylinders is time consuming and therefore not feasible. The mesh is shown below.
Figure 2 Mesh in the Vicinity of Four Cylinders placed in an Inline Array
2.4. Solver Settings
All numerical simulations are performed under the double precision solver as
opposed to the single precision solver. The double precision solver performs better
where pressure differences are involved and high convergence with accuracy is
demanded [14]. A pressure based solver which in previous versions of FLUENT was
referred as the segregated solver was selected, as the present study deals with an
incompressible flow. A second order upwind scheme was used to discretize the
convective terms in the momentum and energy equations. This scheme though is time
consuming but it yields an accurate solution. This high order accuracy is achieved by
a Taylor series expansion about the cell centroid [14]. A convergence criterion of 10-6
was found sufficiently accurate for this study and was applied to all residuals except
energy for which the criterion was extended to 10-9.
8
2.5. Boundary Conditions
Following boundary conditions were applied to the boundaries for all cases.
Inlet Boundary: A velocity inlet boundary condition is applied to the inlet
boundary as it is intended for incompressible flows. A uniform velocity profile is
defined normal to the inlet boundary.
Outlet Boundary: An outflow boundary condition is employed at the outlet
boundary. Its use is justified as the flow velocity and pressure at the outlet are
unknown before the solution of the problem. It works on the principle of zero
diffusion flux normal to the outflow boundary for all variables except pressure. It
merely extrapolates information from within the domain and applies to the outlet
without disturbing the upstream flow [14].
Cylinder: A wall boundary condition is selected for the isothermally heated
cylinder. The cylinder is heated to a temperature of 400 K for all simulations. In
addition a no slip condition is employed along the cylinder surface.
Duct Boundary: The fluid flow is bounded within the duct by applying the wall
boundary and no slip condition.
The mesh with dimensions and boundary conditions is shown in the figure below. It is
to be noted that the actual mesh is much finer than the one shown.
Figure 3 Meshed Computational Domain with Boundary Conditions
20 D
15 D
Inlet Boundary
B.C = Velocity Inlet
u = U
v = 0
T = T
Cylinder
B.C = Wall, No slip
u = 0
v = 0
T = Tw = 400 K
Duct Boundaries
B.C = Wall
No slip
u = 0
v = 0
T = Tw = 300 K
Outlet Boundary
B.C = Outflow
W = 20 D
x
y
9
2.6. Grid Independence Study
In order to study the effect of grid size on the results, meshes of three different
densities were created, solved and their results were analyzed. The following table
shows the details of grid sizes for flow over a single circular cylinder and the
corresponding effects on the average Nusselt number at a Reynolds number of 100.
The results were found to be grid independent beyond the “average” mesh size.
Mesh Size
No. of Nodes
Average Nusselt No
Percentage Error
1.
Coarse
4120
5.2513
--
2.
Average
14260
5.1513
1.90
3.
Fine
37220
5.1401
0.22
Table 1 Effect of Grid Size on Average Nusselt Number
3. Results and Discussion
3.1 Flow over a Single Cylinder
3.1.1 Average Nusselt Number
Table 2 represents correlations developed by various researchers relating the
average Nusselt number for a circular cylinder.
Author
Correlation
Range of Re
B.C
Zukauskas [15]
5.0
Re4493.0 LL
Nu
40 1000
Isothermal
Morgan [16]
471.0
Re583.0 LL
Nu
40 4000
Isothermal
Hilpert [17]
466.0
Re615.0 LL
Nu
40 4000
Isothermal
Knudsen
and Katz [18]
3
1
466.0 PrRe683.0 LL
Nu
40 4000
Isothermal
Table 2 Experimental Correlations of NuL for Air
The values of average Nusselt number are calculated from these correlations
and are compared with the results of present study for Reynolds number ranging from
50 600. The results are presented in Table 3 and Fig 5. The analytical results
obtained by Khan et al. [4] are also plotted. Present study is in close agreement with
all previous experimental and analytical studies.
10
Table 3 Values of NuL Obtained From Correlations and Our Results at 50 ≤ Re ≤ 600
ReL Vs NuL
3
4
5
6
7
8
9
10
11
12
13
0100 200 300 400 500 600
ReL
NuL
Zukauskas (1972)
Morgan (1975)
Hilpert (1933)
Knudsen and Katz (1958)
Khan (2005)
Present Study
Figure 4 Comparison of NuL Vs ReL
It can be clearly seen from Fig 4 that as the Reynolds number increases,
Nusselt number also increases. The increase in Reynolds number is brought about
only by an increase in the free stream velocity as all the other parameters are kept
constant. The increased velocity will increase the average heat transfer coefficient
around the cylinder which eventually increases the average Nusselt number.
