NATURAL CONVECTION HEAT TRANSFER INSIDE INCLINED OPEN CYLINDER

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 11, November (2014), pp. 92-103 © IAEME
92
NATURAL CONVECTION HEAT TRANSFER INSIDE
INCLINED OPEN CYLINDER
Ali F. Hasobee1
, Yasin K. Salman2
1,2
Department of Energy Engineering, University of Baghdad
ABSTRACT
Natural convection is investigated experimentally in an inclined open cylindrical passege
heated under constant heat flux condition to study the effect of angle of inclination and heat flux on
heat transfer. Heat transfer results are given for inclination angles of 0o
(horizontal), 30o
, 60o
and 90o
(vertical).Using cylinder diameter of 4.8 cm, cylinder length 50 cm and heat flux from 70 W/m2
to
600 W/m2
. Empirical correlations are given for the average Nusselt number as a function of the
Rayleigh number. The results show that the local and average Nusselt number increase as the heat
flux increase and when angle of inclination changed from 0o
(horizontal) to 90o
(vertical). An
empirical correlations of average Nusselt number as a function of Rayleigh number were obtained.
Keywords: Heat Transfer, Natural Convection, Inclined Cylinder, Empirical Correlation
NOMENCLATURE
AS: Tube surface area (m2
)
D: Tube diameter (m)
R: Tube radius (m)
F1-2: view factor between tube walls
Grm: Mean Grashof number,
୥ ఉ஽యሺ୲౩ഥ ି୲ౘതതതሻ
௩మ
G: Gravitational acceleration (m/s2
)
hX: Local heat transfer coefficient (W/m2
.K)
hഥ:Average heat transfer coefficient (W/m2
.K)
K: Thermal conductivity (W/m.K)
L: Axial length of the tube (m)
X*: Dimensionless axial distance, X/D
NuX: Local Nusselt number, hX.D/K
Num: Mean Nusselt number
Pr: Prandtl number,µ . Cp/k
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND
TECHNOLOGY (IJMET)
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 5, Issue 11, November (2014), pp. 92-103
© IAEME: www.iaeme.com/IJMET.asp
Journal Impact Factor (2014): 7.5377 (Calculated by GISI)
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IJMET
© I A E M E

93
V: Heater voltage, volt.
I: Heater current.Amp.
C: Heat transfer by convection (W)
QCd: Heat transfer by conduction (W)
Qt: Total heat input (W)
Qcr: Heat transfer by convetion and radiation (W)
qc: Convetion heat flux (W/m2
)
qr: Radiation heat flux (W/m2)
qcr: Convetion –radiation heat flux (W/m2
)
Ram: Mean Rayleigh number, Gm.Pr
Cp: Specific heat at constant pressure, (kJ/kg.Co
)
(Tb )x: Local bulk air temperature
ܶത௕=Average bulk air temperature
(Ts)x : local tube surface temperatures (Co
)
ܶௌ
ഥ : Average tube surface temperature (Co
)
Greek symbols
ߚ=Coefficient for volumetric thermal expansion (K-1
)
ߝ=Emissivity; inner surface and outer surface
µ=Fluid viscosity (kg/m.s)
‫=ݒ‬Kinematics viscosity (m2
/s)
ߩ=Fluid density (kg/m3
)
ߪ=Stefan-Boltzman constant (W/m2
.K4
)
ߠ=Inclination angle
I. INTRODUCTION
Natural convection induced by thermal buoyancy effects in a gravitational force field is
observed in many applications. These include electronic components design, air conditioning of
buildings, design of storage of hot fluids in solar power plants and food. Inclination of containers
filled with fluid, inside which convective heat or mass transfer occur, may have either desirable or
undesirable effects depending on the application. Effects of inclination on heat transfer have been
explored in practical applications involving solar energy heaters and double glazed windows. Martin
[1] made predictions of the lower limiting conditions of free convection in the vertical open circular
cross-section passage with uniform wall temperature. The overall heat transfer rate was independent
of tube length but proportional to radius, unless the length-radius ratio is about 1.8, in which case it
depends also on temperature conditions at the closed end..Shigeo and Adrian [2] studied
experimentally natural convection in a vertical pipe with different end temperature with (L/D=9).
The Rayleigh number was in the range 108<Ra<1010. It was concluded that the natural convection
mechanism departs considerably from the pattern known in the limit Ra → 0. Specifically, the end-
to-end heat transfer was affected via two thin vertical jets, the upper (warm) jet proceeding along the
top of the cylinder toward the cold end and the lower (cold) jet advancing along the bottom in the
opposite direction. The Nusselt number for end-to-end heat transfer was shown to vary weakly with
the Rayleigh number. Shenoy [3] presented a theoretical analysis of the effect of buoyancy on the
heat transfer to non-newtonian power-law fluids for upward flow in vertical pipes under turbulent
conditions. The equation for quantitative evaluation of the natural convection effect on the forced
convection has been suggested to be applicable for upward as well as downward flow of the power-
law fluids by a change in the sign of the controlling term. Rahman and Sharif [4] conducted a
numerical investigation for free convective laminar flow of a fluid with or without internal heat
generation (Ra= 2 × 1010) in rectangular enclosures of different aspect ratios (from 0.25 to 4), at

