Experimental Thermal and Fluid Science 44 (2013) 199–208

Contents lists available at SciVerse ScienceDirect

Experimental Thermal and Fluid Science

journal homepage: www.elsevier.com/locate/etfs

Natural convection experiments on a heated horizontal cylinder

in a differentially heated square cavity
C. Butler ⇑, D. Newport, M. Geron
Stokes Institute, Dept. of Mechanical, Aeronautical & Biomedical Engineering, University of Limerick, Limerick, Ireland

a r t i c l e i n f o a b s t r a c t

Article history: Natural convection heat transfer from a heat generating horizontal cylinder enclosed in a square cavity,
Received 18 July 2011 where a temperature difference exists across its vertical walls has been experimentally investigated for
Received in revised form 11 June 2012 the range 2  104 < Racyl < 8  104 and a Pr of 0.71. Temperature and cylinder Nusselt number measure-
Accepted 15 June 2012
ments were taken for a range of h . h is defined as a ratio of cylinder and cavity Grashof numbers. It has
Available online 23 June 2012
been found that at the lower values of Racyl , the heat transfer from the cylinder compares well with cor-
relations available in literature. As Racyl increases however, it deviates away and the overall heat transfer
Keywords:
from the cylinder is increased when compared to these correlations due to the interaction from the cav-
Natural convection
Horizontal cylinder
ity. 2D-PIV measurements of the flow structures inside the compartment were conducted. They show an
Square cavity increased interaction between the flow structures generated by the cylinder and by the cavity with
Differential heating increasing h , corresponding to the increase in the heat transfer from the cylinder. It is observed that
the recirculation generated by the temperature gradient imposed on the cavity is broken down as the
plume from the cylinder becomes stronger and a transition process is observed, whereby the flow tran-
sitions from being dominated by the temperature difference across the cavity to that dominated by the
temperature difference due to the cylinder.
Ó 2012 Elsevier Inc. All rights reserved.

1. Introduction the numerical study of the steady state convective heat transfer
between a differentially heated square cavity with an internal
The study of natural convection in enclosed spaces is important square cylinder generating heat for Rayleigh numbers in the
in a wide range of engineering applications, such as evaluating en- range 103 —104 . It was shown that there is a transition process
ergy transfer in buildings, fluid-filled storage tanks and thermal from the flow dominated by the temperature difference across
management of aviation and consumer electrical equipment, with the enclosure to that dominated by the temperature difference
a significant amount of time being dedicated to its study [1]. due to the internal heated body. Lee and Ha [6,7] studied the ef-
Warrington and Powe [2] investigated natural convection be- fect of various parameters on a square cylinder conducting heat
tween concentrically located inner bodies and their isothermal in a differentially heated square cavity, which included varying
cubical enclosures. Their paper also includes a comparison of the thermal conductivity ratio and observing the effects on the
most of the data available at the time of its publication for natu- modes of heat transfer and steadiness of the flow for Rayleigh
ral convection heat transfer between concentrically located 3D numbers in the range 103 —106 . Ha and Jung [8] numerically ana-
isothermal inner bodies with their 3D isothermal outer bodies. lysed the three dimensional heat transfer from a cubic body
Moukalled and Acharya [3] numerically investigated the convec- which generates heat within a cubic enclosure. They found that
tive heat transfer from a heated horizontal cylinder enclosed in the presence of the conducting body had a significant influence
a square cavity for Rayleigh numbers in the range 104 —107 . It on both the fluid flow and heat transfer. Jami et al. [9,10] numer-
was found that at the lower values of Rayleigh number studied, ically studied the effect of varying position of a heat generating
conduction is the dominating mode of heat transfer, while at cylinder in a differentially heated square cavity and also the effect
the higher values of Rayleigh number, convection dominates. of varying the temperature difference ratio, DT  , for Rayleigh
Cesini et al. [4] investigated the convective heat transfer from a numbers in the range 103 —106 . The temperature difference ratio,
horizontal cylinder in a rectangular cavity, using both numerical defined in Oh et al.’s paper [5], is a dimensionless representation
and experimental analyses. Oh et al. [5] presented results for of the temperature difference across the enclosure related to the
heat generated by the internal body. Recently, Yoon et al. [11,12]
⇑ Corresponding author. Tel.: +353 61 202449; fax: +353 61 202393. has numerically studied the 2- and 3D effects of a heated spher-
E-mail addresses: colin.butler@ul.ie (C. Butler), david.newport@ul.ie (D. Newport).
ical body inside an isothermal enclosure for a Rayleigh number of

0894-1777/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved.
http://dx.doi.org/10.1016/j.expthermflusci.2012.06.009
200 C. Butler et al. / Experimental Thermal and Fluid Science 44 (2013) 199–208

Nomenclature

A area (m2) Abbreviations

Bi Biot number (–) PIV Particle Image Velocimetry
cp specific heat (J kg1 K1)
dt laser pulse separation time (s) Greek symbols
d diameter (m) b thermal expansion coefficient (T1)
E emissive power (W m2) e emissivity (–)
F view factor (–) d3 ðT T ref Þ
2 3 h ¼ H3 ðcyl Grashof ratio (–)
Gr ¼ q gbll2
DT
Grashof number (–) T T Þ
h c

g gravity (9.81 ms2) l dynamic viscosity (kg m1 s1)