3.1.2 Local Nusselt Number
Figure 5 shows the plot of Nusselt number at the stagnation point and is
compared with the results given by Kays, Crawford and Weigand [19]. Again a good
agreement is found with the previous study.
Reynolds
Number
Zukauskas
[15]
Morgan [16]
Hilpert [17]
Knudsen and
Katz [18]
Khan [4]
Present
Study
Experimental
Experimental
Experimental
Experimental
Analytical
Numerical
50
3.18
3.68
3.81
3.83
3.7
3.82
100
4.49
5.10
5.26
5.29
5.2
5.15
200
6.35
7.07
7.26
7.31
7.4
7.12
300
7.78
8.56
8.77
8.83
9.0
8.59
400
8.99
9.80
10.03
10.10
10.3
9.97
500
10.05
10.89
11.13
11.20
11.5
11.17
600
11.01
11.86
12.12
12.20
12.5
12.28
11
ReL Vs NuL (θ=0)
5
10
15
20
25
30
35
0100 200 300 400 500 600 700 800 900 1000
ReL
NuL (θ=0)
Kays ,Crawford &
Weigand
Present Study
Figure 5 Comparison of ReL Vs NuL (θ=0)
The variation of local Nusselt number along the cylinder is presented in Figs 6
and 7 in comparison with the results of Krall and Eckert [20] for Reynolds numbers
100 and 200. Krall and Eckert kept the same boundary condition of no slip and
uniform wall temperature on the cylinder as is done in the present study.
Re=100
0
2
4
6
8
10
12
030 60 90 120 150 180
θ
NuL (θ)
Krall & Eckert (1970)
Present Study
Figure 6 Variation of NuL (θ) at Re=100
Re=200
0
2
4
6
8
10
12
14
16
030 60 90 120 150 180
θ
NuL (θ)
Krall & Eckert (1970)
Present Study
Figure 7 Variation of NuL (θ) at Re=200
12
Again the results are in good agreement. In both the graphs presented above the
values obtained by Krall and Eckert are slightly higher than the present study. The
possible reason of deviation may be related to a higher blockage factor in the study of
former authors. Present study is based on a blockage factor of 0.05.
3.1.3 Local Pressure Coefficient
The analytical results of local pressure coefficient along the surface of the
cylinder have been provided by Zdravkovich [21]. He has reported the results of
Kawaguti and Apelt. Figure 8 provides a comparison of those results with present
study at Reynolds number of 40.
Re=40
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
030 60 90 120 150 180
θ
Cp (θ)
Apelt (1961)
Kawaguti (1953)
Present Study
Figure 8 Variation of Cp (θ) at Re=40
An excellent agreement with the analytical results is observed. Experimental
study over cylinders at such low Reynolds number yields a greater percentage of
error. Therefore the significance of analytical and numerical study at low Reynolds
number is much more feasible. Similarly Zdravkovich [20] has reported the results of
Thoman & Szewczyk who carried out a computational study of flow over a circular
cylinder. The results at a Reynolds number of 200 are compared with the study and
found to be very close.
Re=200
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
030 60 90 120 150 180
θ
Cp (θ)
Thoman & Szewczyk (1969)
Present Study
Figure 9 Variation of Cp (θ) at Re=200
13
3.2 Flow over an Inline Array of Cylinders
The next stage of analysis was to simulate flow over circular cylinders placed
in an inline configuration as shown in Fig 10. Results were first obtained for 4
cylinders placed in a 2 x 2 array for which the longitudinal and transverse distances
between the cylinders were kept at 2 times the diameter of the cylinder. Later flow
over 25 cylinders placed in a 5 x 5 array was simulated.
Figure 10 Four Cylinders Placed in an Inline Arrangement
3.2.1 Local Nusselt Number
Distribution of local Nusselt number has been obtained for the inline
configuration. The results are compared with that of Buyruk [12] for a Reynolds
number of 200 and shown in Figs 11 and 12 for upstream and downstream cylinders.
A very good agreement is observed for both the cylinders.
