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Research Papers: Piper and Riser Technology

# Heat Loss of Insulated Pipes in Cross-Flow WindsPUBLIC ACCESS

[+] Author and Article Information
Bjarte O. Kvamme

Department of Mechanical and Structural
Engineering and Materials Science,
University of Stavanger,
Randabergveien 10E,
Stavanger 4025, Rogaland, Norway
e-mail: bjarte@valhall.onl

Jino Peechanatt

Department of Mechanical and Structural
Engineering and Materials Science,
University of Stavanger,
Ernakulam 682506, Kerala, India
e-mail: jino_2239@yahoo.co.in

Professor
Department of Mechanical and Structural
Engineering and Materials Science,
University of Stavanger,
Stavanger 4036, Rogaland, Norway

Knut E. Solberg

Department of Mechanical and Structural
Engineering and Materials Science,
University of Stavanger,
Stavanger 4036, Rogaland, Norway
e-mail: knut.espen.solberg@gmc.no

Yaaseen A. Amith

Department of Mechanical and Structural
Engineering and Materials Science,
University of Stavanger,
Stavanger 4036, Rogaland, Norway
e-mail: yaaseen.a.amith@uis.no

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received July 26, 2017; final manuscript received September 6, 2018; published online October 12, 2018. Assoc. Editor: Søren Ehlers.

J. Offshore Mech. Arct. Eng 141(2), 021701 (Oct 12, 2018) (11 pages) Paper No: OMAE-17-1126; doi: 10.1115/1.4041458 History: Received July 26, 2017; Revised September 06, 2018

## Abstract

In recent years, there has been unprecedented interest shown in the Arctic region by the industry as it has become increasingly accessible for oil and gas exploration. This paper reviews existing literature on heat transfer coefficients and presents a comprehensive study of the heat transfer phenomenon in horizontal pipes (single/multiple pipe configurations) subjected to cross-flow wind besides the test methodology used to determine heat transfer coefficients through experiments. In this study, cross-flow winds of 5 m/s, 10 m/s, and 15 m/s blowing over several single pipe and multiple pipe configurations of diameter 25 mm and 50 mm steel pipes with insulation are examined. Based on the findings, the best correlation for use by the industry for single and multiple pipe configurations was found to be Churchill–Bernstein correlation. The deviation from the theoretical calculations and the experimental data for this correlation was found to be in the range of 0.40–1.61% for a 50 mm insulated pipe and −3.86% to −2.79% for a 25 mm insulated pipe. In the case of a multiple pipe configurations, the deviation was in the range 0.5–2.82% for 50 mm insulated pipe and 12–14% for 25 mm insulated pipes.

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## Introduction

The activity level in the Polar regions is increasing and is expected to continue to increase over the next years. Oil and gas production, shipping, fishing, and transport activities are all areas that are expected to increase over the coming years. The decrease in ice extent in the Arctic has renewed the interest in the Northern Sea Route (NSR) necessitating further research to evaluate the adequacy of the equipment and appliances used on vessels traversing in polar waters. The introduction of the Polar Code by the International Maritime Organization (IMO) attempts to mitigate some of the risks endangering vessels in Polar waters. The objective of this paper is to check the validity of commonly used heat transfer correlations against commonly used pipes and mounting methods in the industry. Pipes with closed-cell foam (like Armaflex) are very common in Norway, and have been selected as representative examples. Cold bridging is also of interest, and the mounting mechanisms selected for the experiments are also common in Norway.

###### Shipping.

The decrease in the ice extent makes the NSR a more viable option for shipping. The northern sea route is a shipping lane between the Atlantic Ocean and the Pacific Ocean, which goes along the coastline of Siberia and the Far East. A route suggested in Ref. [1] is: Barents Sea - Kara Sea - Laptev Sea - East Siberian Sea - Chukchi Sea, with estimated time savings of 17.5 days.

