1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME
54
EXPERIMENTAL ANALYSIS OF NATURAL CONVECTION OVER A
VERTICAL CYLINDER AT UNIFORM TEMFERATURE
D. Subramanyam 1
M. Chandrasekhar 2
R. Lokanadham 3
1
Professor, Department of Mechanical Engg, CREC, Tirupati, India
2
Associate Professor, Department of Mechanical Engg, CREC, Tirupati, India
3
Associate Professor, Department of Mechanical Engg, CREC, Tirupati, India
ABSTRACT
In the present work, an experimental study of natural convection heat transfer in
vertical circular cylinders immersed in air at uniform wall temperature has been
presented. The outcome of the study is summarized with practical correlation equations
linking to the Nusselt number to the Rayleigh number and Prandtl number. The proposed
regression model was good agreement with the regression models given by previous
authors.
Keywords: Vertical Cylinder, Natural Convection, Uniform Temperature
1 INTRODUCTION
Study of natural convection from over vertical heated cylinders is important in
many applications like vertical tubes of HVAC systems in resistive heating of electronic
components, space shuttle launch pads, wasted nuclear rods stored in repositories,
refrigerating coils and hot radiators etc. To facilitate approximate solution of the set of
coupled conservation equations descriptive of natural convection from a vertical cylinder,
various assumptions need to be implemented, such as uniform surface temperature or
uniform surface heat flux, unidirectional heat transfer, geometrically similar boundary
layer flows etc. Sparrow and Gregg [14] provided the first approximate solution for the
laminar buoyant flow of air bathing a vertical cylinder heated with a prescribed surface
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2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
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temperature by applying the similar method and later using a power series expansion.
Aziz and Na [1] have applied the method of extended perturbation series to solve laminar
natural convection from an isothermal, thin vertical cylinder. Laminar natural convection
along the outer surface a vertical cylinder is compared with a vertical flat plate
numerically by Fujii and Uehara [5].
Large eddy simulations of natural convection along a vertical isothermal surface
have been carried out by Yan and Nilsson [15] using a parallel CFD code. Three-
dimensional convection of air in a vertical cylinder isothermally heated and cooled from a
side wall was numerically computed both in magnetic and gravity fields by Filar et al. [4].
Natural convection in vertical cylinder at variable temperature have been studied
numerically by Jose et al. [7], Kalabin et al. [8], Kwang Hyo Chung et al. [9], Natural
convection from the outer surface of a vertical cylinder to liquids – has been studied
experimentally by Fujii et al. [6].. Sad Jar all and Campo [12] have studied the natural
convection heat transfer in vertical cylinders at constant heat flux experimentally.
In the present investigation, the analysis was carried out to study the natural convection
over a vertical circular cylinder in laminar steady state at uniform wall temperature
enclosed in a large rectangular duct, experimentally.
2 EXPERIMENTAL SETUP AND MEASUREMENT PROCEDURE
When a uniform wall temperature is given, the natural convection heat transfer
problem consists of predicting the wall-to-ambient temperature difference. For
experiment, three cylindrical test sections of different sizes made from stainless steel 301
SS were used. For test section #1, diameter (d1) = 5 cm and length (L1) = 20 cm; for test
section #2, d2 = 6 cm and L2 = 30.5 cm; and for test section # 3, d3 = 6 cm and L3 = 45.1
cm. Each cylinder was placed vertically on a wooden stand inside a large wooden four-
side box about 60 cm x 60 cm x 60 cm. The top ends of the vertical cylinders were
plugged with wooden pieces to avoid internal circulation of air.
The required heat is generated by fixing heating coils inside the inner surface of
the cylinder. An AC power supply is the available source to heat the vertical cylinders to
pre-set temperature values. The power supply is varied with the help of autotransformer.
The voltage and current are measured with voltmeter (0-300 V) and ammeter (0-2A).
Four RTD thermo couples of range 10°C---200°C with 0.1°C resolution, accuracy ±1°C
per the given range are fixed on the outer surface of the cylinder and connected to the
temperature indicator to measure the temperature. The surface temperature of a cylinder
is the average temperature of the four thermo couples. The temperature difference
between these thermo couples is ± 5°C. Fluid properties are evaluated at the film
temperature, T= (Ti+To)/2.
The experiments have been conducted for all the three test sections at uniform
temperatures. For all voltages, the delivering surface temperatures stayed within the
range of 38-78°C. Heat conduction losses through the electric cables and wooden pieces
were not taken into consideration. The schematic diagram of experimental set-up is
shown in Fig 1.1.

