DOI: 10.3303/CET2188100 

 
 

 
 
 

 
 

 
 

 
 
 
 
 
 
 

 
 
 

 

 

 
 
 

 
 
 

 
 
 

 
 
 

 
 
 

 
 

Paper Received: 2 May 2021; Revised: 22 July 2021; Accepted: 5 October 2021 
Please cite this article as: Toman F., Kracík P., Pospíšil J., 2021, Influence of Tube Diameter and Steam Flow Rate on Heat Transfer in a 
Vertical Pipe of Condenser: Experimental Investigation of Copper Pipes, Chemical Engineering Transactions, 88, 601-606 
DOI:10.3303/CET2188100 

CHEMICAL ENGINEERING TRANSACTIONS

VOL. 88, 2021 

A publication of

The Italian Association
of Chemical Engineering
Online at www.cetjournal.it 

Guest Editors: Petar S. Varbanov, Yee Van Fan, Jiří J. Klemeš

Copyright © 2021, AIDIC Servizi S.r.l. 
ISBN 978-88-95608-86-0; ISSN 2283-9216

Influence of Tube Diameter and Steam Flow Rate on Heat
Transfer in a Vertical Pipe of Condenser: Experimental

Investigation of Copper Pipes
 Filip Toman*, Petr Kracík, Jiří Pospíšil
 Faculty of Mechanical Engineering, Brno University of Technology, Technická 2896/2, 61669 Brno, Czech Republic

The overall condensing power at condensers is affected by many factors. A condensate film on the pipe wall
plays a crucial role in heat transfer. The velocity of the gas phase inside the tubes has a fundamental influence
on the movement of the liquid film and the specific course of the velocity profile in the condensate film. The
magnitude of the shear stress at the steam-condensate interface affects the film thickness and its integrity. This
paper presents a study to evaluate the effect of the flow velocity inside a vertical pipe on the heat transfer
coefficient during water vapour condensation. Specifically, steam flow on heat transfer for two different pipes is
evaluated, namely with inner diameters 16 and 26 mm. A common feature is a detailed investigation of the
steam condensation process for a parallel flow and counterflow of steam and liquid film. Furthermore, the
influence of the temperature and flow direction of the water cooling the outer side of the condenser tube on the
transmitted power is evaluated. The condensation process is experimentally investigated on a copper pipe-in-
pipe heat exchanger with a possible change of the direction of the cooling water flow. Determination of the
condensation heat transfer coefficient is based on experimental identification of the overall heat transfer
coefficient and subsequent inverse calculation of the condensation heat transfer coefficient. The condensation
heat transfer coefficient ranges from 3,000 to 6,500 W/(m2∙K) for all configurations measured. The results 
generally show that as the Reynolds number of steam flow increases, the condensation heat transfer coefficient
increases too. At Reynolds number of 35,000 the same heat transfer coefficient value is identified either for
parallel flow or counterflow of cooling water. For higher Reynolds numbers, the parallel flow of cooling water
enables to reach the higher heat transfer coefficient compared to counterflow configuration. At lower Reynolds
numbers, the dependency is reversed.

1. Introduction

Condensation is a process which is an important part of many technological devices, for example, in the thermal 

circuits of steam power plants, in flue gas condensers or humid air condensers. The condensation process takes
place in heat exchangers called condensers. One of the most widely used types of heat exchangers is a pipe 
heat exchanger. To produce a thermal design of a pipe exchanger with phase change requires good knowledge
of the phase change process in pipes. This paper focuses on an experimental analysis of film condensation of
water vapour in a vertical pipe depending on the Reynolds number.   