H height (m) q density (kg m3)
h convective heat transfer coefficient (W m2 K1) r Stefan–Boltzmann constant (5.67  108 W m2 K4)
I current (A) s time (s)
J radiosity (W m2) x uncertainty (–)
k thermal conductivity (W m1 K1)
L length (m) Subscripts
l characteristic length (m) b inner body
N number of images (–) c cold wall
Nu Nusselt number (–) conv convection
c l
Pr ¼ pk Prandtl number (–) cyl cylinder
q heat transfer rate (W) e enclosure
Ra ¼ GrPr Rayleigh number (–) f fluid
T  temperature
 (K) film film temperature
DT ¼ T  T ref temperature difference (K) h hot wall
DT  ¼ ðkqbMT
Ab Þ
temperature difference ratio (–) n normal direction
ðf Þ p increment
V voltage
rad radiation
v velocity (ms1)
ref reference
v =v max dimensionless velocity (–) s solid
vol volume (m3)
ss steady state
W width (m)
x; y; z cartesian coordinates (m)

107 . They found that the position of the body has a significant Thus, the aim of this paper is to study the natural convection
influence on the heat transfer, fluid flow and the steadiness in from a heated horizontal cylinder enclosed in a square cavity, with
the enclosure. air as the working fluid, where a temperature difference exists
While there are numerous studies available in literature that across its side walls and to investigate by experimental methods
deals with the case of a heat generating body located inside a cav- the influence that the natural convective plume from the cylinder
ity, where a temperature difference exists across the enclosure, for has on the heat transfer and internal fluid flow structures. The
various different arrangements and boundary conditions, the vast compartment has a square cross section of L = H = 0.31 m and a
majority analyse this problem using numerical methods and the horizontal cylinder (d = 0.03 m) that is centrally located inside
number of experimental papers are very limited. Ekundayo et al. the cavity at L/2 and H/2 (see Fig. 1). The longitudinal dimension
[13] presents results for the experimental measurement of the heat of W is also the same size as L and H, i.e. 0.31 m, giving the enclo-
transfer of a heat generating cylinder in a cooled rectangular enclo- sure a cubical shape. The heated surfaces are assumed isothermal
sure for Rayleigh numbers 7  104 and 1  105 . By varying the po- with all remaining surfaces approximately adiabatic. Temperature
sition of the cylinder inside the enclosure, they were able to find an measurements were taken in various locations on the cylinder and
optimal position to enhance the rate of heat transfer. Davies et al. wall surfaces to measure the Nusselt numbers. The flow structures
[14] analysed the heat transfer between an isothermal cylinder and
its isothermal enclosure experimentally and analytically. They
examined the scaling effects in the context of its Boussinesq
approximation and presents the argument that the boundary con-
ditions should be defined between the cylinder and its enclosure
rather than the cylinder and the surrounding fluid region. Newport
et al. [15] numerically and experimentally investigates the heat
transfer between a cylinder in a cubic isothermal enclosure for cyl-
inder Rayleigh numbers of 104 . Temperature profiles and Nusselt
numbers are presented and compared with simulation results with
excellent comparison achieved. varo and Paroncini [16,17] con-
ducted 2D-PIV and interferometry analysis of a heated strip inside
a differentially heated square enclosure between Rayleigh number
values of 6:5  104 —3:2  105 . The main reason for the lack of pa-
pers dealing with natural convection using air as the fluid inside a
cavity is due to the difficulty of creating an experimental setup
capable of producing acceptable data [17]. Fig. 1. Experimental compartment.
 C. Butler et al. / Experimental Thermal and Fluid Science 44 (2013) 199–208 201

generated by the convective flow were analysed using 2D Particle the working fluid. Heat transfer from the supposedly adiabatic
Image Velocimetry (PIV). walls is unavoidable [18].