Re=200 - First Cylinder
0
2
4
6
8
10
12
14
16
060 120 180 240 300 360
θ
NuL (θ)
Buyruk (2002)
Present Study
Figure 11 Variation of NuL (θ) at Re=200 along the First Cylinder
Second
Cylinder
First
Cylinder
14
Re=200 - Second Cylinder
0
1
2
3
4
5
6
7
8
9
10
060 120 180 240 300 360
θ
NuL (θ)
Buyruk (2002)
Present Study
Figure 12 Variation of NuL (θ) at Re=200 along the Second Cylinder
3.2.2 Contours of Static Pressure and Velocity
The contours of static pressure are shown in Fig 13 at a Reynolds number of
200 around the cylinders. The shifting of the front stagnation points on the front
cylinders (red region) and the rear cylinders (green region) is evident. This is due to
the venturi effect created between the two rows of cylinders which creates suction and
shifts the front stagnation point.
Figure 13 Contours of Static Pressure at Re=200
15
Velocity contours are also shown below at a Reynolds number of 40 and 200.
Figure 14 Contours of Velocity at Re=40
Figure 15 Contours of Velocity at Re=200
The increase in velocity between the cylinders as Reynolds number increases
is shown by the red region. The wakes generated by the cylinders at the front are
disturbed due to the presence of rear cylinders. The disturbance is much greater at a
Reynolds number of 200 than at 40.
3.2.3 Average Nusselt Number
The results of average Nusselt Number were obtained for the inline array of 5
by 5 and are presented in Table 4. The longitudinal and transverse distances were kept
at 2.5 times the diameter of the cylinder.
16
Reynolds
Number
Nu
100
3.005
500
6.907
1000
11.277
2000
18.064
3000
23.453
4000
28.192
5000
33.175
6000
38.235
7000
43.581
8000
49.150
9000
54.433
10000
59.462
Table 4 Variation of Nu with Re for a 5 x 5 Inline Array
3.2.4 Contours of Temperature
The contours of temperature are shown below for various Reynolds numbers.
Figure 16 Contours of Temperature at Re=100
Figure 17 Contours of Temperature at Re=1000
17
Figure 18 Contours of Temperature at Re=5000
The plots above show the decrease in the thermal boundary layer as Reynolds
number increases from 100 to 1000 and finally to 5000. So the temperature gradient at
a higher Reynolds number is very steep which gives a better heat transfer. It is also
evident that the diffusion of temperature contours occurs much early downstream of
the cylinders at a lower Reynolds numbers. Lastly, the symmetry of temperature
contours can be observed about the central row. It is to be noted that there is no shift
in the stagnation points of the cylinders present in the central row while every other
cylinder experiences some change in stagnation point.
3.3 Flow over a Staggered Array of Cylinders
The flow was also simulated over a staggered array of 3 cylinders as shown in
Fig 19 and then for 23 cylinders. The longitudinal and transverse pitches for the three
cylinders are kept 2.
Figure 19 Three Cylinders Placed in a Staggered Arrangement
First
Cylinder
Second
Cylinder
18
3.3.1 Local Nusselt Number
Variation of local Nusselt number is obtained and compared with the results of
Buyruk [12]. The comparison is shown in Figs 20 and 21 at a Reynolds number of
200 for the first and second cylinders.
Re=200 - First Cylinder
0
2
4
6
8
10
12
14
060 120 180 240 300 360
θ
NuL (θ)
Buyruk (2002)
Present Results
Figure 20 Variation of NuL (θ) at Re=200 along the First Cylinder
Re=200 - Second Cylinder
0
2
4
6
8
10
12
14
16
18
060 120 180 240 300 360
θ
NuL (θ)
Buyruk (2002)
Present Study
Figure 21 Variation of NuL (θ) at Re=200 along the Second Cylinder
A close examination of the plot reveals that the values of local Nusselt number
obtained by Buyruk for the second cylinder are not exactly symmetrical over the
upper and lower surfaces. The configuration of the cylinders is such that flow should
be symmetrical for the second cylinder. On the other hand our results are exactly
symmetrical.
19
3.3.3 Contours of Static Pressure and Velocity
The contours of static pressure are shown in Fig 22 at a Reynolds number of
120. The shifting of the front stagnation points is clearly visible on the two cylinders
at the front. As expected symmetrical pressure contours are obtained for the second
cylinder.
Figure 22 Contours of Static Pressure at Re=120
The contours of velocity at Reynolds number 40 and 500 are shown in the following
figures.
Figure 23 Contours of velocity at Re =40
20
Figure 24 Contours of Velocity at Re=500
It can be clearly seen that at a higher Reynolds number separation of the
boundary layer from all three cylinders occurs early. Therefore the wakes created in
Fig 24 are much greater than those in Fig 23.