The first derivation of the analytical relation for laminar film condensation was made by Nusselt  in 1916.
Nusselt derived the relation for the heat transfer coefficient during condensation on a vertical wall with the 

vertical steam velocity being zero. Many other scientists then used his relations as a basis. Rohsenow  focused 

on non-linear temperature field distribution in the condensate film. Sparrow and Gregg (1959) included 
in Nusselt’s theory a change in the momentum of a liquid film in a gravitational field caused by the acceleration 

of the film flow.  A considerable change in the consideration of liquid film is respecting the fact that the surface
of a liquid film is not perfectly smooth and due to gravity and the friction of the gas and liquid molecules inside
the film, it becomes deformed and its surface becomes wavy. This problem was mathematically commented on 
by Aktershev and Alekseenko (2005), who describes the effect of flowing gas on the film of a liquid for parallel 
flow and counterflow. In articles by Aktershev and Alekseenko (2013) and Aktershev and Alekseenko (2017),
used the finite element method to investigate the formation of natural waves and expresses the conditions for
the stability of the condensate film flow. The undulation of the surface significantly increases the heat transfer. 

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According to Whitham, the increase reaches up to 20.6 % in comparison with the original Nusselt’s 
theory. Blangetti and Naushahi (1980) included in the calculations the suction effect, which occurs during mass 
transfer due to condensation. Due to the different steam pressures in the core of the steam flow and at the 
steam-condensate interface, a radial component of velocity occurs increasing the amplitude of the film 
undulation. The suction effect is expressed by a so-called blowing parameter, which primarily depends on the
steam velocity and the condensation intensity. In the recent years, new numerical models of water vapour
condensation have been developed. Lee and Son (2018) studied the influence of the flow on the condensation
process during parallel flow and counterflow of steam and condensate. They compared the analytical approach 

proposed by Nusselt and the numerical approach proposed in . Their work primarily shows the necessity of a
correct setting of the numerical simulations, where, for example, even the size of the numerical network is very 

important. The numerical approach was also used by Hssain and Hammami (2019), who developed a model for 
predicting water vapour condensation in relation to the relative humidity and the input Reynolds number
of steam. The simulation showed that with the Reynolds number and the relative steam humidity increasing, the 

condensation intensity grows. A common feature of the above-mentioned studies is a detailed investigation into
the steam condensation process for a parallel flow configuration of the condenser pipe cooling. None of the 

studies focused on assessing the impact of a change in the cooling configuration (parallel flow/counterflow)
on the resulting heat transfer coefficient. This study focuses on assessing the influence of a change in the 

character of the cooling (parallel flow/counterflow), in the Reynolds number, and in the vertical pipe diameter on
the condensation heat transfer coefficient at atmospheric pressure. The results obtained allow the formulation
of suggestions leading to minimizing the material demands of steam condensers.

2. Experiment a data treatment

2.1 Experimental device 

Figure 1 shows the testing apparatus. It is based on a pipe-in-pipe heat exchanger, where the condensation
process is monitored. The steam runs through the inner pipe and the cooling water flows in the inter-annular
space of the shell of the exchanger. Both the concentric pipes are made of copper. It is possible to change the 

direction of the cooling water flow in the experimental device and thus to change the cooling flow configuration
of the condenser pipe from parallel flow to counterflow. The experimental section, where the controlled
condensation takes place, is 1 m long. The source of the water steam is a steam generator with a maximum
amount of the generated steam of 0.0097 kg/s. The output of the steam generator is controllable with a step
of 2.7∙10-5 kg/s of steam.

Figure 1: Experimental loop scheme 

 At the steam inlet into the exchanger, the temperature (Ts) and pressure (ps) of the incoming steam are 

measured and the temperature of the outgoing condensate (Tc) is measured at the exchanger outlet. The cooling
loop maintains the required temperature of the cooling water at the inlet into the shell of the exchanger (Tw,in) and 

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at the outlet (Tw,out) with the mass flow (Mw). Further, at the side of the cooling loop, water pressures are 
measured at the inlet (pw,in) and outlet (pw,out). Heat is removed from the cooling loop using a plate exchanger 

into the central cooling water available in the laboratory.  

2.2 Determining the condensation heat transfer coefficient  

To correctly determine the condensation heat transfer coefficient, it is necessary to know the overall heat transfer
coefficient. It depends both on the intensity of cooling from outside and on the material and thickness of the pipe 

wall. The overall heat transfer coefficient is given by Eq(1). 

