Convection Heat Transfer in a Smooth Pipe

A Graduation Project Report
CONVECTION HEAT TRANSFER IN A SMOOTH PIPE
By
SALİH GÜVEN
Department of Mechanical Engineering
Faculty of Engineering and Architecture
Yeditepe University
June 2015, Istanbul, Turkey

CONVECTION HEAT TRANSFER IN A SMOOTH PIPE
By
SALİH GÜVEN
DATE OF APPROVAL: 10 June 2015
APPROVED BY:
Assoc. Prof. Hojin AHN
Thesis Supervisor
Department of Mechanical Engineering
Faculty of Engineering and Architecture
Yeditepe University
June 2015, Istanbul, Turkey

CONVECTION HEAT TRANSFER IN A SMOOTH PIPE GÜVEN
Department of Mechanical Engineering, Yeditepe University iii
ACKNOWLEDGEMENT
I would like to express my deepest gratitude to my teacher, supervisor Assoc. Prof.
Hojin AHN for his excellent guidance, support, knowledge and contribution to my graduation
thesis. His guidance helped me in all the time of research and writing of this thesis. I could
not have imagined having a better advisor and mentor for my graduation thesis. Thank you for
supporting and guidance.
I would like to thank you to Berk KÖTEŞLİ and Göksenin ÖZKAN for their priceless
friendship and contribution to my life. They always support me and I know that they will be
here for me. I am very lucky to have their dear friendships. I will be here for them during rest
of my life. Thanks for all marvelous and memorable memories my dear friends.
The most special and crucial thank goes to my dear family. I would like to thank to my
dear mother Ayşe GÜVEN and my dear father İskender GÜVEN, my lovely sister Makbule
GÜVEN. Without their endless love, encouragement and support, I have never achieved such
a career and facility. I will always be very proud of being their child and their sibling. I will
always love you and be with you forever and ever.

Department of Mechanical Engineering, Yeditepe University iv
ABSTRACT
The purpose of this graduation project is to design an experimental setup and to
conduct experiments for investigating convection heat transfer in a smooth pipe. Also,
comparison of the test results with correlations in the literature is another goal for this
graduation project. In this project 3 meter 316L type stainless steel pipe was selected for
building the experimental setup. Then, 12 T-type thermocouples were installed on the pipe
with certain intervals. After that, electricity was given through the pipe with a power supplier
to heat up the pipe. At the same time, flow rate of the air in pipe, inlet & outlet temperatures
were measured by data acquisition unit. After all these data are combined, satisfactory results
were obtained for laminar and turbulent flow cases. When the test results were compared with
the literature, for the best laminar flow approach there is approximately 15% error and for the
best turbulent approach there is 9% error.

Department of Mechanical Engineering, Yeditepe University v
ÖZET
Bu bitirme projesinin amacı pürüzsüz bir borudaki konveksiyonel ısı transferini
araştırmak için deney düzeneği tasarlamak ve deneyler yapmaktır. Ayrıca, test sonuçlarını
literatürdeki korelasyonlarla karşılaştırmak bu projenin diğer bir amacıdır. Bu projede,
deneysel düzeneği oluşturmak için 3 metre boyunda 316L tipinde paslanmaz çelik boru
seçildi. Ardından, 12 adet T tipi termokulp belirli aralıklarla borunun üzerine yerleştirildi.
Bundan sonra, boruyu ısıtmak için bir güç kaynağı yardımı ile boruya elektrik verildi. Aynı
zamanda, borudaki havanın akış hızı, giriş ve çıkış sıcaklığı veri edinme ünitesi ile ölçüldü.
Tüm bu veriler birleştirildikten sonra, laminar ve türbülanslı akış durumları için tatminkar
sonuçlar elde edilmiştir. Test sonuçları literatür ile karşılaştırıldığında en iyi laminar akış
yaklaşımı için yaklaşık %15 hata var iken en iyi türbülanslı akış yaklaşımı için hata %9
olmuştur.

Department of Mechanical Engineering, Yeditepe University vi
TABLE OF CONTENTS
1. INTRODUCTION........................................................................................................................... 1
2. LITERATURE SURVEY ............................................................................................................... 3
2.1. Internal Forced Convection..................................................................................................... 3
2.2. Hydrodynamic and Thermal Entrance Regions ...................................................................... 3
2.3. General Thermal Analysis....................................................................................................... 6
2.3.1. Constant Surface Heat Flux............................................................................................. 6
2.4. Laminar Flow.......................................................................................................................... 8
2.5. Turbulent Flow........................................................................................................................ 9
3. EXPERIMENTAL SETUP........................................................................................................... 10
3.1. Pipe Selection........................................................................................................................ 10
3.2. Thermocouple ....................................................................................................................... 11
3.3. Pipe Outlet Mixture Box ....................................................................................................... 12
3.4. Flow Measurement Box ........................................................................................................ 13
3.5. Pressure Transmitter.............................................................................................................. 14
3.6. Fan......................................................................................................................................... 15
3.7. Power Suppliers..................................................................................................................... 15
3.8. Agilent 34410A Multimeter.................................................................................................. 16
3.9. GW Instek GDS-806S Digital Oscilloscope ......................................................................... 17
3.10. Agilent 34970A Data Acquisition Switch Unit..................................................................... 18
3.11. Assemble of Experimental Setup .......................................................................................... 19
4. CALCULATIONS & RESULTS.................................................................................................. 21
4.1. Method of the Experiment..................................................................................................... 21
4.2. Resistance.............................................................................................................................. 21
4.3. Heat Loss............................................................................................................................... 23
4.4. Dry Air Properties................................................................................................................. 24
4.5. Flowrate Calculation ............................................................................................................. 24
4.6. Main Calculations ................................................................................................................. 25
4.6.1. Reynolds Number: 795.................................................................................................. 26
4.6.2. Reynolds Number: 1115................................................................................................ 29
4.6.3. Reynolds Number: 1779................................................................................................ 32
4.6.4. Reynolds Number: 2274................................................................................................ 35
4.6.5. Reynolds Number: 3134................................................................................................ 38
4.6.6. Reynolds Number: 4127................................................................................................ 41

Department of Mechanical Engineering, Yeditepe University vii
4.6.7. Reynolds Number: 5659................................................................................................ 44
4.6.8. Reynolds Number: 6598................................................................................................ 47
4.6.9. Reynolds Number: 7719................................................................................................ 50
4.6.10. Reynolds Number: 8649................................................................................................ 53
4.6.11. Reynolds Number: 10006.............................................................................................. 56
4.6.12. Reynolds Number: 11147.............................................................................................. 59
4.6.13. Reynolds Number: 13747.............................................................................................. 62
4.6.14. Reynolds Number: 15097.............................................................................................. 65
5. CONCLUSION............................................................................................................................. 68
6. REFERENCES.............................................................................................................................. 69
7. BIOGRAPHY ............................................................................................................................... 70

Department of Mechanical Engineering, Yeditepe University viii
LIST OF FIGURES
Figure 1: Seamless stainless steel pipes in stock..................................................................................... 1
Figure 2: The general layout of the system............................................................................................. 2
Figure 3: The development of the velocity boundary layer in a tube[2]................................................. 4
Figure 4: The development of the thermal boundary layer in tube (The fluid is being cooled)[4]......... 5
Figure 5: Variation of the tube surface and the mean fluid temperatures along the tube[6] ................... 7
Figure 6: Energy balance in a control volume[7].................................................................................... 7
Figure 7: Nusselt number versus Greatz number for laminar flow[8] .................................................... 8
Figure 8: A typical thermocouple.......................................................................................................... 11
Figure 9: A soldered thermocouple....................................................................................................... 11
Figure 10: The top view of unassembled mixture box.......................................................................... 12
Figure 11: The front view of unassembled mixture box ....................................................................... 12
Figure 12: The rear view of unassembled mixture box......................................................................... 12
Figure 13: Grids of the mixture box...................................................................................................... 12
Figure 14: Assembled mixture box with insulation .............................................................................. 12
Figure 15: Assembled box on the system.............................................................................................. 12
Figure 16: The flow rate measurement chamber................................................................................... 13
Figure 17: The 9.92mm orifice ............................................................................................................. 13
Figure 18: The 14.07mm orifice ........................................................................................................... 13
Figure 19: The 20.17mm orifice ........................................................................................................... 13
Figure 20: Different ranged pressure transducers ................................................................................. 14
Figure 21: Armfield Air Flow Rig ........................................................................................................ 15
Figure 22: A big power supply.............................................................................................................. 15
Figure 23: A small power supply.......................................................................................................... 15
Figure 24: Agilent 34410A Multimeter ................................................................................................ 16
Figure 25: GW Instek GDS-806S Oscilloscope.................................................................................... 17
Figure 26: Agilent 34970A Data Acquisition Switch Unit ................................................................... 18
Figure 27: Multiplexer connection of thermocouples ........................................................................... 18
Figure 28: Electricity transfer cable...................................................................................................... 19
Figure 29: Mounting type 1................................................................................................................... 20
Figure 30: Mounting type 2 & 3............................................................................................................ 20
Figure 31: 3 different mounting test...................................................................................................... 20
Figure 32: Final layout before experiment............................................................................................ 20
Figure 33: Resistance versus temperature graph................................................................................... 22
Figure 34: Power versus temperature graph.......................................................................................... 23