3.3.4 Average Nusselt Number
Flow is simulated over a staggered array of 23 cylinders. Longitudinal and
transverse pitches are kept at 2.5 each. The results of average Nusselt numbers are
obtained for various Reynolds Numbers.
Reynolds
Number
Nu
100
3.470
500
9.941
1000
14.875
2000
22.346
3000
28.661
4000
34.495
5000
40.432
6000
46.784
7000
54.304
8000
61.821
9000
68.310
10000
74.671
Table 5 Variation of Nu with Re for a Staggered Array
21
3.3.5 Contours of Temperature
The contours of temperature are shown in Figs 25, 26 and 27 at different
Reynolds numbers.
Figure 25 Contours of Temperature at Re=100
Figure 26 Contours of Temperature at Re=1000
Figure 27 Contours of Temperature at Re=5000
22
As the Reynolds number increases from 100 to 5000 the thickness of the
thermal boundary layer decreases significantly. Therefore the temperature gradient at
Reynolds number 5000 is much greater than that at Reynolds numbers 1000 or 100.
This high temperature gradient is responsible for the increased heat transfer as
Reynolds number increases. As in the case of an inline array, the symmetry of
temperature contours can also be observed for a staggered array about the central row.
Figure 28 shows a comparison of the Nusselt number for inline and staggered arrays.
NuL Vs ReL
0
10
20
30
40
50
60
70
80
100
500
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
ReL
NuL
Inline Array
Staggered Array
Figure 28 Variation of NuL Vs ReL for Inline and Staggered Arrays
It can be concluded that the heat transfer from a staggered array is higher than
that from an inline array when subjected to the same Reynolds number. This is also
confirmed by the temperature contours of the two arrangements as the diffusion of
contours is more intense in the staggered array as compared to the inline array.
Conclusions
Numerical study has been undertaken to analyze heat transfer and flow
characteristics past a single cylinder, inline array and staggered array at various
Reynolds numbers. It can be concluded from the results that:
1. Heat transfer from a staggered array of cylinders is slightly higher than
that from an inline array of cylinders.
2. The simulated results of local Nusselt number, average Nusselt number
and local pressure coefficient from circular cylinders are in well agreement
with the analytical, experimental and numerical results available in
existing literature.
23
References
[1] V. D. H. Zijnen, “Modified correlation formulae for the heat transfers by natural and
by forced convection from horizontal cylinders”, Appl. Sci. Res, Vol. 6, 1956, pp.
129140.
[2] G. R. Ahmed and M. Yovanovich, “Analytical method for forced convection from flat
plates, circular cylinders and spheres”, Journal of Thermophysics and Heat Transfer,
Vol. 9, No. 3, 1995, pp. 516523.
[3] W. A. Khan, J. Culham, and M. Yovanovich, “Fluid flow and heat transfer from a pin
fin: analytic approach”, American Institute of Aeronautics and Astronautics, Vol. 163,
2003, pp. 112.
[4] W. A. Khan, J. Culham and M. Yovanovich, “Fluid flow around and heat transfer
from an infinite circular cylinder”, Journal of Heat Transfer, Vol. 27, 2005, pp. 785-
790.
[5] D. Meel, “A method for the determination of local convective heat transfer from a
cylinder placed normal to an air stream”, Int. J. Heat Mass Transfer, Vol. 5, 1962, pp.
715722.
[6] T. Igarashi, “Characteristics of the flow around two circular cylinders arranged in
tandem”, JSME, Vol. 24, No. 188, 1981, pp. 323331.
[7] T. Igarashi, “Characteristics of a flow around two circular cylinders of different
diameters arranged in tandem”, JSME, Vol. 25, 1982, pp. 349357.
[8] T. Igarashi and K. Suzuki, “Characteristics of the flow around three circular cylinders
arranged in-line”, JSME, Vol. 27, 1984, pp. 23972404.
[9] E. Buyruk, “Heat transfer and flow structures around circular cylinders in cross flow”,
Tr. Journal of Engineering and Environmental Science, Vol. 23, 1997, pp 299315.
[10] M. Mehrabian, “Heat transfer and pressure drop characteristics of cross flow of air
over a circular tube in isolation and/or in a tube bank.”, The Arabian Journal for
Science and Engineering, Vol. 32, No. 2B, 2005, pp. 365376.
[11] T. Wung and C. Chen, “Finite analytic solution of convective heat transfer for tube
arrays in cross flow”, Journal of Heat Transfer, Vol. 111, 1989, pp. 633648.
[12] E. Buyruk, “Numerical study of heat transfer characteristics on tandem cylinders,
inline and staggered tube banks in cross flow of air”, Int. Comm. Heat Mass Transfer,
Vol. 29, No. 3, 2002, pp. 355366.