𝑘𝑐 =
�̇�𝑐

𝐿 ∙ ∆𝑇𝑙𝑛
 , (1)

where �̇�𝑐  is the heat output of a phase change. Two situations occurred during the experiments. In the first 

case, such an amount of steam was let into the pipe that, even after running through the exchanger, it could not 

condense completely. In such a case, the active length L equals the entire experimental length of the exchanger,
and the output �̇�𝑐 equals the output transmitted to the cooling water. In the other case, such an amount of steam 
was used that all the steam condensed in the exchanger and the condensate started to subcool. In this case, 
the length L equals only the condensation length shortened by the length needed for the subcooling of the 

condensate. This length is different for each of the measured states and it depends on the outlet temperature of
the condensate. The heat transfer in the condensate during subcooling is based on the available analytical
relationships for the heat transfer in the liquid film. The output �̇�𝑐 is only the output of the phase change. After 
identifying the overall heat transfer coefficient, it is possible to determine the condensation heat transfer
coefficient using Eq(2).

𝛼𝑖𝑛 =
1

𝑑𝑖𝑛 ∙ 𝜋 ∙ [
1
𝑘𝑐

−
1

𝑑𝑜𝑢𝑡 ∙ 𝜋 ∙ 𝛼𝑜𝑢𝑡
−

𝑙𝑛 (
𝑑𝑜𝑢𝑡
𝑑𝑖𝑛

)

2 ∙ 𝜋 ∙ 𝜆𝑐𝑢
]

(2)

Where 𝛼𝑜𝑢𝑡  [W/(m2∙K)] is heat transfer coefficient which is calculated according to the relations for forced
convection in the annulus from the VDI heat atlas (2010)

2.3 Predicted condensation heat transfer coefficient 

The condensation heat transfer coefficient can be determined using analytical equations derived from physical
phenomena or obtained from experiments. This text presents two approaches. The first one is based on the
Eq(3) published by Nusselt, who derived the condensation heat transfer coefficient on a vertical wall
for immovable steam. This equation is still used in practice. 

𝛼𝑖𝑛,𝑛𝑢 = 0,943 [
𝑔 ∙ 𝜌𝑐 ∙ ℎ𝑐 ∙ 𝜆𝑐

3

𝜈𝑐 ∙ (𝑡𝑠 − 𝑡𝑤) ∙ 𝐿
]

0,25

(3)

Where ℎ𝑐  [J/kg] is latent heat. As can be seen, Nusselt’s equation does not include the influence of 
the steam velocity and thus the possible effects of the moving steam on the condensate film. From more
recent analytical relations, Eq(4) by Pashkevich and Muratov (2015) is used. He proposed the relation for the
mean value of the condensation heat transfer coefficient depending on the mass flow rate of steam at the
inlet.  He validated this equation using a vertical pipe with a diameter of 20 mm.

𝛼𝑖𝑛,𝑝𝑎 =
�̇�𝑣 ∙ ℎ𝑐

𝜋 ∙ 𝑑𝑖𝑛 ∙ (𝑡𝑠 − 𝑡𝑤) ∙ 𝐿
(4)

3. Results

In this study, the impact of the Reynolds number at the inlet into the condensation section on the condensation
heat transfer coefficient was measured in vertical pipes of two different inner diameters. The first measurement
included a vertical exchanger with the pipe inner diameter of 16 mm. The other case included an exchanger
with the pipe inner diameter of 26 mm. The mass flow rates of the steam were set for the given diameters during
the measurements, as is shown in Table 1. The determination of the mass flow rates of steam was based on 
the pipe with a diameter of 26 mm and then the flow rates were recalculated for the pipe with a smaller diameter
maintaining the same input steam velocity for both pipes. Each of the studied mass flow rates of steam was

603



assessed for three different temperatures of the incoming cooling water, particularly, 30, 40, and 50 °C. All the
combinations of the parameters tested were evaluated for both the parallel flow and the counterflow of the
cooling water. The fluid properties were calculated for middle temperature. The first configuration was parallel
flow cooling, when the cooling water flows in the same direction as the steam and the condensate. The other
configuration is counterflow cooling, when the cooling water flows in the opposite direction to the steam and the
condensate. The mass flow rate of the cooling water was adjusted so that the intensity of cooling was equal for
both heat exchangers.