Department of Mechanical Engineering, Yeditepe University ix
Figure 35: Surface and Fluid temperature versus non-dimensional pipe length for Re: 795................ 26
Figure 36: Nusselt Number versus non-dimensional length for Re: 795.............................................. 28
Figure 37: Surface and Fluid temperature versus non-dimensional pipe length for Re: 1115.............. 29
Figure 38: Nusselt Number versus non-dimensional length for Re: 1115............................................ 31
Figure 55: Surface and Fluid temperature versus non-dimensional pipe length for Re: 10006............ 56
Figure 56: Nusselt Number versus non-dimensional length for Re: 10006.......................................... 58
Figure 63: Nusselt Number versus Reynolds Number for every trial................................................... 68

Department of Mechanical Engineering, Yeditepe University x
LIST OF TABLES
Table 1: Pipe selection .......................................................................................................................... 10
Table 2: The dimensions of selected pipe ............................................................................................. 10
Table 3: Resistance calculation............................................................................................................. 21
Table 4: Resistance change according to pipe temperature................................................................... 22
Table 5: Heat Loss calculation.............................................................................................................. 23
Table 6: Dry air properties calculation table [12] ................................................................................. 24
Table 7: Reynolds Number and Mass Flow Rate Calculation .............................................................. 24
Table 8: Miscellaneous data for Re: 795............................................................................................... 26
Table 9: Preliminary analysis for Re: 795............................................................................................. 26
Table 10: Convection heat transfer analysis for Re: 795 ...................................................................... 27
Table 11: Miscellaneous data for Re: 1115........................................................................................... 29
Table 12: Preliminary analysis for Re: 1115......................................................................................... 29
Table 13: Convection heat transfer analysis for Re: 1115 .................................................................... 30
Table 20: Nusselt Number comparison with literature for Re: 2274 .................................................... 36
Table 24: Nusselt Number comparison with literature for Re: 3134 .................................................... 39
Table 28: Nusselt Number comparison for Re: 4127............................................................................ 42

Department of Mechanical Engineering, Yeditepe University xi
Table 45: Miscellaneous data for Re: 10006......................................................................................... 56
Table 46: Preliminary analysis for Re: 10006....................................................................................... 56
Table 47: Convection heat transfer analysis for Re: 10006 .................................................................. 57
Table 48: Nusselt Number comparison for Re: 10006.......................................................................... 57

Department of Mechanical Engineering, Yeditepe University 1
1. INTRODUCTION
The aim of this graduation project is to investigate heat transfer to air flow in a
smooth stainless steel pipe. Also an experimental setup was designed to obtain surface
temperature of the pipe according to pipe length. Another aspect of this project is to
compare the experimental results with theoretical results. This report shows that whether
the experimental results and theoretical results are in agreement.
Heat transfer is a science that investigates the thermal energy transition between
physical bodies which were in different temperatures. Heat transfer studies are so crucial
because everything in the world dissipates or absorb the heat even human body.
According to this, products that cause thermal energy transition as a side effect must be
examined in terms of heat transfer.
In this project, it was decided to use seamless stainless steel pipe because it is easy
to cut, has a smooth internal surface and readily available in different sizes. According to
these features; in 3 meters long, in 0.022 meters diameter and 0.001 meters thickness
316L type seamless stainless steel pipe was obtained.
Figure 1: Seamless stainless steel pipes in stock

The next step is to obtain temperature of the pipe according to pipe length. For
this reason, thermocouples were installed on pipe with a certain distance. A thermocouple
is a temperature measuring device that consisting two different conductors. It is in form
of long cable and these two different conductors contact in one point. When temperature
changes in this contact point, it produces voltage at the other end. Also these voltages
were read by a data acquisition system.
After that this pipe was connected to the chamber which measures flow rate. Here,
the key point is to investigate the system behavior in different Reynolds numbers. In the
chamber, different diameter orifices were used to determine different Reynolds numbers.
Lastly, electricity was given to the pipe by an adjustable DC power supply. Power
supply was connected to pipe with bundle of cables to prevent excessive heating of
cables. Moreover, pipe voltage during the experiment was measured with data acquisition
system and an oscilloscope.
Figure 2: The general layout of the system

2. LITERATURE SURVEY
2.1. Internal Forced Convection
Convective heat transfer that usually called convection is the transfer of heat by the
movement of the fluid [1]. Convection heat transfer can occur in two ways that are Free
(Natural) convection and Forced convection. Free convection is the heat transfer between a
fluid and other heat source without any external force. On the other hand, forced convection is
the heat transfer event of fluid flow over a body or surface by the help or a source like fans,
pumps, etc. Internal forced convection clarifies convective heat transfer in pipes or ducts. Pipe
and ducts are widely using in engineering applications like HVAC, heat exchangers thus
internal convection is important area of heat transfer.
2.2. Hydrodynamic and Thermal Entrance Regions
A flow in a pipe can be laminar or turbulent according to conditions of the flow.
Laminar flow can be seen with high viscous fluids like oils in small diameter pipes. In many
applications pipe flows are turbulent. For circular pipes the Reynolds number of the flow can
be defined as
where is the density of the fluid, is the velocity of the fluid in pipe, is the internal
diameter of the pipe and is the dynamic viscosity of the fluid. Also, noncircular tubes can be
used for different applications. Thereby, hydraulic diameter (Dh) term defined as
where is the cross section area of the tube and is the perimeter of the tube.
For different flows Reynolds numbers defined precisely but in practice this is not
valid. For pipe flow Re < 2300 can be considered as laminar flow, 2300 < Re < 4000 can be
considered as transitional flow and Re > 4000 turbulent flow. In most practical applications,
flows will be turbulent by Re > 4000 but in some applications where disturbances are small,
the flow may not be fully turbulent until Re >10000.

Velocity profile of the flow in pipe is another significant issue for internal convection.
In pipe flow likewise external flow, particles that contact with surface of the tube will come to
a complete stop. These particles will also slow down the particle of adjacent fluid particles
gradually. As a result a curved velocity profile developed after fully developed region.
Figure 3: The development of the velocity boundary layer in a tube[2]
The region from the tube inlet to the point at which the boundary layer merges at the
centerline is called the hydrodynamic entrance region, and the length of this region is called
the hydrodynamic entry length [3]. In laminar flow, hydrodynamic entry length is usually
taken as
where is the Reynolds number of the flow and is the internal diameter of the pipe. In
turbulent flow, there is less dependence on Reynolds number because the hydraulic entry
lenght is much shorter. It is generally agreed that entrance effects for turbulent flow are
confined with 10 times of tube diameter. In general hydrodynamic entry length for turbulent
flow taken as

Also, thermal profile of the flow in pipe is an important issue. As can be seen in the
Figure 4 thermal profile of the flow look alike hydraulic velocity profile of the flow.
Figure 4: The development of the thermal boundary layer in tube (The fluid is being cooled)[4]
The region of flow over which the thermal boundary layer develops and reaches the
tube center is called the thermal entrance region, and the length of this region is called the
thermal entry length [5]. In laminar flow, thermal entry length is usually taken as
where is the Reynolds number of the flow, is the internal diameter of the pipe and is
the Prandtl number of the flow. In turbulent flow, the thermal entry length is same with
hydrodynamic entry length.

2.3. General Thermal Analysis
In internal pipe flow the main aim is heating or cooling the fluid. These two conditions
can be provided by changing surface temperature of the pipe. There are two different
approaches for thermal condition of the surface. These are constant surface heat flux and
constant surface temperature. In this study constant surface heat flux condition was applied to
the system.
2.3.1. Constant Surface Heat Flux
In the constant surface heat flux condition the rate of heat transfer can be defined as
where is the constant surface heat flux, is the surface area of the pipe, is the inlet
temperature and is the exit temperature. The surface temperature can be determined from
where is the convection heat transfer coefficient, is the surface temperature and is the
mean temperature of the fluid. In fully developed region, have to be constant because
is constant.

Figure 5: Variation of the tube surface and the mean fluid temperatures along the tube[6]
The slope of the mean fluid temperature Tm on a T-x diagram can be determined by
applying the steady-flow energy balance to a tube slice of thickness dx shown in Figure 6. It
gives
where is the change of the mean temperature and is the perimeter of the pipe.
Figure 6: Energy balance in a control volume[7]

2.4. Laminar Flow
In pipe flow the Reynolds number must be below 2300 to classify it laminar flow. In
laminar flow it takes time to be fully developed and the tube must be sufficiently long. Thus,
entrance region effects are negligible in laminar flow.
Figure 7: Nusselt number versus Greatz number for laminar flow[8]
Greatz number is a dimensionless number that characterizes laminar flow in a pipe. It
can be defined as
According to researches Nusselt number for laminar flow with constant surface heat
flux is 4.36.