2. Experimental setup and apparatus 2.1. Material properties

The experimental compartment is schematically presented in The thermal material properties of the aluminium and polycar-
Fig. 1. It consists of a six wall cubical cavity containing a horizontal bonate were assumed constant and their values were taken from
cylinder of a circular cross section. The two vertical side walls of data tables in Holman [19] and manufacturers specifications. They
the cavity were constructed from 10 mm thick aluminium plate; are shown in Table 1. For the cylinder, it is also assumed the values
the top, bottom and back walls were constructed from 6 mm thick are constant through its entire cross section. The emissivity e of the
polycarbonate; and the front wall was constructed from 6 mm material surfaces was measured experimentally using a Fluke Ti32
thick glass. Glass was used for the front wall to give greater optical Infrared Thermal Imaging Camera. It can record temperatures from
access compared to polycarbonate when capturing images during 20 °C to 150 °C with an accuracy of 2%. By measuring the surface
PIV experimental testing. Two 400 W silicon heater mats were at- temperature using a thermocouple and comparing it to the tem-
tached to the right vertical side wall and were used to heat this perature value on the IR camera, it is possible to correct on the
wall to T h Power was supplied to the heater mats to set up either on-screen emissivity value on the camera until the two tempera-
isothermal or isoflux conditions. For the isothermal conditions, ture values match. Using this method it was determined that the
two Eurotherm 2216e PID controllers were connected to the mats e for the aluminium is 0.12. This indicates a moderately oxidised
with two feedback thermocouples attached to the aluminium sur- surface [20,21]. For the polycarbonate, the value of e is 0.95. The
face. The required temperature can be set on their digital operator values of emissivity were assumed to be constant and independent
display to an accuracy of 0.1 K and the controllers immediately at- of direction, i.e. diffuse emittance. This condition is a reasonable
tempts to reach and maintain this temperature with PID control approximation even though all real surfaces exhibit some depar-
algorithms. For isoflux conditions, the mats were connected to a ture from diffuse behaviour. Although there are preferential direc-
Elektro-Automatik EA-STT 2000 B 4,5 Variable Transformer. This tions for emission, the hemispherical emissivity will not differ
power supply has a variable output voltage of 0–260 V AC at markedly from the emissivity normal to the surface, en . The ratio
4.5 A. To reduce as much heat loss from the hot wall to the envi- seldom falls outside the range 1:0 6 ðe=en Þ 6 1:3 for conductors
ronment as possible, the exterior of the hot wall was insulated and the range of 0:95 6 ðe=en Þ 6 1:0 for non-conductors. Therefore,
with a 25 mm block of insulation, and a second aluminium wall it is reasonable to assume that e  en [21].
was placed next to this. This wall was heated with a 400 W heater All of the air fluid thermal properties were calculated at the film
mat, with the temperature controlled by an additional Eurotherm temperature. This is defined as
2216e PID controller. The temperature of this second hot wall T þ T ref
was set to the same temperature as the enclosure hot wall, produc- T film ¼ ð1Þ
2
ing a minimal temperature gradient between the enclosure hot
wall and its surrounding environment. The cold wall was cooled where T is the temperature of the cylinder T cyl , or the hot wall T h ,
using a desktop fan mounted next to the wall, which supplies a depending on the analysis being conducted, and T ref is the selected
constant flow of air at ambient temperature, producing the cold reference temperature which is described in later sections.
wall temperature, T c .
The aluminium cylinder was made from 30 mm diameter alu- 2.2. Thermocouples
minium rod. A tight fit hole of 8 mm was centrally drilled through
the cylinder and two Fast Heat CH 29452 500 W cartridge heaters A total of 13 K-type thermocouples were fitted in various loca-
were inserted into either end of the cylinder and any remaining tions on all surfaces inside the cavity with the exception of the
gaps were filled with thermal heat sink compound. The cartridge front wall which was kept free of any obstructions for PIV analysis.
heaters are resistor core assembled with a maximum voltage of For calculations, the front wall temperature was assumed to be the
240 V AC. They have dimensions of 8 mm diameter and 150 mm same as the back wall temperature due to the geometrical symme-
length. The cartridge heaters were connected to a TTi EL302D try of the compartment. The exact location of each thermocouple is
bench power supply. The power supply has variable outputs from given in Table 2. The origin is located at the front bottom side of
0 to 30 V DC and 0 to 3 A. Its meter accuracies are 0.3% for voltage the cold wall (see Fig. 1). The thermocouples were offset back from
and 0.6% for current.
During assembly, all walls and the cylinder were isolated from
each other with a thin strip of rubber to minimise any conduction Table 2
Thermocouple locations.
heat transfer between them. The thermal conductivity of the rub-
ber was measured as 0.275 W m1 K1 which is approximately Location x (mm) y (mm) z (mm)
three orders of magnitude less than that of the aluminium. The Cylinder 155 170 70
compartment was sealed up with a silicon based sealant to prevent 155 170 240
any air leaks. During testing, all walls except the cold wall were Hot wall 0 70 165
insulated to set up approximate adiabatic wall conditions and re- 0 155 165
duce heat loss to the environment. In experiments, it is nearly 0 240 165
impossible to perfectly insulate all surfaces when air is chosen as Cold wall 310 70 165
310 155 165
310 240 165
Table 1 Top wall 155 310 70
Solid material thermal properties. 155 310 240
Material q (kg m3) cp (J kg1 K1) k (W m1 K1) Bottom wall 155 0 70
155 0 240
Aluminium 2707 896 206
Polycarbonate 1200 1300 0.21 Back wall 155 240 310
202 C. Butler et al. / Experimental Thermal and Fluid Science 44 (2013) 199–208

the centre line (W/2) by 10 mm to prevent interfering with the PIV 1

experiments. Each individual thermocouple is a pair of stranded
conductors with a PTFE insulation. Number of strands and strand
size is 1 mm and 0.2 mm respectively. To mount the thermocou-
ples to get an accurate reading of the cavity wall surface tempera-
tures, a 2 mm hole was drilled from the exterior side of the wall
down to a depth of 1 mm from the interior side. The thermocouple
was then imbedded into the body ensuring the tip was in direct
contact with the material surface. The remaining gaps were filled
with thermal heat sink compound and the fixed in placed with
epoxy. Using this method the thermocouple cables did not inter-
Fig. 2. Time averaged v =v max for different image sequence sizes N at three different
fere with flows inside the compartment. For the cylinder, a 1 mm
locations.
indentation was made on the surface and the thermocouple tip
was imbedded inside. Again it was fixed in place with epoxy. The
cables were run along the cylinder surface and out the cylinder
mounting hole on the back wall.
The thermocouples had been calibrated in a Lauda Ecoline
Staredition Re104 waterbath prior to fixing them to the rig to an
accuracy of 0.2 K. The temperatures were recorded by the Agilent
34970A data logging system fitted with a 34902A 16 Channel Mul-
tiplexer setup to record temperatures. It has a built-in thermocou-
ple reference junction. The data logger was connected to a PC for
monitoring and downloading of the results via the Aglient Bench-
Link Data Logger software.