94
various angles of inclination, of insulated side walls, heated bottom, and cooled top walls. They
observed that the convective flow and heat transfer were almost the same as that in a cavity without
internal heat generating fluid. Akeel A. Mohammed [5] carried out Experiments to investigate
natural convection heat transfer in an inclined uniformly heated circular cylinder. The effects of
surface heat flux and angle of inclination on the temperature and local Nusselt number variations
along the cylinder surface are discussed. The investigation covers heat flux range from 92 W/m² to
487 W/m², and angles of inclination 0° ( horizontal) , 30° , 60° and 90° (vertical) . Results show an
increase in the natural convection as heat flux increases and as angle of inclination moves from
vertical to horizontal position and the effect of buoyancy is small at the cylinder entrance and
increases downstream. Boris Brangeon et al. [6] carried out with the numerical investigation of
unsteady laminar, natural convection in an asymmetrically heated inclined open channel (θ = 00,
450, 600 and 750) with walls at uniform heat flux (q = 10, 50, 75 and 100W/m2). Two
methodological approaches have been adopted to investigate the air flow in this case: 2D and 3D
DNS and four sets of inlet-outlet velocity-pressure boundary conditions have been considered. The
literature survey indicates that most researchers have studied natural convection heat transfer through
open and closed horizontal and vertical cylinder, but there was little information about the inclined
cases. The purpose of the present study was to provide experimental data on free convective heat
transfer from open ended inclined circular tube with a constant heat flux and to propose a general
empirical equations for this problem.
2. EXPERIMENTAL APPARATUS
A schematic diagram and photograph of the experimental setup of the apparatus are shown in
Fig. (1) and Fig.(2)respectively. It consists essentially of an aluminum tube .The internal diameter of
the tube is 46 mm and its length is 500 mm. The tube is mounted in the entrance on a well-designed
teflon Bellmouth (A) fitted at the entrance of the tube which have the same inside diameter of the
tube, the teflon piece is 12 cm in length, another teflon piece (B) with the same length and diameter
of (A) was fixed on the exit section of the tube. Teflon was chosen because of its low thermal
conductivity in order to reduce the heat loss from the tubes ends. The tube components mounted on
wooden board (W) with four long rivets fitted with nets on the board .The board can rotated around a
horizontal spindle. The inclination of the tubes to the horizontal can thus be adjusted as required. The
tube surface is electrically heated by means of nickel –chromium wire (main heater) of 0.3 mm in
diameter and 5Ω per meter resistance. The wire is electrically insulated by means of ceramic beads
and is wound uniformaly along the tube length with an asbestos rope of 5 mm thickness in order to
give auniform heat flux. As seen in Fig.(3) The main heater is covered by 30 mm thick asbestos
ropes on which three pairs of thermocouples (A1/A2, B1/B2, C1/C2) are fitted at an aluminum
plates with 10 mm thickness asbestos rope between it and 10 mm thickness asbestos rope was
wounded on it where an electric (guard-heater) is uniformly wounded . For a certain main heater
input the guard-heater input could adjusted so that the thermocouple forming in each pair registered
the same temperature ensuring that all heat generated by the main heater flows to the inner surface of
the tube .An asbestos rope of 10 mm thickness covered the guard- heater. A fiber-glass layer (H) of 7
mm thickness serves as an outside cover for the heating system The axial temperature distribution of
the tube surface have been measured by using 17 Type K (chromel – alumel) thermocouples of 0.276
mm in size. The 17 thermocouples are drilled in the surface at a uniform distances along the axis of
the tube, all of the thermocouples are fixed with (Defcon adhesive). Three additional thermocouples
were fixed at the midpoint of the outer surface tube, spaced 90 angle dgree, to measure the
temperature distribution in the circumferential direction. The temperature difference was found
negligible in the circumferential direction, hence the tube surface was assumed to be
circumferentially isothermal. One thermocouple is fixed in the entrance of the tube to measure the