2.5. Turbulent Flow
In pipe flow the Reynolds number must be above 4000 to classify it turbulent flow.
However, as mentioned before, in smooth pipe applications sometimes disturbances are small
the flow may not be turbulent until Re > 10000. In smooth pipes, the friction factor in
turbulent flows can be expressed with Petukhov equation as
This equations is only valid for 104
< Re < 106
. Also, Moody Chart can be used to obtain the
friction factor. For turbulent flow there are different approaches for Nusselt number
correlation. In this study, two of these correlation approaches were used. The first one is
Dittus - Boelter equation that given as
where for heating and for cooling. The second one is Gnielinski equation
which given as
where is the friction factor. Also, this approach is only valid for 0.5 ≤ Pr ≤ 2000 &
3x103
≤ Re ≤ 5x106
.

3. EXPERIMENTAL SETUP
3.1. Pipe Selection
In this project the major aim is to investigate the internal forced convection in a
smooth pipe. So, the significant point is here to find a seamless stainless steel pipe in
appropriate measurements. The pipe diameter and length is crucial for this experiment
because the fluid must be hydraulically and thermally fully developed quickly to
investigate. Before obtaining the pipe, diameter, thickness and length of the pipe had to
be decided. According to this, the table that given below was prepared for choosing right
pipe to build up the setup.
Table 1: Pipe selection
Pipe Turbulent Laminar
Do (m) 0,022 0,022 0,022 0,022
Ao (m2) 0,000380132 0,000380132 0,000380132 0,000380132
Cd 0,6 0,6 0,6 0,6
rho-300K 1,177 1,177 1,177 1,177
Kin Visc 0,00001568 0,00001568 0,00001568 0,00001568
Q (m3/s) 0,0045 0,0045 0,0002 0,0002
Dpipe (m) 0,02 0,02 0,02 0,02
Apipe (m2) 0,000314159 0,000314159 0,000314159 0,000314159
Lpipe (m) 2,5 3 2,5 3
Reynolds 18270,35329 18270,35329 812,0157017 812,0157017
f 0,0269 0,0269 0,07881621 0,07881621
∆Po (Pa) 229,0863652 229,0863652 0,452516277 0,452516277
∆Pp (Pa) 406,0081729 487,2098075 2,349811401 2,819773681
∆Pt (Pa) 635,0945382 716,2961728 2,802327678 3,272289958
L entry (m) 0,2 0,2 0,812015702 0,812015702
When the table examined, 3 meters pipe length would be more appropriate to
designed setup. The dimensions of selected pipe were given below.
Table 2: The dimensions of selected pipe
Dimension In meters
Outer Diameter, Do 0,022
Inner Diameter, Di 0,020
Length 3

3.2.Thermocouple
Thermocouple is a device that measures temperature by the help of wires which
have different conducting properties. To use thermocouple, first at the one side of the
thermocouple these dissimilar wires must be soldered. At this spot when the temperature
changes it produces electrical potential related to temperature in the other end of the
cable. After this process, the end side of the thermocouple can be connected to data
acquisition system to read this electrical potential (voltage) or voltage difference can be
read with a multimeter and it can be changed into temperature by the help of the
widespread equations.
Thermocouples are widely using in many applications. Science, industry, engines,
gas turbines are known use areas of thermocouples. There are many types of
thermocouples based on their production material. In this study, copper-constantan
namely Type T thermocouples were used to determine the surface temperature of the
pipe. Type T (copper – constantan) thermocouples are suited for measurements in the
−200 to 350 °C range. Type T thermocouples have a sensitivity of about 43 µV/°C [9].
Figure 9: A soldered thermocoupleFigure 8: A typical thermocouple

3.3.Pipe Outlet Mixture Box
A little mixture box was used to mix the flow at the outlet of the pipe. It contains
2 sparse grid and 1 frequent grid for mixture the exit flow. In the pipe, when the fluid
reached thermally developed region temperature is decrease trough the centerline of the
pipe from the wall of the pipe. Thereby, at the outlet to measuring an accurate
temperature the flow should be mixed. The box was made from 3mm latex material that
is widely using in model making. The parts were precisely cut by laser in a model shop.
00
Figure 12: The rear view of
unassembled mixture box
Figure 15: Assembled box on the
system
Figure 14: Assembled mixture
box with insulation
Figure 11: The front view of
Figure 10: The top view of
Figure 13: Grids of the mixture
box

3.4. Flow Measurement Box
A custom flow measurement box was using during the experiment. It helps to
measure flow rate of the fluid and some other specifications about fluid. The system
consists from a plexiglass box and two main region (high and low pressure field). The
area that stainless steel pipe was connected is high pressure area and the area that next to
the orifice is low pressure area. Pressure difference between these two area were
measured by differential pressure transmitters. Furthermore, for obtaining different flow
rates 3 different orifices were used in this chamber.
Figure 16: The flow rate measurement chamber
Figure 17: The 9.92mm orifice Figure 18: The 14.07mm orifice Figure 19: The 20.17mm orifice

3.5.Pressure Transmitter
Pressure transmitter is a device that measures pressure difference between low and
high pressure points. It generates a current according to change of pressure and works at
DC 12V. In this experiment, 3 different pressure transmitter were used which have
100Pa, 500Pa and 1000Pa ranges. Also, transducers measure with 0.8% accuracy which
is a good result. Every transducer has different standby current. These current were
recorded for using in the pressure calculating equations.
Figure 20: Different ranged pressure transducers

3.6.Fan
A standard centrifugal fan was used to create flow in the system. The fan was
produced by Armfield who is a big company that produces engineering teaching
equipments.
Figure 21: Armfield Air Flow Rig
3.7.Power Suppliers
Power suppliers are generally using to operate an electrical device. They can be in
many types and different working intervals. There are two main groups of power
suppliers that separate from electricity production type. These two groups are DC and AC
power suppliers. In this project, different sized DC power suppliers were used. A big
power supplier was used for generating heat on the pipe by giving electricity in high
current. A small power supply was used for operate the pressure transducers.
Figure 22: A big power supply Figure 23: A small power supply

3.8.Agilent 34410A Multimeter
Measuring voltage or current is important issue for experiments which includes
electricity. A multimeter is an instrument that combines several measurement functions
like voltage, current or resistance in one device. In this experiment, the voltage and
current measurement features were used to determine some variables about the system.
Figure 24: Agilent 34410A Multimeter

3.9.GW Instek GDS-806S Digital Oscilloscope
An oscilloscope is an instrument that tests constantly varying signal voltages and
plots these variables in two dimensional plots as a function of time [10]. In this
experiment, oscilloscope was used to control voltage values of unreliable power supply.
Moreover, it was used to measure pipe voltage.
Figure 25: GW Instek GDS-806S Oscilloscope

3.10. Agilent 34970A Data Acquisition Switch Unit
A data acquisition unit is the key part of the experimental setup. It collects data
with external cables like thermocouple and converts them meaningful outputs like
voltage, current or temperature. It uses RS232 interface to communicate with Agilent pc
software. Also, it has accuracy of 0.0041 % in normal operating conditions [11].
Figure 26: Agilent 34970A Data Acquisition Switch Unit
Figure 27: Multiplexer connection of thermocouples

3.11. Assemble of Experimental Setup
In this experiment, the main part of the system is 0.022 m diameter stainless steel
pipe. It has 0.02 m internal diameter and 2.935 m length. It was connected with 7 cables
from both two sides to transformer (Figure 28). Also 2 cables were measured the voltage
of the pipe during the experiment.
On the pipe surface, 12 T-Type thermocouples were fitted on a straight line. When
the fitting was considered, 3 different way of mounting of thermocouple were tried. The
first one was using thermal paste with Pattex ® glue (Figure29). The second one was
using a thin thread for fasten the thermocouple and then paste with Japan glue (Figure30).
The third one is just using Japan glue (Figure 30). It was obvious that in every trial some
teflon tape was used under the thermocouples because electricity on the pipe interfere the
operation of the thermocouples. Moreover, after thermocouples mounted on the pipe they
were covered with 2 cm x 2cm insulation to prevent unexpected heat loss (Figure 31).
Lastly, the pipe was covered full of insulation (Figure 31). After the first attempt, the best
resulting temperature was come from the third trial.
Figure 28: Electricity transfer cable

After all thermocouples were mounted on the pipe, the pipe was connected to the
box & fan system. Then the system was ready to measure (Figure 32).
Figure 29: Mounting type 1 Figure 30: Mounting type 2 & 3
Figure 31: 3 different mounting test
Figure 32: Final layout before experiment