[13] K. Szczepanik, A. Ooi1, L. Aye and G. Rosengarten, “A numerical study of heat
transfer from a cylinder in cross flow”, Proceedings of 15th Australasian Fluid
Mechanics Conference, Sydney, December 13-17, 2004.
[14] “FLUENT 6.3 User’s Guide” , 2006.
[15] A. Zukauskas, “Advances in heat transfer”, Academic Press New York, 1972, pp. 93-
160.
[16] V. Morgan, “The overall convective heat transfer from smooth circular cylinders”,
Advances in Heat Transfer, Vol.11, Academic Press, New York, 1975, pp. 199264.
[17] R. Hilpert, “Warmeabgabe von geheizten drahten und rohren”, Forch. Geb.
Ingenieurwes, Vol. 4, 1933, pp. 215224.
24
[18] J. Knudsen and D. Katz, Fluid Dynamics and Heat Transfer”, McGraw Hill, New
York, 1958.
[19] Kays, W. Crawford and B. Weigand, “Convective Heat and Mass Transfer”, 4th
Edition McGraw-Hill, 2005.
[20] K. Krall and E. Eckert, “Heat transfer to a transverse circular cylinder at low
Reynolds Numbers including rarefaction effects”, Fourth International Heat Transfer
Conference”, Vol. 3, 1970, pp. 111.
[21] M. Zdravkovich, “Flow around circular cylinders”, Vol. 1, 1997, pp. 260273.
... ey found that the leading-edge flow separation from the cylinders disturbs the wake structures and vortex shedding patterns in case of shear-thinning fluids which was not earlier observed in case of Newtonian fluids [15]. Another numerical study has been carried out by Haider [16] to analyse the heat flow characteristics of Newtonian fluid past clusters of isothermal cylinders fixed within the flow domain. Cylinders were placed in-line or scattered manner and found that the heat flow from the scattered cylinders is slightly higher than when the cylinders are placed in-line. ...
... It can be deduced from these graphs that maximum value of pressure Figures 10-12, respectively. ese figures show that there is significant decrease in thickness of thermal layer along the horizontal line through the center of heated cylinder if the value of the Reynolds number increases from Re � 1000 to Re � 4000 and finally to Re � 10000. is type of investigations has also been reported by [16]. ey have put different cylinders in in-line settings and scattered way and observed temperature changes in the fluid domain. ...
Article
Full-text available
In this paper, the ow of a power law uid has been investigated for Newtonian and non-Newtonian uids with the temperature distribution in a rectangular channel containing a heated circular cylinder near the inlet with di erent blockage ratios. e generalized non-Newtonian power law model coupled with the energy equation is solved numerically, considering power law index in the range of 0.8 ≤ n ≤ 1.2 and Reynolds number in the range from 1000 to 10000. A heated circular cylinder is xed near the inlet of the channel with blockage ratios (from radius to the height of the channel) of 1: 10, 2: 10, and 3: 10 e governing partial di erential equations coupled with energy equation are discretized to investigate the simulation of the current problem with nite element-based software of COMSOL Multiphysics 5.4. e results are shown with the help of surface plots, tables, and graphs. e computational results for maximum and minimum pressure around the cylinder, temperature along the center line of the cylinder, and local Nusselt number are specially discussed in detail.
... The use of numerical simulations or models to predict the fluid flow and heat transfer in tube banks has made tremendous efforts for development. They have been applied in many previous studies at anin-line configuration only [42][43][44][45][46][47][48][49][50][51][52][53][54], to an SG only [55][56][57][58][59][60][61][62][63][64][65][66], and both configurations [67][68][69][70][71]. Numerous researches have been conducted in the field of heat transfer and fluid flow in the analysis of two-and three-dimensional HEs with fins and without fins using FLUENT [72][73][74][75][76][77][78][79][80][81][82][83][84][85][86], ANSYS CFX [87][88][89][90][91], CFX4.4 [92], COMSOL Multiphysics [93]. A small number of scholars have presented numerical analyses of three-dimensional modeling for finnedtube HEs. ...