95
inlet temperature and three thermocouples are fixed in the exit part to measure the outlet
temperature. . All thermocouples were used with leads, the thermocouples with and without lead
were calibrated against the melting point of ice made from distilled water and the boiling points of
several pure chemical substances .The power consumed by the heater was measured by an ammeter
and voltmeter. A three variac units was used to control the power supplied to the heaters by
controlling the voltage across the heaters, a data logger pico- (Tc-008) was used to record the
thermocouple outputs to accuracy within 0.03 mV.
Fig.(1) Schematic diagram of experimental apparatus:
(A) Lower Teflon piece(Bellmouth); (B) Upper teflon piece; (C)Thermocouples of the outlet
hole;(D) Outer tube; (E)Asbestos layer heater;(F)Guard heater;(G)Thermocouples for the inlet hole;
(H)Fiber glass layer; (K)Wooden box; (W) Wooden board.
Fig.(2):Photographic of Test apparatus

96
Fig.(3) Cross-section through apparatus. (1) thermo couples of the tube; (2)tube heater with 5 mm
(thickness) asbestos rope ; (3) 30 mm (thickness) asbestos rope; (4) 10 mm (thickness) asbestos
rope; (5) 10 mm (thickness) asbestos rope; (6) Guard Heater; (7) 10 mm (thickness) asbestos rope
(8) 7 mm (thickness) fiber glass layer.
3. EXPREMENTAL PROCEDURE
To achieve the experiments with working conditions, the following procedures were followed:
A. The test apparatus prepared to insure the well performance of all components.
B. Adjusting the required inclined angle.
C. The supply power to the electric elements was switched on, and it was adjusted by variac to
obtain the same required constant heat flux, then it was left in operation action for a period
until the surface temperature of the cylinders reached to steady state after about (6hours) .
D. During each experiment, at all selected temperature recording position the temperature
recorded by data logger for each interval time about of (15 minutes), together with the input
voltage and current.
4. EXPERIMENTAL DATA REDUCTION
The experimental apparatus described in Section (2) has been used to provide the
experimental data for heat transfer calculations through the tube .The tube was subjected to uniform
heat flux. The total power supplied to the cylinder calculated as follows:
Qt =V×I ….. (1)
The convection radiation heat transferd from the any of the tubes suface is:
Qcr = Qt-Qcond …... (2)

97
Where Qcond is the axial conduction heat loss which was found experimentally equal to 3% of the
input power.The convection and radiation heat flux can be represented by:
qcr= (Qcr )/As …………… (3)
where: (AS=2πRL)
The convection heat flux which is used to calculate the local heat transfer coefficient is obtained
after deduce the radiation heat flux from qcr.The local radiation heat flux can be calculated as
follows:
qr = F1-2ߪߝ((ܶ௦+ 273)4
- ሺܶ௦
ഥ+ 273)4
) …… ... (4)
where:
Fଵିଶ ≈ Fଶିଵ ≈ 1
Hence the convection heat flux at any position is:
qc=qcr-qr …… (5)
The radiation heat flux is very small and can be neglected.
Hence:qc=qcr
The local heat transfer coefficient can be obtained as:
(hX) =
௤೎
ሺ୘౩ሻ౮ି ሺ୘ౘሻ౮
…… (6)
All the air properties were evaluated at the mean film air temperature:
(Tf) x =
ሺ୘౩ሻ౮ାሺ୘ౘሻ౮
ଶ
…….... (7)
where:
(Tf)x is the local mean film air temperature atሺTୱሻ୶ .
The local nusselt number for the cylinder (Nux) then can be determine as:
(Nux) =
ሺ୦౮ሻ ஽
୩
…….. (8)
Tୱ
ഥ =
ଵ
୐
‫׬‬ ሺTୱሻ୶ dx
୶ୀ୐
୶ୀ଴
...... (9)
Tୠ
തതത =
ଵ
୐
‫׬‬ ሺTୠሻ୶ dx
୶ୀ୐
୶ୀ଴
..….. (10)
T୤
ഥ=
୘౩തതതത ା୘ౘതതതത
ଶ
…… (11)