4. CALCULATIONS & RESULTS
4.1. Method of the Experiment
After the experimental setup was completed primarily thermocouples were tested.
After that resistance of the pipe was found for various temperatures. Then, using the
resistance data the power loss from surface of the pipe was found for various
temperatures. On the next step, standby current outputs of pressure transmitters’ were
obtained for using in the pressure equations. By the help of pressure difference
knowledge, flow rate and Reynolds Number of the flow were found with an excel table.
Finally, analysis of experiments was done with processing temperature data with the
secondary data mentioned above.
4.2. Resistance
In electricity, resistance is a noteworthy variable that could change everything in a
system. Thus, in the beginning of the experiments the resistance of the pipe was found for
different pipe temperatures. At first, the pipe was heated up until 70o
C with big power
supply. After that, little power supply, oscilloscope and multimeter were connected to the
system. Then, nearly 100mA current was given through the system. Lastly, voltage and
current in the pipe were recorded parallel to cooling.
Table 3: Resistance calculation
Temp (o
C) Voltage (V) Current (mA) Resistance (Ohm) Difference (%)
69 3,598 99,650 0,0361 4,664
64 3,555 99,192 0,0358
60 3,531 98,964 0,0357
55 3,501 98,738 0,0355
50 3,473 98,523 0,0353
45 3,448 98,381 0,0350
40 3,426 98,239 0,0349
35 3,399 97,987 0,0347
30 3,378 97,843 0,0345
27 3,363 97,698 0,0344

Also, the change of resistance was checked by temperature coefficient of
resistance that showed only 0.63% difference between experimental and theoretical
calculation.
Table 4: Resistance change according to pipe temperature
Ro (Ohm) To (o
C) T (o
C) a R (Ohm) Difference (%)
0,0344 27 69 0,001 0,0359 4,031
Figure 33: Resistance versus temperature graph
y = 2,096E-09x3 - 9,283E-08x2 + 3,345E-05x + 3,355E-02
0,0342
0,0344
0,0346
0,0348
0,0350
0,0352
0,0354
0,0356
0,0358
0,0360
0,0362
0 10 20 30 40 50 60 70 80
Resistance(Ohm)
Temperature (oC)
Resistance (Ohm) vs Temperature (oC)

4.3. Heat Loss
It is obvious that energy could not transferred 100% from one source to another.
During the transfer some miscellaneous factors cause energy loss. Based on this
information, the heat energy of the pipe could not transfer totally to the flow. Thus, heat
loss from pipe surface was defined. Likewise, heat loss calculations were done for
different temperatures. It was started at 71o
C and in each temperature the system reached
steady state region.
Table 5: Heat Loss calculation
Temp (o
C) Current (A) Voltage (V) Resistance (Ohm) Power (W)
71 29,2 0,911 0,0362 22,938
65 26,2 0,838 0,0359 19,558
60 25,3 0,787 0,0357 17,357
55 24,1 0,742 0,0355 15,518
50 22 0,676 0,0352 12,974
45 20,1 0,618 0,0351 10,911
40 18 0,549 0,0349 8,649
35 16,2 0,484 0,0347 6,739
31 12,2 0,373 0,0346 4,034
Figure 34: Power versus temperature graph
y = 1,335E-04x3 - 2,040E-02x2 + 1,453E+00x - 2,522E+01
0
5
10
15
20
25
0 10 20 30 40 50 60 70 80
Power(W)
Temperature (oC)
Power (W) vs Temperature (oC)

4.4. Dry Air Properties
Dry air properties table was created to find different specifications of air for
various temperatures. These specifications are Cp, Dynamic Viscosity, Thermal
Conductivity, Prandtl Number and density.
Table 6: Dry air properties calculation table [12]
Temp
Temp
(K)
Cp
(kJ/kgK)
Dyn Visc
(10-5
kg/m.s)
Ther Cond
(W/m.K)
Pr
Density
(kg/m3
)
275 1,004 1,725E-05 2,428E-02 0,713 1,284
19,908 293,058 1,005 1,812E-05 2,570E-02 0,709 1,207
300 1,005 1,846E-05 2,624E-02 0,707 1,177
49,017 322,167 1,006 1,949E-05 2,794E-02 0,702 1,096
325 1,006 1,962E-05 2,816E-02 0,701 1,086
55,419 328,569 1,007 1,978E-05 2,843E-02 0,700 1,075
350 1,008 2,075E-05 3,003E-02 0,697 1,009
78,493 351,643 1,008 2,082E-05 3,015E-02 0,697 1,005
375 1,011 2,181E-05 3,186E-02 0,692 0,941
4.5. Flow rate Calculation
In this study the aim is to investigate the equality of the Ts-Tm difference in the
thermally developed region. For this reason, the experiment was conducted for various
Reynolds Numbers and there is need to calculate Reynolds Number for each attempt.
Table 7: Reynolds Number and Mass Flow Rate Calculation
Pressure Range
(Pa)
Orifice Temp
(°C)
Current
(mA)
Flow Rate
(m3/s)
Reynolds
100 21,771 5,560 0,000190 795
Orifice Diameter
(m)
Density
(kg/m3)
∆P
(Pa)
Velocity
(m/s)
0,00992 1,199 10,028 0,604
Dynamic Viscosity
(kg/m.s)
Mass Flow Rate
(kg/s)
1,821E-05 0,000227

4.6. Main Calculations
In this part of the analysis, power given to the system, heat loss of the pipe,
convection heat transfer to the fluid and Nusselt Number were calculated along the pipe.
During the experiment, for each trial 50 data were taken after the system reached steady
state region. Then, Reynolds Number checked by the Reynolds Number calculation table
and mass flow rate was also calculated here. After that, the average temperatures of each
point on the pipe, inlet, and mixture box were taken from data set and inlet & outlet
temperatures were used to define fluid temperature line along the pipe. Also, average of
the voltage and current were taken for calculating power and pressure difference. On the
next step, the power loss along the pipe was calculated and then coefficient of heat
transfer was calculated. Finally, Nusselt Number was calculated along the pipe.
The experiment was conducted for 14 different Reynolds Numbers. These are
795, 1115, 1779, 2300, 3134, 4127, 5659, 6598, 7719, 8649, 10006, 11147, 13747 and
15097.
(14)
(15)
(16)
(17)
(18)
The equations that were used in calculations were given above. The first one is
well known equation about power calculation. This calculation used in order to using
current based one because in the experiment there was not any device that could measure
high currents. The second equation represents the resistance variation at different
temperatures. The third equation shows the power loss variation at different temperatures.
The fourth equation is used to found the heat transfer coefficient. The fifth equation
indicates the Nusselt Number.

4.6.1. Reynolds Number: 795
Table 8: Miscellaneous data for Re: 795
Area
(m2)
Diameter
(m)
Orifice Temp
(°C)
Pr
Cp
(kJ/kg.K)
Mass Flow Rate
(kg/s)
0,184 0,02 21,771 0,708 1004,68 0,000227
Table 9: Preliminary analysis for Re: 795
x/D Tm (°C) Ts (°C) k (W/m.K)
6,25 19,899 40,679 2,570E-02
18,75 23,399 45,495 2,597E-02
31,25 26,900 49,553 2,624E-02
43,75 30,400 53,668 2,651E-02
56,25 33,901 56,913 2,678E-02
68,75 37,401 59,555 2,705E-02
81,25 40,902 61,702 2,732E-02
93,75 44,402 64,601 2,759E-02
106,25 47,903 66,122 2,786E-02
118,75 51,403 67,500 2,813E-02
131,25 54,904 68,444 2,839E-02
143,75 58,405 79,146 2,865E-02
Figure 35: Surface and Fluid temperature versus non-dimensional pipe length for Re: 795
y = 0,28004x + 18,14837
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100 120 140 160
Temperature(C)
x/D
Ts & Tm vs Non-Dimensional Length
Ts
Tm
Linear (Tm)

Figure 35 shows that the relationship between mean temperature and surface
temperature. As can be seen the mean temperature increases linearly due to the constant
surface heat flux case. On the other hand, the surface temperature increases in developing
region. However, this trend was maintained until middle of the pipe. After this point
because of the unexpected heat loss the constant temperature difference condition was
lost. At the end of the pipe, there is a temperature increase because the cable that transfers
electricity from power supplier is such close that thermocouple. Thereby, excessive
heating occurs there.
Table 10: Convection heat transfer analysis for Re: 795
Q Total
(W)
Q Fluid
(W)
Q Loss
(Calc)
Q Loss
(Exp)
q"total
(W/m2
)
q"loss
(W/m2
)
q"s
(W/m2
)
h
(kJ/kg.C)
Nu
32,200 8,796 23,404 9,118 174,612 49,446 125,166 6,023 4,688
32,036 23,240 11,235 173,721 60,922 112,800 5,105 3,932
31,893 23,096 12,936 172,944 70,147 102,797 4,538 3,458
31,742 22,946 14,643 172,127 79,404 92,723 3,985 3,006
31,619 22,823 16,012 171,461 86,829 84,632 3,678 2,746
31,516 22,720 17,163 170,902 93,069 77,833 3,513 2,598
31,431 22,634 18,133 170,437 98,328 72,109 3,467 2,538
31,312 22,515 19,507 169,793 105,780 64,013 3,169 2,297
31,248 22,451 20,263 169,447 109,882 59,565 3,269 2,347
31,189 22,393 20,973 169,128 113,729 55,399 3,442 2,447
31,148 22,352 21,474 168,907 116,444 52,464 3,875 2,730
30,657 21,860 28,183 166,242 152,828 13,414 0,647 0,451