2.3. PIV measurements

PIV was used to measure the velocity fields within the compart-
ment after steady-state conditions were reached. Steady-state is
defined as less than a 0.1 K change in temperature over a 1 h period.
This period was found to be approximately equal to 12 h. A Litron
LP-1000 400 mJ Nd-Yag laser with a wavelength of 532 nm was
used as the light source. The laser was equipped with a lens system Fig. 3. Experimental setup.
which produced a diverging laser sheet with a thickness of 2.5 mm.
The laser light sheet entered the cavity by reflecting it off of a mirror 600 ls. A small hole in the back wall of the cavity was used to seed
positioned at 45° from horizontal and down through a slot cut in the particles into the flow. The hole was sealed again during testing.
top insulation. The laser plane for testing was set up half way be- Approximately 15 min was given for the flow structures to re-sta-
tween the front and back walls of the cavity, i.e. W/2. A TSI Power- bilise after the particles were introduced into the flow.
view Plus 11MP digital CCD camera with 4008  2671 pixels was Fig. 3 is the experimental setup in the laboratory. Note that the
used to capture the images. The camera was fitted with a 60 mm Ni- front and top insulation have been removed for clarity. Shown is
kon lens. The camera was mounted on a traverse system which the square cavity and enclosed cylinder. The double hot wall setup
could be controlled from the PIV Insight 3G software. The traverse can be clearly seen to the right hand side of the cavity, as well as
position could be accurately moved in three directions to a preci- the PID controller, data logger and power supplies. Also shown is
sion of 0.01 mm. For this setup, it was necessary to divide the laser the cold wall fan to the left of the cavity. The PIV equipment is
plane into nine individual sections so the required level of detail in not shown in the figure.
the flow field could be achieved, especially close to the boundary
layers. The instantaneous velocity components of each section were
2.4. Uncertainty analysis
captured and were used to calculate the time average velocities in
the PIV software over a sequence of images. The data for each sec-
The uncertainty in the experimental results was calculated
tion was imported into Matlab, and using the recorded position val-
using the method described in Holman [23], which is based on
ues for each section from the traverse, the overall flow field for the
the method presented by Kline and McClintock [24]. The method
cavity could be stitched together. When stitching together, an over-
lap of 10 mm was allowed between neighbouring sections. To as-
sure that the sampling size for the sequence of images was large Table 3
enough, the time averaged velocity after N number of images was Measurement variable uncertainties.
calculated from Eq. (2) Variable Uncertainty
PN L 0.1 mm
vi
v¼ i¼1
ð2Þ H
N W
d
A sample of the time averaged dimensionless velocity at differ-
T 0.2 K
ent points in the flow field for one of the PIV experiments is shown
V cyl 0.3%
in Fig. 2. It was found that a sequence of 100 images was more than Icyl 0.6%
adequate to achieve less than 3% deviation [22] in the recording of
Vh 1%
the steady state v =v max . Smoke particles were used as seeding. The
Ih
average dt used between laser pulses in these experiments was
 C. Butler et al. / Experimental Thermal and Fluid Science 44 (2013) 199–208 203

is based on the specification of the uncertainties in the various pri- Assuming the cylinder acts as a lumped capacity solid, and that
mary experimental measurements. The list of primary variables it loses heat to a convective environment, then the rate of change
and their associated uncertainties are presented in Table 3. These in internal energy is equal to the heat transfer from the solid by
uncertainties propagate through the calculations with combina- convection and radiation
tions of the different measurement variables. When a function of  
@T
a calculated result R, takes the form of a product of these primary qs cp;s v ol ¼ hAðT conv  T Þ þ reA T 4rad  T 4 ð7Þ
@s
variables and raised to exponents and expressed by
where T conv is defined as the temperature of the surrounding fluid
R ¼ xa11 xa22    xann ð3Þ temperature, T rad is the temperature of the surrounding enclosure
which exchanges heat with the solid by radiation. For this setup,
then the resulting uncertainty x is
T conv and T rad are calculated as the average enclosure temperature
" #12
xR X 1 @Rwx 2 T e , which is defined as the average temperature for all the surfaces
¼ i
ð4Þ not acting as the lumped capacity. Due to the size of the cavity it is
R R @xi reasonable to assume that the average temperature of all the walls
When the result function has an additive form, expressed as is equal to the average temperature of the fluid, therefore
T conv ¼ T rad . The values of h, T conv and T rad vary with time and tem-
R ¼ a1 x1 þ a2 x2 þ    þ an xn ð5Þ perature of the solid.
Applying Eq. (7) to the current setup for a known time incre-
then x for the result is
ment, Ds, and designating the temperatures at the start of a time
( " #)12 increment with p and the temperatures at the end of the period
X  @R 2
xR ¼ x2xi ð6Þ with p þ 1, Eq. (7) becomes
@xi
h    i  
T pþ1 ¼ T p þ hp A T conv ;p  T p þ reA T 4rad;p  T 4p  Ds=qs cp;s v ol
Eqs. (4) and (6) are used in combination when the result func-
tion includes both product and additive terms. Full details are gi- ð8Þ
ven in [23].
Rearranging this in terms of the heat transfer coefficient h, Eq.
(8) becomes
3. Checks on experimental setup 2 3
  