###### Oil and Gas.

While current oil prices do not easily allow for a significant development of the oil and gas resources in the Arctic, demand for oil and gas in 2035 is expected to increase by 18% and 44%, respectively [2]. 60% of the planned oil and gas production in 2035 is estimated to come from fields that have not yet been discovered [2]. In 2008, The United States Geological Survey (USGS) [3] estimated that a total of 25% of the undiscovered oil and gas reserves are located in the Arctic. Considering that the Arctic only composes 6% of the world's area, this is a significant amount. This assessment was performed using a geology-based probabilistic methodology. In the assessment, it is estimated that a total of 90 billion barrels of oil, 1669 trillion cubic feet of natural gas, and 44 billion barrels of natural gas liquids could be present in Arctic regions, of which 84% is expected to be located in offshore areas [3]. Despite the increased cost of oil and gas exploration in remote, Arctic areas, it is expected that the rise in demand will cause the exploration and production for oil and gas in the Arctic to increase. This will result in more seismic survey vessels and exploration drilling vessels in the Arctic, and eventually oil and gas-producing vessels. Exploration and production vessels and platforms are highly dependent on the piping facilities, and the ability to maintain flow assurance is crucial. If the winterization of pipes is not done properly, this could lead to massive costs due to production shut-down or even worse, accidents. A temperature drop between the different areas of the production facilities will change the flow properties of the fluids, and can, in a best case scenario, cause the processing of the crude oil to become inefficient.

###### Tourism.

Tourism and travel to polar regions is getting more popular, and the number of shipborne tourists in Antarctica increased from around 7,000 in 1992, to over 30,000 in 2007 [4]. The increase in activity together with the enforcement of the Polar Code has led to more ships being modified or built for polar conditions.

###### Polar Code.

The international maritime organization (IMO) has adopted the international code for ships operating in polar waters (polar code) and related amendments, and has made it mandatory under the International Convention of the Safety of Life at Sea (SOLAS). The Polar Code was adopted in November 2014, and is expected to enter into force on 01.01.2017. It applies to ships operating in Arctic and Antarctic waters. The Polar Code aims to provide safe ship operations and protect the polar environment by addressing risks present in polar waters, which are not adequately mitigated by other instruments in IMO [5]. The Polar Code covers a wide range of potential problems and issues, only some of which are applicable for this paper.

###### Summary.

All things considered, the interest for the Polar regions has increased and is expected to continue to increase in the years to come. An increased knowledge about the challenges the Polar regions can pose is required. This paper will investigate one very common piece of infrastructure, namely heated pipes. Most pipes on vessels and buildings will be well protected inside the superstructure where wind is not a major concern. Some external piping is, however, not possible to avoid. Fire safety systems and equipment located on the deck are among the systems not possible to protect in all circumstances. Equipment with hydraulic lines might need some heat tracing and/or insulation to ensure that the viscosity of the hydraulic fluid is maintained. The objective of this paper is to check the validity of commonly used heat transfer correlations against commonly used pipes and mounting methods in the industry. Pipes with closed-cell foam (like Armaflex) are very common in Norway, and have been selected as a representative example. Cold bridging is also of interest, and the mounting mechanisms selected are also common in Norway.

## Theory

###### Conduction.

Conductive heat transfer is the mode of thermal energy transfer due to the difference in temperature within a body, or between bodies in thermal contact without the involvement of mass flow and mixing [6]. The thermal conductivity of the object defines how efficiently the object will transfer the thermal energy. For the conductive heat transfer of a cylinder with length L, we have Eq. (1) [6]. Display Formula

(1)$qcond,cyl=2πLk(Ti−T∞ln(ro/ri))$

where k is the average thermal conductivity.

###### Convection.

Convective heat transfer is the transfer of thermal energy by a fluid in motion. Convective heat transfer can be divided into two subcategories: forced convection and free/ natural convection. Forced convection is used when an external flow (such as a fan, pump, or atmospheric winds) passes over a surface. Free/natural convection takes place when no fluid is flowing over the objects surface. The change in temperature of the fluid results in a change of the density of the fluid, causing circulating currents due to buoyancy forces as the denser fluid descends, and the lighter fluid ascends. The heat loss from free/natural convection can be observed in experimental data, but will not be subject to calculation in this paper. The mathematical formulation for convective heat transfer rate is found in the following equation: Display Formula

(2)$qconv=hA(Ti−T∞)=Ts−T∞1hA$

where h is the convective heat transfer coefficient and A is the surface area. From Eq. (2), the relationship to the average heat transfer coefficient, $h¯$, is established. The difference between h and $h¯$ is that the latter takes the average surface conditions, while the first takes the local surface conditions. The average heat transfer coefficient can be written as Display Formula