Figure 36: Nusselt Number versus non-dimensional length for Re: 795
In Figure 36, behavior of Nusselt Number against non-dimensional length can be seen.
In literature, Nusselt number must be 4.36 for “Constant surface heat flux” in laminar flow
condition. However, here Nusselt number in fully developed region is around 2 because of
heat losses from surface of the pipe. Also, Nusselt number at the outlet of the pipe shows a
sudden decline due to the excessive heating at the last thermocouple.
0
1
2
3
4
5
6
7
8
9
10
0 20 40 60 80 100 120 140 160
Nusselt#
x/D
Nu vs Non Dimensional Length

Area
(m2)
Diameter
(m)
Orifice Temp
(°C)
Pr
Cp
(kJ/kg.K)
Mass Flow rate
(kg/s)
0,184 0,02 22,106 0,708 1004,69 0,000319
6,25 19,908 41,124 2,570E-02
18,75 23,357 46,014 2,597E-02
31,25 26,806 49,434 2,624E-02
43,75 30,255 53,294 2,650E-02
56,25 33,703 56,556 2,677E-02
68,75 37,152 59,266 2,703E-02
81,25 40,601 61,472 2,730E-02
93,75 44,050 64,395 2,756E-02
106,25 47,498 66,057 2,783E-02
118,75 50,947 67,557 2,809E-02
131,25 54,396 68,626 2,835E-02
143,75 57,844 81,259 2,861E-02
y = 0,2759x + 18,184
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100 120 140 160
Temperature(C)
x/D
Ts
Tm
Linear (Tm)

region. However, this trend was maintained until middle of the pipe. After this point
because of the unexpected heat loss the constant temperature difference condition was
lost. At the end of the pipe, there is a temperature increase because the cable that transfers
electricity from power supplier is such close that thermocouple. Thereby, excessive
heating occurs there.
Q Total
(W)
Q Fluid
(W)
Q Loss
(Calc)
Q Loss
(Exp)
q"total
(W/m2
)
q"loss
(W/m2
)
q"s
(W/m2
)
h
(kJ/kg.C)
Nu
35,293 12,169 23,124 9,320 191,384 50,542 140,842 6,639 5,167
35,110 22,941 11,455 190,389 62,118 128,271 5,661 4,361
34,977 22,808 12,887 189,670 69,881 119,788 5,294 4,035
34,823 22,653 14,487 188,832 78,558 110,274 4,786 3,612
34,688 22,518 15,860 188,099 86,001 102,098 4,468 3,338
34,572 22,403 17,035 187,473 92,375 95,098 4,300 3,182
34,476 22,307 18,027 186,950 97,755 89,195 4,274 3,131
34,345 22,175 19,407 186,239 105,235 81,004 3,981 2,889
34,268 22,099 20,230 185,826 109,702 76,123 4,102 2,948
34,198 22,029 21,003 185,446 113,890 71,555 4,308 3,067
34,148 21,978 21,572 185,171 116,976 68,195 4,792 3,381
33,503 21,334 29,783 181,676 161,505 20,172 0,861 0,602

In literature, Nusselt number must be 4.36 for “Constant surface heat flux” in laminar flow
condition. However, here Nusselt number in fully developed region is around 3 because of
heat losses from surface of the pipe. Also, Nusselt number at the outlet of the pipe shows a
0
1
2
3
4
5
6
7
8
9
10
0 20 40 60 80 100 120 140 160
Nusselt#
x/D

Area
(m2)
Diameter
(m)
Orifice Temp
(°C)
Pr
Cp
(kJ/kg.K)
Mass Flow rate
(kg/s)
0,184 0,02 22,610 0,708 1004,71 0,000510
6,25 19,938 40,670 2,570E-02
18,75 23,083 46,448 2,594E-02
31,25 26,226 49,831 2,619E-02
43,75 29,370 53,008 2,643E-02
56,25 32,514 55,884 2,668E-02
68,75 35,658 58,592 2,692E-02
81,25 38,801 60,929 2,716E-02
93,75 41,945 63,915 2,740E-02
106,25 45,089 65,777 2,764E-02
118,75 48,233 67,486 2,788E-02
131,25 51,376 68,737 2,812E-02
143,75 54,513 82,959 2,836E-02
y = 0,2515x + 18,367
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100 120 140 160
Temperature(C)
x/D
Ts
Tm
Linear (Tm)

region. At lower Reynolds numbers, the difference between surface temperature and
mean temperature has a downward trend after middle of the pipe but here heat loss effects
seen less. At the end of the pipe, there is a temperature increase because the cable that
transfers electricity from power supplier is such close that thermocouple. Thereby,
excessive heating occurs there.
Q Total
(W)
Q Fluid
(W)
Q Loss
(Calc)
Q Loss
(Exp)
q"total
(W/m2)
q"loss
(W/m2)
q"s
(W/m2)
h
(kJ/kg.C)
Nu
39,904 17,723 22,181 9,114 216,386 49,421 166,965 8,054 6,268
39,659 21,936 11,639 215,058 63,113 151,945 6,503 5,013
39,510 21,787 13,051 214,251 70,773 143,478 6,078 4,642
39,366 21,643 14,368 213,471 77,913 135,557 5,735 4,339
39,232 21,509 15,574 212,744 84,453 128,291 5,489 4,116
39,103 21,380 16,738 212,042 90,767 121,275 5,288 3,929
38,988 21,265 17,779 211,420 96,411 115,009 5,198 3,828
38,838 21,114 19,174 210,603 103,976 106,628 4,853 3,543
38,741 21,018 20,090 210,081 108,940 101,142 4,889 3,537
38,651 20,928 20,966 209,593 113,690 95,903 4,981 3,573
38,584 20,861 21,631 209,230 117,300 91,930 5,295 3,766
37,756 20,033 31,149 204,740 168,908 35,832 1,260 0,888

In Figure 40, behavior of Nusselt Number against non-dimensional length can be
seen. In literature, Nusselt number must be 4.36 for “Constant surface heat flux” in laminar
flow condition. In this approach Nusselt number is a little bit close to the theoretical value. It
is understood that increment in Reynolds number compensate the error due to the heat loss.
According to the results mentioned above, Re: 1779 is best approach for laminar flow case.
Likewise here Nusselt number at the outlet of the pipe shows a sudden decline due to the
excessive heating at the last thermocouple.
0
1
2
3
4
5
6
7
8
9
10
0 20 40 60 80 100 120 140 160
Nusselt#
x/D

4.6.4.Reynolds Number: 2274
Area
(m2)
Diameter
(m)
Orifice Temp
(°C)
Pr
Cp
(kJ/kg.K)
Mass Flow rate
(kg/s)
0,184 0,02 23,536 0,708 1004,65 0,000654
6,25 19,925 38,141 2,570E-02
18,75 22,855 45,536 2,593E-02
31,25 25,784 50,002 2,616E-02
43,75 28,714 53,455 2,638E-02
56,25 31,643 56,160 2,661E-02
68,75 34,573 58,554 2,683E-02
81,25 37,503 60,719 2,706E-02
93,75 40,432 63,437 2,728E-02
106,25 43,362 65,289 2,751E-02
118,75 46,292 67,182 2,773E-02
131,25 49,221 68,702 2,796E-02
143,75 52,151 84,692 2,818E-02
y = 0,2344x + 18,46
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100 120 140 160
Temperature(C)
x/D
Ts
Tm
Linear (Tm)

region. At Re: 2247, it can be seen easily heat loss effects are decreasing gradually. At the end
of the pipe, there is a temperature increase because the cable that transfers electricity from
power supplier is such close that thermocouple. Thereby, excessive heating occurs there.
Q Total
(W)
Q Fluid
(W)
Q Loss
(Calc)
Q Loss
(Exp)
q"total
(W/m2
)
q"loss
(W/m2
)
q"s
(W/m2
)
h
(kJ/kg.C)
Nu
44,896 21,159 23,736 7,932 243,454 43,011 200,443 11,004 8,564
44,548 23,389 11,252 241,569 61,016 180,553 7,961 6,141
44,328 23,169 13,122 240,378 71,157 169,221 6,988 5,343
44,152 22,993 14,554 239,424 78,922 160,501 6,487 4,918
44,011 22,851 15,691 238,654 85,086 153,568 6,264 4,708
43,882 22,722 16,722 237,956 90,679 147,278 6,141 4,577
43,763 22,603 17,684 237,311 95,896 141,415 6,091 4,502
43,610 22,450 18,945 236,480 102,734 133,746 5,814 4,262
43,503 22,343 19,846 235,900 107,617 128,283 5,850 4,254
43,391 22,232 20,807 235,296 112,829 122,467 5,862 4,228
43,300 22,141 21,612 234,802 117,196 117,605 6,037 4,319
42,246 21,086 32,616 229,083 176,864 52,219 1,605 1,139
Table 20: Nusselt Number comparison with literature for Re: 2274
Friction Factor Nu Dittus - Boelter Nu Gnielinski
0,0499 9,708 7,091