1 4 T pþ1  T p 4 4 5
A number of tests were carried out on the experimental setup to hp ¼      reA T rad;p  T p ð9Þ
A T conv ;p  T p Ds
test its validity compared to data from literature before conducting qs cp;s v ol
experiments, where there is interaction between the cylinder and
cavity. A Ds of 300s was used in Eq. (9) to calculate the values of h over
a longer time period. The average Nusselt number for each time
step can be calculated from
3.1. Cylinder
hl
The cylinder was analysed to test whether it acted as expected Nu ¼ ð10Þ
kf
when compared to data from literature. A transient cool down test
was carried out using the lumped capacity method described in where l is the characteristic length defined here as the cylinder
Holman [19] and is similar to methods outlined in other studies diameter d.
in literature [25–28]. This method allows for a larger range of data To determine the applicability of the lumped capacity analysis
to be collected much faster compared to running individual steady which assumes a uniform temperature distribution throughout
state tests. the solid body, the Biot number was calculated using
The cylinder was heated to approximately 370 K and allowed
reach steady state. Experiments done by Clemes et al. [25] found hl
Bi ¼ ð11Þ
that a starting temperature of at least 303 K above ambient is rec- ks
ommended to generate good results. All of the compartment walls For calculation of the Biot number, it is customary to define l as
were insulated with no active heating or cooling applied. The the ratio of the solids volume to surface area [21]. This analysis
power to the cylinder was then switched off and the cooling was would be expected to yield reasonable estimates within 5% when
recorded by the thermocouple data logging system every 60 s. Bi < 0:1 [19]. The average Biot number was calculated from Eq.
See Fig. 4. (11) and found to be 7:40  104 . It is noted that while it is as-
sumed that the thermal properties of the cartridge heaters, such
as the density and specific heat, are similiar to that of aluminium,
others such as the thermal conductivity may be different. This can
possibly lead to some small errors but they have neglected in this
study.
Implicit in the transient cooling method adopted in this work is
the assumption that the rate of cooling is slow enough that mea-
sured results are near enough to steady state, so that what is being
measured is equivalent to steady state data, and hence can be com-
pared to correlations in literature. This approach has been used by
others [25–28], whereby the process of cooling is assumed quasi-
steady. This assumption is checked in the present experiment
using methods outlined in literature [25,29] by calculating the true
steady state value. To calculate the h for steady state analyses, the
Fig. 4. Cylinder cooling curve. following equation was used,
204 C. Butler et al. / Experimental Thermal and Fluid Science 44 (2013) 199–208

  
hss ¼ ðq  qrad Þ= A T cyl;ss  T e;ss ð12Þ

where q is the power supplied to the cylinder and qrad is the radia-
tion heat transfer rate, and the reference temperature is selected as
the average enclosure temperature. To calculate qrad , the thermal
resistance network was defined for the geometry, see Fig. 5. A radi-
osity node was placed on each surface. Applying energy conserva-
tion at each node, then the net heat transfer from any one surface
i must be equal to the sum of the net radiation to each of the other
surfaces j,
0 1
Ei  J i X@J i  J j A
qrad;i ¼ ¼ 1
ð13Þ
1ei
ei A i j ðAi F ij Þ

where J is the radiosity,is the view factor from one surface to an-
other, and E is the emissive power defined by

Ei ¼ rT 4i ð14Þ
Eq. (13) can be re-written for the ith equation as
X 
J i  ð1  ei Þ F ij J i ¼ ei Ei ð15Þ Fig. 6. Cylinder data compared to correlations.
j

which generates the same number of equations as surfaces which

can then be solved simultaneously to find the values of J. When
all these values are found, the heat transfer coefficient in Eq. (12)
and Nu in Eq. (10) can be calculated.
The results are plotted in Fig. 6 compared with the correlations of
Churchill and Chu [30], Raithby and Hollands [31], and Morgan [32]
for natural convection from horizontal cylinders. The results agree
with the transient data and the correlations within the experimental
uncertainty meaning the assumption of achieving a quasi-steady
state for calculating h in Eq. (9) is justified. Because it takes 12 h to
reach a steady state condition, it is not practical to do this for all
the measurements. The average experimental uncertainty for
xNu =Nu in Fig. 6 for the transient and steady state data is 18.2%
and 5.2% respectively. The uncertainty in the transient data is great-
 
er mainly due to the T pþ1  T p term in Eq. (9). The uncertainty in-
creases as Racyl decreases because as the cylinder cools T p ! T conv ;p .
 
This causes the temperature difference in T pþ1  T p between each

Fig. 7. Cylinder velocity vector map.

Fig. 5. Thermal resistance network for cylinder and cavity, where subscripts 1, 2, 3,
4, 5, 6 and 7 represent the cylinder, hot wall, cold wall, top wall, bottom wall, front
wall and back walls respectively. Fig. 8. Cavity cooling curve.
 C. Butler et al. / Experimental Thermal and Fluid Science 44 (2013) 199–208 205

time step to reduce until it becomes the same order of magnitude as

the uncertainty in the temperature measurement. Fig. 6 only pre-
sents data, where the average xNu =Nu < 20%. This corresponds to
the temperature data between s ¼ 0 and the line of ‘‘useful data’’
in Fig. 4. To show whether the enclosure size will influence Nu, the
criteria described by [33] was used. It is given by

H
¼ 1:26Ra0:0593 ð16Þ
d
For the largest Racyl in the present study, Hd is over four times lar-
ger than this criteria meaning the enclosure size will have no effect
on the cylinder Nu and the cylinder acts as though it is in infinite
atmosphere.
Shown in Fig. 7 is the velocity vector map of the compartment
with power supplied to the cylinder and no temperature difference
across the cavity and all walls insulated. The flow structures were
found to be quite similar to those presented by Moukalled and
Acharya [3] and Kim et al. [34] for the case of a cylinder generating
heat inside an enclosure.
Fig. 9. Cavity data compared to correlations.
3.2. Cavity

Checks similar to those conducted on the cylinder were done for

the differential cavity to see if it acted as expected compared to the
Table 4 literature. The cylinder was left inside the compartment to see
Experimental test matrix. whether or not it would effect the differential cavity setup. A sim-
DT cav (K) qcyl (W) ilar transient test was carried out with a starting DT of 60 K. Power
h  104 (–)
was supplied to the hot wall by the Elektro-Automatik Variable
40 3 3.96
Transformer and the cold wall was cooled using the desktop fan.
5 5.85
8 7.89 Again the cavity was allowed to cool and the temperatures were
13 12.76 recorded every 60 s. See Fig. 8.
50 3 3.33 The values of hh were calculated using Eq. (9) and the values of
5 4.94 Nuh were calculated using Eq. (10), where l ¼ H. The average Bi cal-
8 7.16 culated from Eq. (11) for the experiment was 1:172  104 < 0:1.
13 10.56 Again, to test the assumption of achieving a quasi-steady state
60 3 2.93 for the cooling process, some true steady state measurements were
5 4.24 taken. The steady state values of hh and Nuh were calculated from
8 6.08
13 9.08
Eqs. (12) and (10) respectively. The temperature difference in Eq.
(12) was chosen as DT ¼ T h  T c .