98
The averge heat transfer coefficient and the average Nusselt number (Num) based on the
calculation of the averge tube surface temperature and the average bulk air temperature were
calculated as follows:
hത =
ଵ
୐
‫׬‬ h௫ dx
୶ୀ୐
୶ୀ଴
……. (12)
Num =
୯ ஽
୩ሺ୘౩തതതതି୘ౘ
തതതതሻ
……. (13)
Grm =
୥ ఉ஽య ሺ୘౩തതതതି୘ౘതതതതሻ
୴మ
……. (14)
where β =
ଵ
ሺଶ଻ଷା ୘౜
തതതതሻ
Pr=
µ େ౦
୩
……. (15)
Ram = Grm. Pr ……. (16)
All the air physical properties ρ, µ, v and k were evaluated at the average mean film temperature
ሺT୤
ഥሻHolman [7].
5. EXPERIMENTAL UNCERTAINTY
Generally the accuracy of experimental results depends upon the accuracy of the individual
measuring instruments and the manufacturing accuracy of the circular tube. The accuracy of an
instrument is also limited by its minimum division (its sensitivity). In the present work, the
uncertainties in heat transfer coefficient (Nusselt number) and Rayleigh number were estimated
following Kline and McClintock differential approximation method reported by Holman [8]. For a
typical experiment, the total uncertainty in measuring the heater input power, temperature difference
(Ts-Tb), the heat transfer rate and the circular tube surface area were 0.38%, 0.48%, 2.6%, and1.3%
respectively. These were combined to give a maximum error of 2.12% in heat transfer coefficient
(Nusselt number) and maximum error of 2.51% in Rayleigh number.
6. RESULTS AND DISCUSSION
6.1 Temperature variation
The variation of tube surface temperature for different heat flux and for angle of inclination
ߠ = 0°(horizontal) , 30o
, 60°, and 90°(vertical) are shown in Figs.(4)-(7) respectively . It is obvious
from these figures that the surface temperature increases as heat flux increases because of faster
increasing of the thermal boundary layer as heat flux increases. It can be seen from Fig.(4) that atߠ =
0o
, the tube surface temperature have no obvious change with the axial distance except at the end of
the tube due the conduction end losses. This behavior explained that there is no flow in the axial
direction so the bouncy effect is just in the radial direction .For ߠ= 30o
, 60°, and 90°, the distribution
of the surface temperature (Ts) with tubes axial distance for different heat fluxes have the same
general shape as shown in Figs.(5)-(7). The surface temperature distribution exhibits the following
trend: the surface temperature gradually increases with the axial distance at the same rate of the
increasing for the tube until a certain limit to reach a maximum value at approximately(X*= 18)
beyond which it begins to decrease.

99
Fig.(4):Surface temperature variation with the
axial distance for different heat fluxes withߠ
=0o
.
=30o
.
axial distance for different heat fluxes
with ߠ=60o
.
=90o
.
Figs.(8)-(11) show the effect of angle of inclination on the temperature distribution along tube
surface .It is clear that the surface temperature increases as angle of inclination moves from vertical
to horizontal position . When the heat transfers through the wall of a horizontal tube, the warmer air
moves upward along the side walls, and by continuity the heavier air near the smallest temperature
wall of the tube flows downward. As a result, a two symmetrical spiral, like motion is formed along
the tube. The circulation is driven by radial temperature variation, and at the same time it reduces
this temperature variation. These two spiral vortex weak as the angle of inclination moves from
horizontal to vertical position to be single vortex only and the flow would be totally in the axial
direction in the vertical position.
Fig.(8) Surface temperature variation with the axial distance for different angles of inclination, q=70
W/m2
.
Fig.(9) Surface temperature variation with the axial distance for different angles of inclination,
q=300 W/m2
.

100
Fig.(10) Surface temperature variation with
the axial distance for different angles of
inclination,q=400 W/m2
.
Fig.(11) Surface temperature variation with
the axial distance for different angles of
inclination,q=600 W/m2
.
6.2 Variation of local Nusselt number
The local Nusselt number variation along the tube surfaces for different heat fluxs (70 W/m2
to 600 W/m2
) and for angle of inclinationߠ = 00
(horizontal) , 30° ,60°, and 90° (vertical);are shown
by plotting the local Nusselt number with the dimensionless axial distance in Figs.(12)-(15)
respectively. Generally, It is obvious from these figures that the local Nusselt number values increase
as the heat flux increases because of increasing natural convection currents which improves the heat
transfer process. Therefore, as the heat flux increases, the fluid near the wall becomes hotter and
lighter than the bulk fluid in the core. As a consequence, in the vertical position two upward currents
flow along the sides walls, where for the horizontal case the flow near the tubes walls would be in
the radial direction .For inclined positions the flow will be combined of the axial and radial direction
and by continuity, the fluid near the tube center flows downstream.
Fig.(12) : Local Nusselt number variation with
the axial dimensionless distance for different
heat fluxes with=0o
.
(13): Local Nusselt number variation with the
axial dimensionless distance for different heat
fluxes with=30o
.
heat fluxes with=60o
.
heat fluxes with=90o
.