In Figure 42, behavior of Nusselt Number against non-dimensional length can be
seen. When we look at the correlation of Dittus – Boelter, there is nearly 55% error for fully
developed region which is relatively high. Also, there is nearly 38% error for fully developed
region according to Gnielinski correlation. Again, the reason of the error is heat loss from the
outer surface of the pipe. Likewise here Nusselt number at the outlet of the pipe shows a
0
1
2
3
4
5
6
7
8
9
10
0 20 40 60 80 100 120 140 160
Nusselt#
x/D

Area
(m2)
Diameter
(m)
Orifice Temp
(°C)
Pr
Cp
(kJ/kg.K)
Mass Flow rate
(kg/s)
0,184 0,02 25,218 0,707 1004,83 0,000905
6,25 20,000 37,039 2,570E-02
18,75 23,389 44,217 2,597E-02
31,25 26,779 48,107 2,623E-02
43,75 30,169 50,791 2,649E-02
56,25 33,558 53,358 2,676E-02
68,75 36,948 56,185 2,702E-02
81,25 40,337 58,910 2,728E-02
93,75 43,727 61,952 2,754E-02
106,25 47,117 64,238 2,780E-02
118,75 50,506 66,390 2,806E-02
131,25 53,896 68,458 2,831E-02
143,75 57,286 83,917 2,857E-02
y = 0,2712x + 18,305
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100 120 140 160
Temperature(C)
x/D
Ts
Tm
Linear (Tm)

region. At Re: 3134, again here heat loss effects are decreasing gradually. Also, we can see
here the difference between surface temperature and mean temperature start to decrease
because of increasing heat transfer due to the increasing Reynolds number. At the end of the
pipe, there is a temperature increase because the cable that transfers electricity from power
supplier is such close that thermocouple. Thereby, excessive heating occurs there.
Q Total
(W)
Q Fluid
(W)
Q Loss
(Calc)
Q Loss
(Exp)
q"total
(W/m2
)
q"loss
(W/m2
)
q"s
(W/m2
)
h
(kJ/kg.C)
Nu
53,205 33,905 19,299 7,397 288,510 40,109 248,401 14,578 11,344
52,809 18,903 10,687 286,363 57,951 228,412 10,967 8,446
52,585 18,680 12,335 285,151 66,886 218,265 10,234 7,802
52,426 18,521 13,449 284,291 72,930 211,361 10,249 7,737
52,271 18,366 14,514 283,448 78,702 204,746 10,341 7,730
52,096 18,191 15,701 282,497 85,144 197,353 10,259 7,595
51,922 18,017 16,878 281,555 91,524 190,031 10,232 7,503
51,722 17,817 18,248 280,472 98,954 181,518 9,960 7,234
51,568 17,663 19,330 279,636 104,822 174,814 10,210 7,346
51,420 17,514 20,400 278,831 110,620 168,211 10,590 7,549
51,274 17,368 21,481 278,039 116,484 161,556 11,094 7,837
50,073 16,168 31,950 271,532 173,252 98,279 3,690 2,584
Table 24: Nusselt Number comparison with literature for Re: 3134
0,0449 12,543 10,537

When we look at the correlation of Dittus – Boelter, there is nearly 40% error for fully
region according to Gnielinski correlation. With these results, we can expect that error will be
decrease gradually with the increase of the Reynolds number. Likewise here Nusselt number
at the outlet of the pipe shows a sudden decline due to the excessive heating at the last
thermocouple.
0
2
4
6
8
10
12
14
16
18
20
0 20 40 60 80 100 120 140 160
Nusselt#
x/D

Area
(m2)
Diameter
(m)
Orifice Temp
(°C)
Pr
Cp
(kJ/kg.K)
Mass Flow rate
(kg/s)
0,184 0,02 27,053 0,707 1004,91 0,00120
6,25 20,032 37,328 2,571E-02
18,75 23,458 43,370 2,597E-02
31,25 26,884 46,523 2,624E-02
43,75 30,310 49,718 2,651E-02
56,25 33,736 52,635 2,677E-02
68,75 37,162 55,402 2,703E-02
81,25 40,588 58,139 2,730E-02
93,75 44,014 61,237 2,756E-02
106,25 47,440 63,774 2,782E-02
118,75 50,866 66,108 2,808E-02
131,25 54,292 68,394 2,834E-02
143,75 57,718 83,904 2,860E-02
y = 0,2741x + 18,319
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100 120 140 160
Temperature(C)
x/D
Ts
Tm
Linear (Tm)

region. At Re: 4127, again here heat loss effects are decreasing gradually. Also, we can see
here the difference between surface temperature and mean temperature start to decrease
because of increasing heat transfer due to the increasing Reynolds number. At the end of the
pipe, there is a temperature increase because the cable that transfers electricity from power
supplier is such close that thermocouple. Thereby, excessive heating occurs there.
Q Total
(W)
Q Fluid
(W)
Q Loss
(Calc)
Q Loss
(Exp)
q"total
(W/m2
)
q"loss
(W/m2
)
q"s
(W/m2
)
h
(kJ/kg.C)
Nu
63,843 45,347 18,496 7,538 346,201 40,879 305,322 17,652 13,734
63,444 18,097 10,319 344,036 55,955 288,082 14,467 11,140
63,229 17,882 11,670 342,868 63,285 279,584 14,236 10,850
63,005 17,658 13,005 341,653 70,519 271,134 13,970 10,541
62,795 17,447 14,213 340,514 77,074 263,439 13,939 10,414
62,590 17,243 15,370 339,405 83,346 256,059 14,038 10,386
62,382 17,035 16,541 338,277 89,697 248,580 14,163 10,378
62,140 16,793 17,920 336,964 97,172 239,792 13,923 10,104
61,936 16,589 19,107 335,857 103,609 232,248 14,218 10,221
61,743 16,396 20,257 334,812 109,844 224,968 14,759 10,510
61,550 16,203 21,446 333,764 116,297 217,468 15,421 10,882
60,105 14,758 31,939 325,930 173,193 152,737 5,833 4,079
Table 28: Nusselt Number comparison for Re: 4127
0,0410 15,633 13,959

decrease gradually as the Reynolds number increase. Again here, Nusselt number at the outlet
of the pipe shows a sudden decline due to the excessive heating at the last thermocouple.
0
2
4
6
8
10
12
14
16
18
20
0 20 40 60 80 100 120 140 160
Nusselt#
x/D

Area
(m2)
Diameter
(m)
Orifice Temp
(°C)
Pr
Cp
(kJ/kg.K)
Mass Flow rate
(kg/s)
0,184 0,02 30,102 0,707 1004,91 0,00165
6,25 20,386 37,340 2,573E-02
18,75 24,043 42,779 2,602E-02
31,25 27,429 45,888 2,628E-02
43,75 30,815 49,017 2,654E-02
56,25 34,202 51,854 2,680E-02
68,75 37,588 54,642 2,706E-02
81,25 40,974 57,480 2,732E-02
93,75 44,360 60,537 2,758E-02
106,25 47,747 63,220 2,784E-02
118,75 51,133 65,751 2,810E-02
131,25 54,519 68,218 2,836E-02
143,75 57,635 83,305 2,859E-02
y = 0,2709x + 18,693
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100 120 140 160
Temperature(C)
x/D
Ts
Tm
Linear (Tm)

region. At Re: 5659, again here heat loss effects are decreasing gradually. Also, there is a
slight improvement in stability of the difference between surface and mean temperature. At
the end of the pipe, there is a temperature increase because the cable that transfers electricity
from power supplier is such close that thermocouple. Thereby, excessive heating occurs there.
Q Total
(W)
Q Fluid
(W)
Q Loss
(Calc)
Q Loss
(Exp)
q"total
(W/m2
)
q"loss
(W/m2
)
q"s
(W/m2
)
h
(kJ/kg.C)
Nu
76,404 61,922 14,481 7,544 414,310 40,910 373,400 22,024 17,117
75,974 14,052 10,059 411,983 54,548 357,435 19,077 14,664
75,721 13,799 11,402 410,612 61,828 348,784 18,895 14,378
75,460 13,538 12,714 409,195 68,943 340,252 18,693 14,084
75,217 13,295 13,889 407,878 75,317 332,562 18,839 14,057
74,972 13,050 15,050 406,550 81,612 324,938 19,053 14,080
74,716 12,794 16,256 405,161 88,149 317,012 19,206 14,058
74,432 12,510 17,602 403,621 95,449 308,172 19,051 13,813
74,176 12,253 18,842 402,229 102,174 300,055 19,392 13,928
73,927 12,005 20,076 400,880 108,867 292,013 19,976 14,216
73,678 11,756 21,353 399,529 115,787 283,742 20,713 14,607
72,003 10,081 31,435 390,448 170,460 219,987 8,570 5,994
Friction Factor Nu Dittus – Boelter Nu Gnielinski
0,0372 20,122 18,636

decrease gradually as the Reynolds number increase. Again here, Nusselt number at the outlet
of the pipe shows a sudden decline due to the excessive heating at the last thermocouple.
0
5
10
15
20
25
30
35
40
45
50
0 20 40 60 80 100 120 140 160
Nusselt#
x/D