3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME
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Fig. 1.1: Physical Model
In the present investigation, the analysis was carried out to study the natural
convection over a vertical cylinder in laminar steady state condition at uniform wall
temperature. The Grashof number, Rayleigh number and Nusselt number were determined by
the following expressions.
2
3
γ
β TLg
Gr
∆
= -- (1)
ϑα
β TLg
Ra
∆
=
3
-- (2)
T4
Wooden box
T1
T2
T3
H
HH
H
Wooden Stand
Wooden cap
Circular
Cylinder
T1 - T4: Thermocouples
H: Heating Coils
Air
Air

4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME
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k
Lh
Nu = -- (3)
=thNu
9
4
16
9
25.0
Pr
492.0
1
67.0
68.0














+
+
Ra
For Ra<109
--(4)
4 RESULTS AND DISCUSSIONS
From the experimental results of three set sections, the relationship between
experimental Nusselt number (Nu), theotical Nusselt number (Nuth), Rayleigh number (Ra)
and Prandtl number (Pr) were established and shown in Fig 1.2, Fig1.3.Fig1.4 respectively.
From the Fig. 1.2, it is observed that the Nusselt number increases with increasing Rayleigh
number. The trend is linear, and the relationship is given by the following equations:
26.0
241.1 RaNu = for d1 --(5)
141.0
125.8 RaNu = for d2 --(6)
35.0
242.0 RaNu = for d3 --(7)
The correlation coefficient for d1 is 0.97; for d2 is 0.89 and for d3 is 0.94, indicating a
fairly good fit.
From Fig.1.3, it is observed that the Nusselt number increases with increasing Rayleigh
number. The trend is linear, and the relationship is given by the following equations:
25.0
554.0 RaNu = for d1 --(8)
22.0
891.0 RaNu = for d2 --(9)
25.0
519.0 RaNu = for d3 --(10)
The correlation coefficient for d1 is 0.99; for d2 is 0.97 and for d3 is 0.99, indicating a
very good fit. The relationship between product of Rayleigh number & Prandtl number
(Ra.Pr) and theoretical Nusselt number is shown in Fig. 1.4. It is observed that the theoretical
Nusselt number increases with increasing the product of Rayleigh number and Prandtl
number. The trend is linear and the relationship is given by the following equation with
correlation coefficient 0.98.
Nuth = 0.678 (Ra.Pr)0.25
--(11)

5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME
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Ra vs Nu
0
50
100
150
200
0 50000000 100000000
Ra
Nue
d1
d3
d2
Fig. 1.2: Ra vs Nu
Ra vs Nuth
0
10
20
30
40
50
60
0 50000000 100000000
Ra
Nuth
d1
d2
d3
Fig. 1.3: Ra vs Nuth
Ra.Pr vs Nuth
0
10
20
30
40
0 5000000 10000000 15000000 20000000
Ra.Pr
Nuth
Fig. 1.4: Ra.Pr vs. Nuth
Nu