Table1: The measured input steam flow rate and velocity 

The result of the measurement is a set of identified heat transfer coefficients. Using a regression analysis, they
were used to establish a continuous dependence of the heat transfer coefficient on the monitored parameters.
See the diagram in Figure 2.

3.1  Impact of the Reynolds number and the cooling water temperature on heat transfer 

Figure 2 shows the influence of the Reynolds number at the inlet into the condensation section on the
condensation heat transfer coefficient depending on the inner pipe diameter and the cooling water temperature.
The states for the Reynolds number ranging from 22,500 to 48,000 were measured experimentally. For all the
states measured, the condensation heat transfer coefficient ranged from 3,000 to 6,500 W/(m∙K), which matches 
the values presented by other authors. The Figure clearly shows that as the Reynolds number increases, the
condensation heat transfer coefficient increases as well. This is true for both the diameters and for different
cooling water temperatures.  

Figure 2: Influence of the Reynolds number on the condensation heat transfer coefficient depending on the inner 

pipe diameter and the cooling water temperature 

The condensation heat transfer coefficient inside the pipe also increases with a growing temperature of the
cooling water at the inlet. This results from the fact that when the heat drop is small, less steam condenses and
thus less condensate, which works as additional resistance to heat conduction, is formed. With the resistance
decreasing, the heat transfer coefficient inside the pipe increases but the total output transmitted in the pipe
decreases with the cooling water temperature increasing. 

3.2 Impact of the pipe diameter on the heat transfer 

The Figure 2 also shows that the heat transfer coefficient in a pipe with a smaller diameter is more sensitive to
a change in the Reynolds number or in the steam velocity than in a pipe with a larger diameter. For the inner

Pipe 26 mm Pipe 16 mm
Case Ṁs [kg/s] us [m/s] Re [−] Ṁs [kg/s] us [m/s] Re [−]

1 0.0055 17.7 22,348
2 0.0069 22.3 28,158 0.0026 22.3 21,658
3 0.0083 26.6 33,585 0.0031 26.6 25,834
4 0.0097 31.3 39,519 0.0037 31.3 30,399
5 0.0047 40.0 38,849
6 0.0059 50.0 48,561

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diameter of 16 mm, there was a 42 % increase in the condensation heat transfer coefficient when the Reynolds
number increased by 50 %, whereas for the inner diameter of 26 mm, there was a 10.7 % increase in the
condensation heat transfer coefficient when the Reynolds number increased by 50 %. This is probably caused
by two effects. Firstly, in a pipe with a smaller diameter, the condensate film is more disturbed because, in a
smaller space, the steam vortices have less room to swirl and, thus, the condensate film is more disturbed and
becomes wavier, which reduces the resistance to heat conduction. Secondly, due to a greater heat transfer, the
condensation is more intense and, thus, the thickness of the condensate film grows more than in a pipe with a
larger diameter. A greater film thickness results in a smaller cross section of the pipe, thus contributing to an
increase in the steam velocity, which leads to greater turbulence inside the pipe. Therefore, if we are not bound
by pressure losses during the flow in the pipe, it is more suitable to use a smaller pipe diameter to achieve a
more efficient heat transfer.  
A pipe with a smaller diameter is also more sensitive to the cooling configuration. In a pipe with a diameter of
26 mm, there is not much difference between the parallel flow and counterflow cooling, whereas in a pipe with
a diameter of 16 mm, there are obvious differences between the cooling configurations. Figure 3 shows a
detailed comparison of the impact of the parallel flow and counterflow cooling configurations for a pipe with the
inner diameter of 16 mm and the input cooling water temperature of 30 °C. The experimentally obtained points
were fitted with a linear curve. 