Area
(m2)
Diameter
(m)
Orifice Temp
(°C)
Pr
Cp
(kJ/kg.K)
Mass Flow rate
(kg/s)
0,184 0,02 32,831 0,706 1005,23 0,00194
6,25 20,481 37,263 2,574E-02
18,75 23,845 42,716 2,600E-02
31,25 27,209 45,839 2,627E-02
43,75 30,573 48,919 2,653E-02
56,25 33,937 51,747 2,678E-02
68,75 37,301 54,526 2,704E-02
81,25 40,664 57,377 2,730E-02
93,75 44,028 60,355 2,756E-02
106,25 47,392 63,043 2,782E-02
118,75 50,756 65,575 2,808E-02
131,25 54,120 68,026 2,833E-02
143,75 57,484 82,595 2,858E-02
y = 0,2691x + 18,799
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100 120 140 160
Temperature(C)
x/D
Ts
Tm
Linear (Tm)

region. At Re: 6598, again here heat loss effects are decreasing gradually. Furthermore, there
is a slight improvement in stability of the difference between surface and mean temperature.
At the end of the pipe, there is a temperature increase because the cable that transfers
electricity from power supplier is such close that thermocouple. Thereby, excessive heating
occurs there.
Q Total
(W)
Q Fluid
(W)
Q Loss
(Calc)
Q Loss
(Exp)
q"total
(W/m2)
q"loss
(W/m2
)
q"s
(W/m2
)
h
(kJ/kg.C)
Nu
85,080 72,231 12,850 7,506 461,362 40,705 420,657 25,067 19,476
84,601 12,371 10,032 458,765 54,398 404,367 21,428 16,480
84,319 12,088 11,381 457,231 61,715 395,516 21,230 16,165
84,033 11,802 12,673 455,680 68,721 386,959 21,092 15,903
83,763 11,533 13,845 454,219 75,076 379,144 21,288 15,896
83,492 11,261 15,002 452,746 81,350 371,397 21,560 15,945
83,205 10,975 16,211 451,195 87,909 363,286 21,738 15,924
82,898 10,667 17,520 449,526 95,006 354,521 21,714 15,758
82,612 10,381 18,758 447,977 101,719 346,258 22,125 15,907
82,335 10,105 19,988 446,476 108,389 338,088 22,815 16,252
82,060 9,830 21,250 444,986 115,233 329,752 23,713 16,741
80,268 8,038 30,850 435,269 167,288 267,980 10,672 7,468
0,0355 22,739 21,261

region according to Gnielinski correlation. In addition, as can be seen in the figure the flow
reaches fully developed region faster as the Reynolds number increase. If we think about the
thermocouple installation it corresponds 37.5cm to reach fully developed region. As
mentioned before, Nusselt number at the outlet of the pipe shows a sudden decline due to the
0
5
10
15
20
25
30
35
40
45
50
0 20 40 60 80 100 120 140 160
Nusselt#
x/D

Area
(m2)
Diameter
(m)
Orifice Temp
(°C)
Pr
Cp
(kJ/kg.K)
Mass Flow rate
(kg/s)
0,184 0,02 33,800 0,706 1005,23 0,00227
6,25 20,448 37,311 2,574E-02
18,75 23,809 42,640 2,600E-02
31,25 27,171 45,802 2,626E-02
43,75 30,532 48,927 2,652E-02
56,25 33,894 51,730 2,678E-02
68,75 37,255 54,529 2,704E-02
81,25 40,617 57,427 2,730E-02
93,75 43,978 60,404 2,756E-02
106,25 47,340 63,126 2,781E-02
118,75 50,701 65,678 2,807E-02
131,25 54,063 68,165 2,833E-02
143,75 57,425 82,589 2,858E-02
y = 0,2689x + 18,767
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100 120 140 160
Temperature(C)
x/D
Ts
Tm
Linear (Tm)

occurs there.
Q Total
(W)
Q Fluid
(W)
Q Loss
(Calc)
Q Loss
(Exp)
q"total
(W/m2
)
q"loss
(W/m2
)
q"s
(W/m2
)
h
(kJ/kg.C)
Nu
94,212 84,650 9,562 7,530 510,882 40,834 470,048 27,873 21,659
93,694 9,044 9,998 508,072 54,215 453,858 24,102 18,539
93,377 8,727 11,365 506,353 61,631 444,723 23,870 18,176
93,056 8,406 12,676 504,611 68,739 435,871 23,695 17,868
92,760 8,110 13,838 503,008 75,038 427,970 23,995 17,919
92,457 7,807 15,003 501,365 81,356 420,009 24,315 17,985
92,135 7,485 16,233 499,617 88,027 411,590 24,484 17,939
91,794 7,144 17,542 497,770 95,124 402,645 24,513 17,792
91,474 6,824 18,798 496,030 101,933 394,098 24,964 17,951
91,165 6,515 20,040 494,354 108,669 385,685 25,752 18,347
90,855 6,205 21,324 492,677 115,635 377,042 26,736 18,877
88,889 4,239 30,845 482,017 167,260 314,757 12,508 8,754
0,0339 25,781 24,250

region according to Gnielinski correlation. In addition, as can be seen in the figure the flow
reaches fully developed region faster as the Reynolds number increase. As mentioned before,
Nusselt number at the outlet of the pipe shows a sudden decline due to the excessive heating
at the last thermocouple.
0
5
10
15
20
25
30
35
40
45
50
0 20 40 60 80 100 120 140 160
Nusselt#
x/D

Area
(m2)
Diameter
(m)
Orifice Temp
(°C)
Pr
Cp
(kJ/kg.K)
Mass Flow rate
(kg/s)
0,184 0,02 35,442 0,706 1005,23 0,00256
6,25 20,228 37,345 2,572E-02
18,75 23,602 42,594 2,599E-02
31,25 26,976 45,803 2,625E-02
43,75 30,350 48,950 2,651E-02
56,25 33,724 51,742 2,677E-02
68,75 37,098 54,554 2,703E-02
81,25 40,472 57,505 2,729E-02
93,75 43,847 60,489 2,755E-02
106,25 47,221 63,257 2,780E-02
118,75 50,595 65,901 2,806E-02
131,25 53,969 68,451 2,832E-02
143,75 57,344 82,660 2,857E-02
y = 0,2699x + 18,541
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100 120 140 160
Temperature(C)
x/D
Ts
Tm
Linear (Tm)

occurs there.
Q Total
(W)
Q Fluid
(W)
Q Loss
(Calc)
Q Loss
(Exp)
q"total
(W/m2)
q"loss
(W/m2)
q"s
(W/m2)
h
(kJ/kg.C)
Nu
112,737 95,594 17,143 7,547 611,334 40,924 570,410 33,323 25,911
112,126 16,532 9,978 608,022 54,106 553,916 29,165 22,447
111,741 16,147 11,366 605,935 61,633 544,302 28,910 22,027
111,354 15,760 12,686 603,836 68,790 535,046 28,767 21,704
111,002 15,407 13,843 601,924 75,065 526,858 29,241 21,848
110,637 15,043 15,013 599,949 81,412 518,536 29,706 21,982
110,245 14,650 16,267 597,819 88,208 509,610 29,920 21,930
109,835 14,241 17,581 595,600 95,334 500,266 30,059 21,825
109,445 13,850 18,860 593,481 102,270 491,211 30,631 22,033
109,061 13,466 20,152 591,400 109,277 482,123 31,498 22,448
108,680 13,086 21,477 589,337 116,463 472,874 32,653 23,062
106,358 10,764 30,903 576,746 167,574 409,172 16,163 11,314
0,0328 28,238 26,627

region according to Gnielinski correlation. When Figure 54 compared with the Figure 52, it is
obvious that there is a significant decrease in the error percentage. This shows that small
disturbances were affected the system until there as mentioned in literature survey. As
mentioned before, Nusselt number at the outlet of the pipe shows a sudden decline due to the
0
5
10
15
20
25
30
35
40
45
50
0 20 40 60 80 100 120 140 160
Nusselt#
x/D