Article
Full-text available
With the beginning of the industrial revolution in the eighteenth century, ICE, refrigeration equipment and power stations developed. All of the above devices use TBHE. The important thing is the recent increase in energy demand, which led researchers to find optimal solutions to save the largest amount of energy. The objective of this review can be summarized in the research published in the field of TBHE of all kinds. In order to improve the performance of the TBHE, two basic conditions must be met, the first is to increase the CHTC, and the second is to reduce the PD across the HE. In order to reach this goal, many influential variables must be studied, including pipe diameters and shapes, vertical and horizontal distances, fins shape, and installation method. In addition to the arrangement of the tubes through the TBHE. It was in the form of IL or staggered, the type of flow that was stratified or turbulent. The most important variables affecting on the performance of HEs can be summarized in general. The shape of the pipes had a greater urgency in the process, as the flat pipes had better performance than the circular TBHE. Both the PD and the CHTC are a function of the Reynolds number, as both increase with the increase in the Reynolds number. Therefore, studies in this field must be intensified to obtain the optimal design TBHE, taking into account all the above variables.
... They also highlighted the effect of cylinder arrangement on the critical Re value. Haider et al. [18] have simulated different arrangements of circular cylinders under uniform flow with low Re. He observed that the cylinders in a staggered arrangement have better heat transfer characteristics. ...
... Rahman et al., [9], investigated the behavior of 2D flow by test the wake zone downstream the circular turbulent and laminar, by computing the drag and pressure coefficients for the range of Reynolds numbers (Re=10 3 to 3.9×10 3 ) . Furthermore, Jibran et al., [10] completed an investigation deals with the flow characteristics across circular cylinder as single circular cylinder and arrays of cylinders by using different Reynolds number changed from 40 to 10000. In regard to the current study, 2d flow across single circular cylinder with various values of Reynolds numbers ranging from 100 to 5000 is studied numerically with diameter of circular cylinder D = 20mm. ...
Article
Full-text available
Among the many experiments Which deals with the study of the characteristics of flow, a numerical study of flow air (Pr=0.71) crosses a circular cylinder is conducted. Variations in flow and thermal characteristics such as average Nusselt number, local pressure coefficient and drag coefficient are presented around the cylinders for Reynold numbers ranging from 100 to 5000 by solving the incompressible two-dimensional unsteady Navier-Stokes and energy equations. Commercial software package FLUENT 19 is applied to solve the equations. The diameter of the circle is D = 20 mm, the width is 20 times the diameter of the cylinder. The results obtained are compared with data of previous study for Nusselt Number values showed acceptable agreement. The results of the drag coefficient confirm a noticeable decrease in the transition from low values of Reynolds numbers to the high values.
... Moreover, it was proved that the staggered arrangement gave higher heat transfer rates than the inline one. The same findings were observed by Haider et al. [27]. ...
Article
Full-text available
The paper presents a theoretical analysis of heat transfer in a heated tube bank, based on the Nusselt number computation as one of the basic dimensionless criteria. To compute the Nusselt number based on the heat transfer coefficient, the reference temperature must be determined. Despite the value significance, the quantity has several different formulations, which leads to discrepancies in results. This paper investigates the heat transfer of the inline and staggered tube banks, made up of 20 rows, at a constant tube diameter and longitudinal and transverse pitch. Both laminar and turbulent flows up to Re = 10,000 are considered, and the effect of gravity is included as well. Several locations for the reference temperature are taken into consideration on the basis of the heretofore published research, and the results in terms of the overall Nusselt number are compared with those obtained by the experimental correlations. This paper provides the most suitable variant for a unique reference temperature, in terms of a constant value for all tube angles, and the Reynolds number ranges of 100-1000 and 1000-10,000 which are in good agreement with the most frequently used correlating equations.
... It is known that cross-sectional shape can both improve and worsen the hydrodynamic characteristics. The study [4] esteems flow characteristics and associated instability of convective flow behind a semi-circular cylinder at incidence with a downstream circular cylinder. Unsteady computations are performed for different incidence angles and Reynolds numbers from 60 up to 160. ...
Article
Full-text available
The paper aims to investigate the dependence of heat transfer classification on the Reynolds number (Re) during flow around circular heated cylinders row. The investigated range of Re number varies from 4.5×10 ³ up to 42×10 ³ . The distance between cylinders S was changed from 0.5d to 4d (where d is the cylinders dia). Cylinders surface temperature was kept constant. For each Re number, the case when the cylinders were mounted one after the other was investigated. To measure heat transfer and flow parameters (velocity, heat flux and heat transfer coefficient) near and at the cylinders surface, two experimental methods were used: gradient heatmetry and PIV. Heat flux and velocity fields were obtained from gradient heatmetry and PIV results, based on which the flow mode could be determined and compared with heat transfer mode. As a result, it was found that heat transfer is influenced by both the Reynolds number and the distance between the cylinders. The observed features are associated with influence on characteristics such as separation point location, boundary layer thickness, change in flow between the cylinders and vortices formation.