101
The effect of angle inclination on the local Nusselt number variation are shown in Figs (16)-
(19). For the horizontal position it can be seen that the values of Nux as they should, are constant and
independent of x. The local Nusselt number increases relatively as angle of inclination moves from
horizontal to vertical position for the same heat fluxs of the tube.
Fig.(16)Nusselt number variation withthe
axial dimensionless distance for different
angles of inclination,q=70 W/m2
.
.
.
.
6.3 Average Nusselt number
Figs.(20)-(23) show the logarithmic of mean Nusselt number versus logarithmic Rayleigh
number for q=70 W/m2
to 600 W/m2
,at ߠ = 0° (horizontal) , 30° , 60° , and 90° (vertical) ;
respectively . An empirical equations have been deduced from these figures as follows:-
Num= 0.02115 Ra௠
଴.ସଷଵସ଼
ߠ =0o
Num= 0.35254 Ra௠
଴.ଶ଼ହ଻଺
ߠ =30o
Num= 0.69371 Ra௠
଴.ଶଶଵ଺ଷ
ߠ =60o
Num= 0.59489 Ra௠
଴.ଶଷଵସ
ߠ =90o

102
Fig.(20) : Logarithm Average Nusselt Number
Versus log(Ram) ,ߠ=0o
.
.
.
.
7. CONCLUSIONS
1. The heat transfer process improves as heat flux increases.
2. The heat transfer process improves as angle of inclination moves from horizontal to vertical.
3. The effect of buoyancy is small at the tube entrance and increases downstream.
REFERENCES
[1] Martin B. W. “Free convection limits in the open thermosyphon” Int. J. of Heat and Mass
Transfer, Vol. 8, No.1, pp.19-25 (1965).
[2] Shigeo K. and Adrian B. “Experimental study of natural convection in a horizontal cylinder
with different end temperatures” Int. J. of Heat and Mass Transfer ,Vol. 23, No.8, pp. 1117-
1126 (1980).
[3] Shenoy, A. V. “Natural convection effects on heat transfer to power-law fluids flowing under
turbulent conditions in vertical pipes” Int. Communications in Heat and Mass Transfer
,Vol.11, No.5, pp.467-476 (1984).
[4] Rahman, M., and Sharif, M. A. R., “Numerical Study of Laminar Natural Convection in
Inclined Rectangular Enclosures of Various Aspect Ratios,” Numer. Heat Transfer A, Vol.
44, pp. 355–373, (2003).

103
[5] Akeel A. Mohammed, Mahmoud A. Mashkour and Raad Shehab Ahmed,”Natural convection
in inclined circular cylinder”, Journal of Engineering,vol 17 ,No.4 , pp.659-674,(2011).
[6] Boris Brangeon, Patrice Joubert and Alain Bastide,”Numerical investigation of natural
convection in inclined channel – chimney system” vol. 13 pp.542-549 (2013).
[7] Jack P. Holman,”Heat transfer”,10th edition, McGraw-Hill Series in Mechanical Engineering
(2010).
[8] Jack P. Holman. “Experimental methods for engineers”, 8th ed. McGraw-Hill Series in
Mechanical Engineering (2011).
[9] Ashish Kumar, Dr. Ajeet Kumar Rai and Vivek Sachan, “An Experimental Study of Heat
Transfer In a Corrugated Plate Heat Exchanger” International Journal of Mechanical
Engineering & Technology (IJMET), Volume 5, Issue 9, 2014, pp. 286 - 292, ISSN Print:
0976 – 6340, ISSN Online: 0976 – 6359.
[10] K. Obual Reddy, M. Srikesh, M. Kranthi Kumar and V. Santhosh Kumar, “CFD Analysis of
Economizer To Optimize Heat Transfer” International Journal of Mechanical Engineering &
Technology (IJMET), Volume 5, Issue 3, 2014, pp. 66 - 76, ISSN Print: 0976 – 6340, ISSN
Online: 0976 – 6359.

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