Fig. 10. Cylinder data with interaction from the cavity compared to correlations.
206 C. Butler et al. / Experimental Thermal and Fluid Science 44 (2013) 199–208

The results are plotted in Fig. 9 compared with the correlations et al. [38] for natural convection in cavities with active vertical
of Berkovsky and Pole [35], Kimura and Bejan [36], Bejan [37], Bäiri walls. The results agree with the transient data and the correlations

Fig. 11. Velocity vector maps of cylinder with cavity interaction.

 C. Butler et al. / Experimental Thermal and Fluid Science 44 (2013) 199–208 207

within the experimental uncertainty. It also shows the cylinder improvement in the convective heat transfer. The average xNu =Nu
seems to have negligible effects on the heat transfer of the cavity for these tests is 5.45%.
in this setup. The average experimental uncertainty for xNu =Nu in The results in Fig. 10 are seen to fall into 4 distinct groups.
Fig. 9 for the transient and steady state data is 19.9% and 3.4% Within each group there are 3 sets of data. The 4 groups corre-
respectively. The reason for the larger uncertainty for the transient spond to the different cylinder powers applied and the 3 contained
data is given in Section 3.1. sets correspond to the temperature gradients applied to the cavity
walls (see Table 4). The lowest value of h occurs at the lowest qcyl
4. Cylinder and cavity interaction and highest DT cav applied. At this point the cylinder fits the corre-
lations as it remains undisturbed by the cavity. There is some ob-
Section 3 has shown that individually, both the cylinder and the served increase in Nu with decreasing DT cav . At the point of
cavity act as expected when compared to other studies in literature greatest h , the qcyl is the highest and the DT cav is the lowest. There-
and there is no interaction between them. The general agreement fore as qcyl is increased, there is an increased interaction with the
between the results and the literature data provided confidence cavity causing the corresponding improvement in Nu compared
in the experimental setup, and measurements were conducted to to the correlations.
investigation the interaction when the cylinder is heated and the The velocity vector maps measured by PIV are shown in Fig. 11.
cavity is differentially heated. They are presented in table format, where values of h are approxi-
For these tests, a constant power was supplied to the cylinder, mately constant along the rows, and values of Racav number are
two vertical side walls were differentially heated to isothermal approximately constant along the columns (It should be noted that
conditions and the remaining walls were insulated and assumed in Fig. 11f a higher value of h could not be achieved due to limitations
adiabatic. A range of tests were conducted for different values of in the power supply used in the experimental setup). Comparing these
qcyl and DT cav ¼ T h  T c , and are presented in Table 4. The value to Fig. 7, it can be seen that the flow structures are now greatly influ-
of h is used to relate the thermal conditions of the cylinder to enced by the temperature difference across the side walls. The flow
the cavity for any given test. It is defined as the ratio of the Grashof structures are made up of a plume rising from the hot wall, flowing
number of the cylinder to that of the cavity. The fluid thermal along the top surface, then being cooled by the cold wall and falling
properties are calculated at T film (Eq. (1)) and hence cancel, giving to the bottom surface. It is then entrained by the hot wall again, setting
3  up a circular flow pattern along the cavity walls. For the lower values
 d T cyl  T ref
h ¼ ð17Þ of h , the cylinder plume is contained within the flow of the cavity, and
H3 ðT h  T c Þ
the values of Nu in Fig. 10 suggest that the cylinder acts as expected.
All measurements for these tests were taken at steady state The vortices in the top half of the cavity are seen to be influenced
(less than a 0.1 K change in temperature over a one hour period). by h . Close to the hot wall, the plume from the cylinder traps a
Each test condition was run three times for repeatability. The val- smaller re-circulating vortex from the faster flowing air rising from
ues of h and Nu for the cylinder were calculated using Eqs. (12) and the hot wall. As h increases, the cylinder begins to draw more air,
(10) respectively. reducing the flow velocity magnitude along the hot wall, allowing
To compare the heat transfer on the cylinder in this analysis to the upper vortex to grow as the lower vortex becomes further en-
the correlations for natural convection from horizontal cylinders, trained into the cylinder plume. This continues to the point, where
an appropriate T ref is required to see whether or not there is any at the higher values of h , this vortex becomes trapped between the
change in the heat transfer due to the interaction from the cavity. cylinder and growing upper vortex. As this trapped vortex contin-
For the literature currently available which deals with the case of a ues to grow it causes the deflection seen in the cylinders plume
heat generating body in a differentially heated enclosure [5,7–10], (Figs. 11e and 11f). At lower values of h it can be seen that the
results have been only presented which examine the effect the plume is drawn towards the hot wall (Fig. 11a), but as h increases,
internal body has on the heat transfer of the enclosure side walls. it becomes increasingly drawn to the cold wall (Fig. 11e). Because
For these cases, T ref is based on the cold wall temperature T c . This the cylinder is now capable of drawing air directly from the cavity
seems like the appropriate T ref to use in these cases as the Nu and flow, a corresponding increase in Nu compared to the correlations is
Ra of the sidewalls are based on the temperature difference be- observed in Fig. 10. What can be seen happening is the progressive
tween them, i.e. DT ¼ T h  T c . The literature data which deals with break down of the cylindrical flow of the cavity sidewalls by the cyl-
a heat generating body in an isothermal enclosure [11,14– inder, and the transition process described by [5] is observed,
17,34,39] choose T ref as the enclosure temperature T e , so for calcu- whereby the flow transitions from being dominated by the temper-
lations, DT ¼ T cyl  T e . Similarly, if the cylinder is in a very large ature difference across the cavity to that dominated by the temper-
enclosure or external flows [27,30,40,41], T ref is chosen as the sur- ature difference due to the cylinder.
rounding bulk or ambient temperature T 1 . For the current analysis,
the most appropriate T ref which can be used to both compare the 5. Conclusions
cylinder data against correlations in literature, and take into ac-
count the temperature difference between the side walls, has been The aim of this study was to experimentally investigate the nat-
chosen as the average enclosure temperature, which is calculated ural convection from a heated horizontal cylinder enclosed in a
as the average temperature of all the cavity surfaces. This defini- square cavity, where a temperature difference exists across its side
tion is based on the choice of T ref from the previous studies just dis- walls and to investigate what influence the interaction has on the
cussed, that also use the enclosure temperature as the reference heat transfer of the cylinder. The investigation was conducted by
temperature. In these cases however, the walls are at an equal tem- measuring surface temperatures so the Nusselt numbers could be
perature, so the average enclosure temperature will still be equal evaluated, and PIV was used to record the flow structures gener-
to the temperature of a single wall. ated. It has been found that at the lower values in the range of cyl-
The results are plotted in Fig. 10 compared with the correlations inder Rayleigh numbers tested, the values of the cylinder Nusselt
of Churchill and Chu [30], Raithby and Hollands [31], and Morgan number follow the correlations from literature. As the cylinder
[32] for natural convection from horizontal cylinders. The values Rayleigh number increases, they deviate from these correlations,
of Nu fit the correlations at the lower values of Racyl , but as Racyl in- as the rate of heat transfer is increased due to the interaction of
creases Nu also increases compared to the correlations. This means the cylinder and cavity. The choice of reference temperature was
that as Racyl increases, the interaction from the cavity causes an found to be very important so a direct comparison between the
208 C. Butler et al. / Experimental Thermal and Fluid Science 44 (2013) 199–208