... A nonisothermal flow of air around the circles was studied [7] with the range of the Reynolds number from 40 to 10,000 by putting the Prandtl number at 0.7 with the use of commercial software FLUENT. e circles were arranged as in-line and staggered and suggested that the heat transfer is optimized when the circles are arranged in a staggered pattern. ...
Article
Full-text available
Nonisothermal flow through the rectangular channel on a circular surface under the influence of a screen embedded at the middle of a channel at angles θ is considered. Simulations are carried out via COMSOL Multiphysics 5.4 which implements the finite element method with an emerging technique of the least square procedure of Galerkin’s method. Air as working fluid depends upon the Reynolds number with initial temperature allowed to enter from the inlet of the channel. The nonisothermal flow has been checked with the help of parameters such as Reynolds number, angle of the screen, and variations in resistance coefficient. The consequence and the pattern of the velocity field, pressure, temperature, heat transfer coefficient, and local Nusselt number are described on the front surface of the circular obstacle. The rise in the temperature and the flow rate on the surface of the obstacle has been determined against increasing Reynolds number. Results show that the velocity magnitudes are decreasing down the surface and the pressure is increasing down the surface of the obstacle. The pressure on the surface of the circular obstacle was found to be the function of the y-axis and does not show any impact due to the change of the resistance coefficient. Also, it was indicated that the temperature on the front circular surface does not depend upon the orientation of the screen and resistance factor. The heat transfer coefficient is decreasing which indicates that the conduction process is dominating over the convection process.
... They found that in the case of shear-thinning the rate of heat transfer is enhanced with enhancement in the Reynolds number and the Prandtl number. A finite volume based commercial software FLUENT was activated to observe the fluid flow and convection [23] by arranging the circles in-line and staggered with ranging the non-dimensional number Re from 40 to 10,000 and the keeping fixed 0.7 P r  . It was found the heat transfer in the domain is enhanced when the arrangements of the circles are staggered. ...
Article
Full-text available
The current article is an understanding of heat transfer and non-Newtonian uid ow with implications of the power-law uid on a facing surface of the circular cylinder embedded at the end of the channel containing the screen. The cylinder is xed with an aspect ratio of 4 V 1 from height to the radius of the cylinder. The simulation for the uid ow and heat transfer was obtained with variation of the angle of screen � 6 � � � � 3 , Reynolds number 1000 � Re � 10; 000 and the power-law index 0:7 � n � 1:3 by solving two-dimensional incompressible Navier-Stokes equations and the energy equation with screen boundary condition and slip walls. The results will be in a good match with asymptotic solution given in the literature. The results are presented through graph plots for non-dimensional velocity, temperature, mean effective thermal conductivity, heat transfer coef cient, and the local Nusselt number on the front surface of the circular cylinder. It was found that the ratio between the input velocity to the present velocity on the surface of the circular cylinder remains consistent and reaches up to a maximum of 2:2% and the process of heat transfer does not affect by the moving of the screen and clearly with the raise of power-law indexes the distribution of the heat transfer upsurges. On validation with two experimentally derived correlations, it was also found that the results obtained for the shear-thinning uid are more precise than the numerically calculated results for Newtonian as well as shear-thickening cases. Finally, we suggest necessary measures to enrich the development of convection when observing with strong effects in uenced by the screens or screen boundary conditions.
... They found that in case of shear-thinning the rate of heat transfer is enhanced with enhancement in the Reynolds number and the Prandtl number. A finite volume based commercial software FLUENT was activated to observe the fluid flow and convection [23] by arranging the circles inline and staggered with ranging non-dimensional number Re from 40 to 10,000 and keeping 0.7 P r  fixed. It was found that the heat transfer in the domain is enhanced when arrangements of circles are staggered. ...