(3)$h¯=qconvA(Ts−T∞)$

###### Thermal Resistance.

Many physical phenomena can be described by the general rate equation showed in Eq. (4) [7]. Display Formula

(4)$flow rate=driving forceresistance$

For heat transfer, the flow rate is heat, or thermal energy. The driving force is the temperature difference, dT between the object and the surroundings, and the resistance will be the thermal resistance, denoted by Rth. Based on this, we get Eq. (5). Display Formula

(5)$q=dTRth$

For resistances in series, the total resistance is given by Eq. (6). For resistances in parallel, the total resistance is given by Eq. (7)Display Formula

(6)$Rtot=∑iRi$
Display Formula
(7)$Rtot=(∑i(1Ri))−1$

When considering the concept of thermal resistance, Eqs. (1) and (2) can be rewritten to Eqs. (8) and (9), respectively. Display Formula

(8)$Rcond,cyl=ln(r2/r1)2πLk$
Display Formula
(9)$Rconv,cyl=12πrLh$

###### Overall Heat Transfer Coefficient.

The average heat transfer coefficient is only suitable for calculation when there is only one layer. For calculating the heat transfer rate through multiple layers, a general equation is shown in Eq. (10), where T1 is the internal temperature at the first resistance and Tn is the temperature at the outermost thermal resistance Display Formula

(10)$q=T1−TnR1+R2+⋯+Rn$

From this, the heat transfer rate can be expressed in terms of an overall heat transfer coefficient, U. It must be noted that U is dependent on a reference area. Throughout this paper, U is calculated with reference to the area of the outermost diameter. For a cylinder with insulation Display Formula

(11)$q=T∞,1−T∞,3Rth,tot=UA(T∞,1−T∞,3)$

Figure 1 shows a cylinder with three layers and inner and outer convective heat transfer. This is representative of an insulated pipe with an internal fluid flow that has an external fluid flow (forced or free convection). Layer A is the pipe wall, layer B is the layer of insulation, and layer C is a protective tube around the insulation. The equation for the heat transfer rate for this configuration is shown in the following equation: Display Formula

(12)$q=T∞,1−T∞,31h12πr1L+ln(r2/r1)2πkAL+ln(r3/r2)2πkBL+1h32πr3L$

As the heat transfer rate is constant throughout the cylinder, q can be expressed as shown in the following equation: Display Formula

(13)$q=T∞,1−Ts,11h12πr1L=Ts,1−T2ln(r2/r1)2πkAL=T2−T3ln(r3/r2)2πkBL=Ts,3−T∞,31h32πr3L$

###### Dynamic Viscosity.

Sutherland [8] presented a relationship between the dynamic viscosity and the absolute temperature of an ideal gas, shown in Eq. (14) for calculating the dynamic viscosity of air at different temperatures Display Formula

(14)$μ=μref(TTref)3/2(Tref+ST+S)$

where Tref is the reference temperature, μref is the dynamic viscosity at Tref, and S is Sutherland's constant for the gas of interest. For air, the constants shown in Table 1 are known from Ref. [8]:

###### Film Temperature.

To account for the variations of the thermodynamic properties with temperature, the term film temperature has been developed [9]. The film temperature is defined as the arithmetic mean of the surface and freestream (ambient) temperatures, and can be found in Eq. (15). When using the film temperature, the fluid properties are assumed to be constant during the entire flow. Display Formula

(15)$Tf=Ts+T∞2$

###### Heat Transfer Coefficient for a Cylinder in Cross-Flow Wind.

To calculate the convective heat transfer coefficient for a cylinder in cross-flow, a correlation must be used. There are numerous correlations that can be used, with different ranges of validity and accuracy. Moran et al. [10] state that the expected accuracy is no more than ±25–30%. Incropera et al. [6] are more optimistic, and suggest an expected accuracy of ±20%. Numerous comparisons of the different correlations have been performed. Morgan [11] did a comprehensive review of the existing literature on convective heat transfer. Manohar and Ramroop [12] performed a comparison of five different correlations using experimental data on pipes at different wind speeds and inclinations of a pipe, although their findings might not be accurate as mistakes were found in the constants used for some of the correlations. Whitaker [13] performed a comprehensive review as well, and presents comparative plots of the different correlations.