current results and the correlations could be achieved. PIV mea- [17] F. Corvaro, M. Paroncini, An experimental study of natural convection in a
differentially heated cavity through a 2D-PIV system, International Journal of
surements were used to illustrate the interaction, and a transition
Heat and Mass Transfer 52 (2009) 355–365.
process is observed, whereby the flow transitions from being dom- [18] T. Fusegi, J. Hyun, K. Kuwahara, B. Farouk, A numerical study of three-
inated by the temperature difference across the cavity to that dom- dimensional natural convection in a differentially heated cubical enclosure,
inated by the temperature difference due to the cylinder. International Journal of Heat and Mass Transfer 34 (1991) 1543–1557.
[19] J. Holman, Heat Transfer, ninth ed., McGraw-Hill, Boston, 2002.
[20] R. Siegel, J. Howell, Thermal Radiation Heat Transfer, seventh ed., Hemisphere
Acknowledgement Publishing Corporation, New York, 1981.
[21] F. Incropera, D. DeWitt, Fundamentals of Heat and Mass Transfer, third ed.,
John Wiley & Sons, New York, 1990.
The research leading to these results has received funding from [22] W. Saleh, R. Bowden, I. Hassan, L. Kadem, Techniques of PIV stratified two-
the European Community’s Seventh Framework Programme FP7/ phase headers, Experimental Thermal and Fluid Science 35 (2011) 82–95.
2007–2013 under Grant agreement No. 213371, MAAXIMUS [23] J. Holman, Experimental Methods for Engineers, seventh ed., McGraw-Hill,
New York, 2001.
(http://www.maaximus.eu). [24] S. Kline, F. McClintock, Describing uncertainties in single-sample experiments,
Mechanical Engineering 75 (1953) 3–8.
References [25] S. Clemes, K. Hollands, A. Brunger, Natural convection heat transfer from long
horizontal isothermal cylinders, Journal of Heat Transfer 116 (1994) 96–104.
[26] W. Liu, J. Davidson, F. Kulacki, S. Mantell, Natural convection from a horizontal
[1] A. Bejan, Convection Heat Transfer, third ed., John Wiley & Sons, New York,
tube heat exchanger immersed in a tilted enclosure, Journal of Solar Energy
2004.
Engineering 125 (2003) 67–76.
[2] R. Warrington, R. Powe, The transfer of heat by natural convection between
[27] C. Popiel, J. Wojtkowiak, Experiments on free convection heat transfer from
bodies and their enclosures, International Journal of Heat and Mass Transfer 28
side walls of a vertical square cylinder in air, Experimental Thermal and Fluid
(1985) 319–330.
Science 29 (2004) 1–8.
[3] S. Moukalled, S. Acharya, Natural convection in the annulus between
[28] C. Popiel, J. Wojtkowiak, K. Bober, Laminar free convective heat transfer from
concentric horizontal circular and square cylinders, Journal of
isothermal vertical slender cylinder, Experimental Thermal and Fluid Science
Thermophysics and Heat Transfer 10 (1996) 524–531.
32 (2007) 607–613.
[4] G. Cesini, M. Paroncini, G. Cortella, M. Manzan, Natural convection from a
[29] A. Hassani, K.G. Hollands, On natural convection heat transfer from three-
horizontal cylinder in a rectangular cavity, International Journal of Heat and
dimensional bodies of arbitrary shape, Journal of Heat Transfer 111 (1989)
Mass Transfer 42 (1999) 1801–1811.
363–371.
[5] J. Oh, M. Ha, K. Kim, Numerical study of heat transfer and flow of natural
[30] S. Churchill, H. Chu, Correlating equations for laminar and turbulent free
convection in an enclosure with a heat-generating conducting body, Numerical
convection from a horizontal cylinder, International Journal of Heat and Mass
Heat Transfer Part A – Applications 31 (1997) 289–303.
Transfer 18 (1975) 1049–1053.
[6] J. Lee, M. Ha, A numerical study of natural convection in a horizontal enclosure
[31] G.D. Raithby, K.G.T. Hollands, in: W.M. Rohensow, J.P. Harnett, E.N. Ganic
with a conducting body, International Journal of Heat and Mass Transfer 48
(Eds.), Handbook of Heat Transfer Fundamentals, second ed., McGraw Hill,
(2005) 3308–3318.
New York, 1985, pp. 6–25.
[7] J. Lee, M. Ha, Numerical simulation of natural convection in a horizontal