Article
Full-text available
The current article is an understanding of heat transfer and non-Newtonian fluid flow with implications of the power-law fluid on a facing surface of the circular cylinder embedded at the end of the channel containing the screen. The cylinder is fixed with an aspect ratio of 4:1 from height to the radius of the cylinder. The simulation for the fluid flow and heat transfer was obtained with variation of the angle of screen π/6≤θ≤π/3, Reynolds number 1000≤Re≤10,000 and the power-law index 0.7≤n≤1.3 by solving the two-dimensional incompressible Navier-Stokes equations and the energy equation with screen boundary condition and slip walls. The results will be in a good match with asymptotic solution given in the literature. The results are presented through graph plots for the non-dimensional velocity, temperature, mean effective thermal conductivity, heat transfer coefficient, and the local Nusselt number on the front surface of the circular cylinder. It was found that the ratio between the input velocity to the present velocity on the surface of the circular cylinder remains consistent and reaches up to a maximum of 2.2% and the process of heat transfer does not affect by the moving of the screen and clearly with the raise of power-law indexes the distribution of the heat transfer upsurges. On validation with two experimentally derived correlations, it was also found that the results obtained for the shear-thinning fluid are more precise than the numerically calculated results for the Newtonian as well as shear-thickening cases. Finally, we suggest the necessary measures to enrich the the development of convection when observing with the strong effects influenced by screens or screen boundary conditions.
Article
Full-text available
In this study an approximate analytical method, known as the Von Karman-Pohlhausen method, is used to investigate fluid flow and heat transfer from cylindrical pin fins. A fourth order velocity profile in the hydrodynamic boundary layer and a third order temperature profile in the thermal boundary layer are used to obtain a closed form solution for the fluid flow and heat transfer from a cylindrical pin fin. The momentum and energy equations in the integral form are used to obtain the solution. Both isothermal and isoflux boundary conditions are applied. The results for both boundary conditions are found to be in a good agreement with experimental/ numerical data for a single circular cylinder. The effects of free stream turbulence and blockage are not considered in this study.
Article
A detailed experimental investigation was carried out on the characteristics of the flow around three circular cylinders arranged in line. There are three cases concerned with the behavior of the shear layers separated from the first cylinder on the downstream ones: the first is a case without reattachment (W), the second is one with reattachment (R) and the third is one rolling up in the front region of the downstream cylinders (J). The flow patterns were classified according to W, R and J as follows: patterns A(W, W), B'(W, W⇌W, , R), B(R, R), C(R, J), E(R, J⇌J, J) and D(J, J). The characteristics of these flow patterns were clarified. The results were compared with conventional results on two and four circular cylinders arranged in line.
Article
Experimental investigations on the characteristics of a flow around two circular cylinders of different diameters with the ratio d2/d1 = 0.68 arranged in tandem were carried out. Reynolds number defined by the diameter of the first cylinder was varied in the range of 1.3×104 ≤ Re ≤ 5.8×104, and the longitudinal spacing between the axes of the cylinders in the interval of 0.9 ≤ L/d1 ≤ 4.0. The reattachment of a separated shear layer from the first cylinder, the jump phenomenon and the bistable flow at the critical region were confirmed in the same manner as the case of two cylinders of equal diameters. The differences between the two cases were discussed. Flow patterns were divided according to the spacing and Reynolds number. Characteristics of those flow patterns and effects of the Reynolds number were clarified.
Article
An experimental study was carried out to investigate heat transfer and flow characteristics from one tube within a staggered tube bundle and within a row of similar tubes. The tube spacing examined St and Sl are 1.51.5 and 1.51.25 where Sl and St denote the longitudinal and transverse pitches respectively. The variation of local Nusselt number was predicted with Reynolds number 4:8104. The aim of the second part of the investigation was to examined the influence of the blockage of a single tube in a duct and transverse pitch for a single tube row with Reynolds number range of 7960 to 47770. Blockage ratio was varied from 0.131 to 0.843. Variation of local Nusselt number and local pressure coecient were shown with dierent blockages and Reynolds numbers. The main results are described below. For single tube row experiments, if the blockage ratio is less than 0.5, the general shape of local Nusselt number distribution around the cylinder varies only slightly with blockage. However the local Nusselt number and pressure coecient distributions are remarkably dierent for the blockage ratio in the range of 0.668-0.843. Tube bundle experiments showed that changing longitudinal ratio did not aect the mean Nusselt number.
Article
An investigation of the published results of heat transfer studies for both natural convection and crossflow forced convection is conducted. It is found that the wide dispersion in the experimental data for the heat transfer from smooth circular cylinders can be attributed to various factors associated with the experiments. Natural convection in horizontal and inclined cylinders is considered. The cases of a cylinder with cross flow and of a yawed cylinder are investigated in connection with studies involving forced convection.
Article
The most widely used shape in engineering, the circular cylinder, provides great challenges to researchers as well as mathematical and computer modellers. This book offers an authoritative compilation of experimental data, theoretical models, and computer simulations which will provide the reader with a comprehensive survey of research work on the phenomenon of flow around circular cylinders. Researchers and professionals in the field will find it an invaluable source for ideas and solutions to design and theoretical problems encountered in their work.