Area
(m2)
Diameter
(m)
Orifice Temp
(°C)
Pr
Cp
(kJ/kg.K)
Mass Flow rate
(kg/s)
0,184 0,02 37,144 0,706 1005,23 0,00297639
6,25 20,446 37,465 2,574E-02
18,75 23,760 42,563 2,600E-02
31,25 27,074 45,710 2,626E-02
43,75 30,388 48,827 2,651E-02
56,25 33,701 51,602 2,677E-02
68,75 37,015 54,397 2,702E-02
81,25 40,329 57,349 2,728E-02
93,75 43,643 60,319 2,753E-02
106,25 46,956 63,108 2,778E-02
118,75 50,270 65,777 2,804E-02
131,25 53,584 68,405 2,829E-02
143,75 56,897 81,812 2,854E-02
y = 0,2651x + 18,79
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100 120 140 160
Temperature(C)
x/D
Ts
Tm
Linear (Tm)

region. At Re: 10006, here the temperature increase in the entrance region is starting to
disappear. This is a result of increasing heat transfer according to increment in Reynolds
number. At the end of the pipe, there is a temperature increase because the cable that transfers
occurs there.
Q Total
(W)
Q Fluid
(W)
Q Loss
(Calc)
Q Loss
(Exp)
q"total
(W/m2
)
q"loss
(W/m2
)
q"s
(W/m2
)
h
(kJ/kg.C)
Nu
125,596 109,059 16,537 7,605 681,065 41,239 639,825 37,596 29,215
124,935 15,876 9,964 677,479 54,032 623,447 33,156 25,507
124,515 15,456 11,326 675,200 61,419 613,781 32,935 25,087
124,087 15,029 12,635 672,884 68,514 604,370 32,776 24,726
123,698 14,639 13,785 670,770 74,751 596,019 33,296 24,879
123,295 14,236 14,948 668,586 81,056 587,530 33,801 25,019
122,858 13,799 16,199 666,215 87,843 578,372 33,982 24,918
122,405 13,346 17,504 663,759 94,919 568,840 34,110 24,781
121,967 12,908 18,789 661,384 101,887 559,497 34,640 24,935
121,536 12,477 20,090 659,046 108,939 550,107 35,475 25,304
121,099 12,040 21,453 656,679 116,331 540,347 36,457 25,774
118,670 9,611 30,219 643,507 163,870 479,637 19,251 13,492
0,0315 31,728 29,957

region according to Gnielinski correlation. Furthermore, at this Reynolds number the system
gives more stable results at fully developed region. As mentioned before, Nusselt number at
the outlet of the pipe shows a sudden decline due to the excessive heating at the last
thermocouple.
0
5
10
15
20
25
30
35
40
45
50
0 20 40 60 80 100 120 140 160
Nusselt#
x/D

Area
(m2)
Diameter
(m)
Orifice Temp
(°C)
Pr
Cp
(kJ/kg.K)
Mass Flow rate
(kg/s)
0,184 0,02 35,321 0,706 1005,37 0,00330
6,25 20,373 37,296 2,573E-02
18,75 23,661 42,463 2,599E-02
31,25 26,949 45,643 2,648E-02
43,75 30,237 48,764 2,650E-02
56,25 33,526 51,552 2,675E-02
68,75 36,814 54,352 2,701E-02
81,25 40,102 57,319 2,726E-02
93,75 43,390 60,281 2,751E-02
106,25 46,678 63,076 2,776E-02
118,75 49,966 65,754 2,802E-02
131,25 53,254 68,398 2,827E-02
143,75 56,542 81,363 2,851E-02
y = 0,263x + 18,729
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100 120 140 160
Temperature(C)
x/D
Ts
Tm
Linear (Tm)

region. At Re: 11147, again here the temperature increase in the entrance region is starting to
disappear. This is a result of increasing heat transfer according to increment in Reynolds
number. At the end of the pipe, there is a temperature increase because the cable that transfers
occurs there.
Q Total
(W)
Q Fluid
(W)
Q Loss
(Calc)
Q Loss
(Exp)
q"total
(W/m2
)
q"loss
(W/m2
)
q"s
(W/m2
)
h
(kJ/kg.C)
Nu
141,731 120,041 21,689 7,523 768,557 40,793 727,763 43,004 33,424
140,975 20,934 9,920 764,461 53,792 710,669 37,797 29,086
140,496 20,455 11,298 761,864 61,263 700,601 37,479 28,312
140,014 19,973 12,609 759,249 68,372 690,877 37,291 28,144
139,572 19,531 13,764 756,854 74,639 682,215 37,845 28,292
139,117 19,076 14,929 754,386 80,954 673,432 38,397 28,437
138,622 18,581 16,186 751,699 87,773 663,926 38,562 28,295
138,112 18,071 17,487 748,936 94,825 654,111 38,726 28,154
137,617 17,576 18,774 746,252 101,804 644,447 39,301 28,312
137,129 17,088 20,078 743,606 108,875 634,731 40,204 28,702
136,634 16,593 21,449 740,919 116,309 624,610 41,246 29,185
133,990 13,949 29,865 726,583 161,945 564,638 22,748 15,958
0,0305 34,592 32,659

region according to Gnielinski correlation. Furthermore, at this Reynolds number the system
gives more stable results at fully developed region. As mentioned before, Nusselt number at
the outlet of the pipe shows a sudden decline due to the excessive heating at the last
thermocouple.
0
5
10
15
20
25
30
35
40
45
50
0 20 40 60 80 100 120 140 160
Nusselt#
x/D

Area
(m2)
Diameter
(m)
Orifice Temp
(°C)
Pr
Cp
(kJ/kg.K)
Mass Flow rate
(kg/s)
0,184 0,02 38,132 0,704 1005,53 0,00410
6,25 20,251 37,416 2,572E-02
18,75 23,466 42,401 2,597E-02
31,25 26,680 45,588 2,623E-02
43,75 29,895 48,680 2,647E-02
56,25 33,110 51,412 2,672E-02
68,75 36,325 54,175 2,697E-02
81,25 39,539 57,143 2,721E-02
93,75 42,754 60,064 2,746E-02
106,25 45,969 62,861 2,771E-02
118,75 49,184 65,517 2,796E-02
131,25 52,398 68,150 2,820E-02
143,75 55,613 79,416 2,844E-02
y = 0,2572x + 18,643
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100 120 140 160
Temperature(C)
x/D
Ts
Tm
Linear (Tm)

region. When we look at the Figure 59, we can see that temperature increment in entrance
region is nearly disappeared. As Reynolds number increased the entrance effects are
eliminated. As it mentioned many times, at the end of the pipe there is a temperature increase
because the cable that transfers electricity from power supplier is such close that
thermocouple. Thereby, excessive heating occurs there.
Q Total
(W)
Q Fluid
(W)
Q Loss
(Calc)
Q Loss
(Exp)
q"total
(W/m2
)
q"loss
(W/m2
)
q"s
(W/m2
)
h
(kJ/kg.C)
Nu
172,598 145,757 26,841 7,581 935,943 41,111 894,832 52,130 40,532
171,711 25,953 9,892 931,129 53,643 877,487 46,341 35,682
171,126 25,369 11,274 927,960 61,138 866,823 45,845 34,960
170,545 24,788 12,573 924,808 68,182 856,626 45,602 34,451
170,018 24,261 13,706 921,952 74,324 847,627 46,313 34,664
169,472 23,715 14,855 918,990 80,552 838,438 46,970 34,834
168,869 23,112 16,111 915,722 87,363 828,359 47,057 34,582
168,259 22,501 17,389 912,410 94,297 818,113 47,264 34,422
167,657 21,899 18,673 909,145 101,255 807,890 47,826 34,521
167,069 21,311 19,959 905,957 108,232 797,725 48,841 34,942
166,469 20,712 21,316 902,706 115,592 787,114 49,970 35,438
163,705 17,947 28,382 887,715 153,908 733,807 30,828 21,678
Friction Factor Nu Dittus – Boelter Nu Gnielinski
0,0288 40,862 38,483

developed region which is low compared to others. Also, there is nearly 9% error for fully
developed region according to Gnielinski correlation. According to the results mentioned
above, Re: 13747 is the best approach for the turbulent flow case. As mentioned before,
Nusselt number at the outlet of the pipe shows a sudden decline due to the excessive heating
at the last thermocouple.
0
5
10
15
20
25
30
35
40
45
50
0 20 40 60 80 100 120 140 160
Nusselt#
x/D

Area
(m2)
Diameter
(m)
Orifice Temp
(°C)
Pr
Cp
(kJ/kg.K)
Mass Flow rate
(kg/s)
0,184 0,02 40,868 0,704 1005,69 0,00450
6,25 20,208 37,403 2,572E-02
18,75 23,409 42,409 2,597E-02
31,25 26,610 45,627 2,622E-02
43,75 29,811 48,735 2,647E-02
56,25 33,012 51,448 2,671E-02
68,75 36,213 54,206 2,696E-02
81,25 39,414 57,192 2,720E-02
93,75 42,615 60,105 2,745E-02
106,25 45,816 62,909 2,770E-02
118,75 49,017 65,596 2,794E-02
131,25 52,218 68,236 2,819E-02
143,75 55,419 80,076 2,843E-02
y = 0,2561x + 18,607
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100 120 140 160
Temperature(C)
x/D
Ts
Tm
Linear (Tm)

Convection Heat Transfer in a Smooth Pipe

Convection Heat Transfer in a Smooth Pipe

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