Figure 3: Dependence of the heat transfer coefficient on the Reynolds number - parallel flow and counterflow 

cooling configurations for the pipe diameter of 16 mm and the cooling water temperature of 30 °C.  

In classic heat exchangers without phase change, counterflow cooling is usually more efficient due to a greater
heat drop. For condensation heat exchangers, this statement cannot be unequivocally confirmed. The main
difference, in comparison to exchangers without phase change, is the presence of the condensate film inside
the pipe, which increases the resistance to heat conduction. In the counterflow cooling configuration, cold water
enters the exchanger where the condensate film layer is the thickest, i.e., at the point of the highest heat
resistance to heat conduction, which reduces the advantage of a greater temperature drop. For this reason, the
counterflow cooling configuration is better for low values of the Reynolds number or of the mass flow rate of
steam at the inlet into the pipe, see Figure 3. This is because, during condensation in the range of these steam
flow rates, a sufficient layer of condensate is not formed and there is still the advantage of a greater heat drop
in comparison to the resistance to heat conduction. As the mass flow rate of steam increases, the efficiency of
both configurations becomes more and more equal. In our case, the point of equal efficiency corresponds to the
Reynolds number of 35 000. At this point, it cannot be determined which cooling configuration is better. When
the mass flow rate of steam is further increased, the liquid film thickness also increases and better efficiency of
cooling is achieved by parallel flow cooling.  
Figure 3 shows the theoretical behaviour. Conditions for both the parallel flow and counterflow cooling were
calculated. Since neither of the authors focused on the cooling configuration, there is not a big difference
between these two cases and the points almost coincide. The only difference, when these relations are applied
to both cooling configurations, results from differences in the wall temperature and the mean temperature for
determining the physical properties of the liquid film. However, these differences are insignificant.
When comparing the experimentally obtained data with the behaviours described by Nusselt and Pashkevich,
we can see a relatively close correspondence. Nusselt's relation corresponds to the experimental data for the 

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counterflow cooling, where the greatest deviation of the data measured from Nusselt's equation does not exceed
10 %. Therefore, it is suitable to apply his equation when calculating film condensation for counterflow
cooling. Pashkevich's relation has a much greater progression, and its behaviour corresponds more to the
parallel flow cooling configuration. When the Reynolds number is 35 000, the experimental data intersect
Pashkevich's relation. However, since the graphs have different gradients, the deviation increases in both
directions from this point. The deviation from the data obtained is the greatest when the Reynolds number is
low, around 22 300, when it reaches approximately 31 %.  

4. Conclusion

This paper evaluates the influence of the Reynolds number and the pipe diameter on the condensation heat
transfer coefficient in a vertical pipe-in-pipe heat exchanger. Experiments were performed for two diameters (16
mm and 26 mm) of the inner pipe. It was proven that as the Reynolds number increases and the pipe diameter
decreases, the condensation heat transfer coefficient increases. A bigger proportional increase in the inner heat
transfer coefficient occurred with a smaller pipe diameter. The data presented above suggest that the most
efficient configuration for dissipating the most power from the steam core is using a condensation pipe with a
smaller diameter when the Reynolds number of the steam at the inlet into the condensation section is high. The
experimental comparison of the parallel flow and the counterflow cooling configurations with a maximum heat
output transmission suggests that using the parallel flow cooling of water with lower input temperature is more
appropriate. This configuration provides a solution for transferring the maximum heat flow while minimizing the
material demands on the condensation exchanger.

Acknowledgements 

This paper has been supported by the EU projects: Sustainable Process Integration Laboratory – SPIL funded
as project No. CZ.02.1.01/0.0/0.0/15_003/0000456 and Computer Simulations for Effective Low-Emission
Energy Engineering funded as project No. CZ.02.1.01/0.0/0.0/16_026/0008392 by Czech Republic Operational
Programme Research, Development and Education, Priority 1: Strengthening capacity for high-quality research
and the collaboration.

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