[32] V. Morgan, Heat transfer by natural convection from a horizontal isothermal
enclosure with a heat-generating body, International Journal of Heat and Mass
circular cylinder in air, Heat Transfer Engineering 18 (1997) 25–33.
Transfer 49 (2006) 2684–2702.
[33] P. Warrington, S. Smith, R. Powe, R. Mussulman, Boundary effects on natural
[8] M. Ha, M. Jung, A numerical study on three-dimensional conjugate heat
convection heat transfer for cylinders and cubes, International Journal of Heat
transfer of natural convection and conduction in a differentially heated cubic
and Mass Transfer 31 (1988) 1322–1325.
enclosure with a heat-generating cubic conducting body, International Journal
[34] B. Kim, D.S. Lee, M. Ha, H. Yoon, A numerical study of natural convection in a
of Heat and Mass Transfer 43 (2000) 4229–4248.
square enclosure with a circular cylinder at different vertical locations,
[9] M. Jami, A. Merzhab, M. Bouzidi, P. Lallemand, Lattice boltzmann method
International Journal of Heat and Mass Transfer 51 (2008) 1888–1906.
applies to the laminar natural convection in an enclosure with a heat
[35] B.M. Berkovsky, V.K. Polevikov, Heat transfer and turbulent buoyant
generating cylinder conducting body, International Journal of Thermal
convection, in: D.B. Spalding, N. Afgan, Numerical Study of Problems on
Sciences 46 (2007) 38–47.
High-Intensive Free Convection, vol. 2, Hemisphere Publishing Corporation,
[10] M. Jami, A. Mezrhab, H. Haji, Numerical study of natural convection in a square
Washington D.C., 1977, pp. 443–455.
cavity containing a cylinder using the lattice boltzmann method, Engineering
[36] S. Kimura, A. Bejan, The boundary-layer natural-convection regime in a
Computations 25 (2008) 480–489.
rectangular cavity with uniform heat-flux from the side, Journal of Heat
[11] H. Yoon, B. Ha, D. Kim, D. Yu, Effect of the position of a circular cylinder in a
Transfer 106 (1984) 98–103.
square enclosure on natural convection at rayleigh number of 10(7), Physics of
[37] A. Bejan, Note on Gill solution for free convection in a vertical enclosure,
Fluids 21 (2009).
Journal of Fluid Mechanics 90 (1979) 561–568.
[12] H. Yoon, D. Yu, M. Ha, Y. Park, Three-dimensional natural convection in an
[38] A. Bäiri, N. Laraqui, J. García de María, Numerical and experimental study of
enclosure with a sphere at different vertical locations, International Journal of
natural convection in tilted parallelepipedic cavities for large rayleigh
Heat and Mass Transfer 53 (2010) 3143–3155.
numbers, Experimental Thermal and Fluid Science 31 (2007) 309–324.
[13] C. Ekundayo, S. Probert, M. Newborough, Heat transfer from a horizontal
[39] D. Angeli, P. Levoni, S. Barozzi, Numerical predictions for stable buoyant
cylinder in a rectangular enclosure, Applied Energy 61 (1998) 57–78.
regimes within a square enclosure, International Journal of Heat and Mass
[14] M. Davies, D. Newport, T. Dalton, On gaseous free-convection heat transfer
Transfer 51 (2008) 553–565.
with well-defined boundary conditions, Journal of Heat Transfer 122 (2000)
[40] M. Ashajee, A.H. Eshtiaghi, M. Yagoubi, T. Yousefi, Experimental investigation
661–668.
on free convection from a horizontal cylinder beneath an adiabtic ceiling,
[15] D. Newport, T. Dalton, M. Davies, M. Whelan, C. Forno, On the thermal
Experimental Thermal and Fluid Science 32 (2007) 614–623.
interaction between an isothermal cylinder and its isothermal enclosure for
[41] T. Saitoh, T. Sakiji, K. Maruhara, Benchmark solutions to natural convection
cylinder rayleigh numbers of order 10(4), Journal of Heat Transfer 123 (2001)
heat transfer problem around a horizontal circular cylinder, International
1052–1061.
Journal of Heat and Mass Transfer 36 (1993) 1251–1259.
[16] F. Corvaro, M. Paroncini, Experimental analysis of natural convection in square
cavities heated from below with 2D-PIV and holographic techniques,
Experimental Thermal and Fluid Science 31 (2007) 721–739.