6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME
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5 VALIDATION
The validity of the proposed regression model for predicting Nusselt number in terms
of Rayleigh number and Prandtl number is best assessed by comparing the predicted values
with values obtained by the other numerical models. For this purpose reported regression
models of different Authors were compared with the proposed regression model.
Comparison of the present results with Bejan & LeFevre
The validity of the proposed regression models for predicting Nusselt number in terms
of Rayleigh number and Prandtl number is best assessed by comparing the predicted values
with values obtained by the other numerical models. For this purpose reported regression
models of Bejan and LeFevre for the case of free convection heat transfer in vertical cylinder
at uniform wall temperature is given below:
According to Bejan , Nu = 0.689 (RaPr)0.25
for Ra < 109
- (12)
proposed regression model, Nu = 0.678 (Ra. Pr)0.25
for Ra < 109
-(13)
According to Le Fevre
DP
HP
P
PR
Nu
r
r
r
ra
)6364(35
)315272(4
)2120(5
7
3
4 4
1
+
+
+





+
= - (14)
Table.1. Comparison of the present results with Bejan
Ra
Nu 2 x 105
2 x 106
2 x 107
2 x 108
2 x 109
Bejan Nu 13.33 23.70 42.15 74.95 133.28
Present Nu 11.65 20.24 35.18 61.14 106.24
Deviation 1.68 3.46 6.97 13.81 27.04
Table. 2. Comparison of the present results with Le Fevre [62]
Ra
Nu 2 x 105
2 x 106
2 x 107
2 x 108
2 x 109
Le Fevre 11.56 20.55 36.54 64.98 115.56
Present Nu 11.65 20.24 35.18 61.14 106.24
Deviation 0.009 0.31 1.36 3.84 9.32

7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
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The predicted values of Nusselt number at Pr = 0.7 from Bejan expression (11), and
the proposed regression model are shown in table 1. The predicted values of Nusselt number
by using proposed regression model are lower than the results of Bejan. The difference being
in the range of 12.6% to 20%, which indicate the good agreement between these two models.
The predicted values of Nusselt number at Pr = 0.7 from expression (14) and
proposed regression model are given in Table 2. The predicted values Nusselt numbers by
both expressions are close to each other. The difference being 0.8% to 8%, which indicated
that these two models are in good agreement each other. The graphical representations of
these three models are shown in Fig. 1.5.
Fig. 1.5: Ra vs Nu
6 CONCLUSIONS
In the present work, an experimental study of natural convection heat transfer in
vertical circular cylinders immersed in air at uniform wall temperature has been presented.
The analysis was carried out along the length and diameter of the cylinders. The outcome of
the study is summarized with practical correlation equations linking to the Nusselt number to
the Rayleigh number and Prandtl number. The proposed regression models were validated
with the regression models given by the Bejan [11], and LeFevre et al. [62]. The proposed
regression models are in good agreement with the above mentioned authors. Further, the
analysis can be extended to the cases of different aspect ratios, with different materials and
with different boundary conditions.
REFERENCES
1. Aziz. A and Na T.Y(1982). Improved Perturbation Solution for laminar natural
convection on a vertical cylinder; J. of Heat and Mass Transfer, Vol. 16, No. 2,
pp. 83-87 .
Ra vs Nu
0
100
200
300
400
2000 2000 2000020000
2E+09
Ra
Nu
Bejan
present
LeFevre
For Pr =0.7

8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME
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2. Bejan, A(1984)., Convection heat transfer, 2nd
edition, John Wiley and sons, Inc.,
3. Bejan, A(2003)., Heat Transfer, John Wiley and Sons, Inc.
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AUTHORS’ INFORMATION
Dr. D. Subramanyam has received Ph.D in 2010 and M.Tech in
2005 from S.V.University, Tirupati, Andhra pradesh, India. His previous
was research focused on Heat transfer. He is working as Professor in
Mechanical Engineering at CREC, Tirupati, India.
M. Chandrasekhar has received M.Tech in Manufacturing
Engineering in 2006 from VIT University, Vellore, India. He is working
as Associate professor in Mechanical Engineering at CREC, Tirupati,
Andhra pradesh, India.
R. Lokanadham is research scholar in mechanical engineering at
S.V.University, Tirupati, Andhra pradesh, India. He has received M.E in
Thermal Engineering in 1999 from Bharatiyar University, Tamilnadu,
India. He is working as Associate Professor in Mechanical Engineering
at CREC, Tirupati, A.P, India.