###### Hilpert Correlation.

The Hilpert correlation was suggested in Hilpert [14], and has proven to be a quite good estimate for the average Nusselts number over a pipe in a cross-flow arrangement. The Hilpert correlation is an empirical correlation, and has the form found in Eq. (16) [6,9,10]. The constants initially proposed by Hilpert are found in Table 2, but have since been revised and recalculated, as new and more accurate thermodynamic data has emerged. The constants presented in Table 3 are recommended for use by [6,9,10]. All properties in Table 3 are evaluated at the film temperature Display Formula

(16)$Nu¯D=CReDm(Pr)1/3[Pr≥0.7]$

Based on Hilpert's work, Fand and Keswani [15] recalculated the constants used in Hilpert's correlation based on more accurate values for the thermodynamic properties of air than what was available in 1933. All temperatures are evaluated at film temperature. The constants proposed by Fand and Keswani [15] are presented in Table 4. Morgan [11] recalculated the constants used in the Hilpert correlation based on an extensive review of existing literature on convective heat transfer. The recalculated values are found in Table 5.

###### Žukauskas Correlation.

Žukauskas [16] presents the correlation found in Eq. (17). In this, all properties are evaluated at the freestream (ambient) temperature, except for Prs, which is evaluated at the surface temperature Display Formula

(17)$Nu¯D=CReDmPrn(PrPrs)1/4[0.7≤Pr≤5001≤ReD≤106]$

The constants used are presented in Tables 6 and 7.

###### Whitaker Correlation.

Whitaker [13] presents the correlation found in the following equation: Display Formula

(18)$Nu¯D=(0.5ReD1/2+0.06ReD2/3)Pr0.4(μbμs)1/4[1.00≤Re≤1×1050.67≤Pr≤300]$

Where μb is the fluid viscosity at bulk temperature (same as free-stream temperature for open systems) and μs is the fluid viscosity at surface temperature. Whitaker [13] notes that this correlation is generally within ±25% of other correlations, except at low Reynolds numbers, where the Hilpert correlation (Table 2) gives considerably higher values.

###### Churchill–Bernstein Correlation.

Churchill and Bernstein [17] present the correlation found in Eq. (19) and had as a goal to provide a single, comprehensive equation for the heat transfer coefficient of a cylinder subjected to a cross-flow wind, for all ranges of Reynolds numbers, and a wide range of Prandtl numbers. All fluid properties are evaluated at film temperature. Display Formula

(19)$Nu¯D=0.3+0.62Re1/2Pr1/3[1+(0.4/Pr)2/3]1/4×[1+(Re282000)5/8]4/5[ReDPr≥0.2]$

###### Heat Transfer Correlation Discussion.

The Žukauskas and the Churchill–Bernstein correlations are recommended by Incropera et al. [6] as they are valid for a wide range of conditions and are the most recent ones. Moran et al. [10] recommend the use of the Churchill–Bernstein correlation unless the simplicity of the Hilpert is advantageous. Theodore [18] recommends the Hilpert correlation, while Çengel [9] recommends the Churchill–Bernstein correlation. As the wind speeds experienced for winterization purposes can be expected to be lower than 20 m/s in most applications, the critical dimension will be the diameter. For wind speeds lower than 20 m/s and pipes with an outer diameter of less than 1.0 m, the Reynolds number will not exceed 400,000. This means that all correlations apart from the Hilpert correlation with Morgan's constants and the Whitaker correlation are valid. Morgan's constants have a limit at Re ≤ 200,000, and the Whitaker correlation has a limit at Re ≤ 100,000. These correlations will therefore not be among the correlations, which will be considered for recommendation, but will still be considered in the theoretical calculations. In general, all of the correlations have different ranges of applicability and some are likely to be more accurate at certain ranges.

## Experiments

To test the heat transfer correlations, experimental testing was performed in GMC Maritime AS's climate laboratory in Stavanger, Norway.

###### Test Apparatus.

A rectangular testing jig seen in Fig. 2 was designed and built to experimentally determine the average heat transfer coefficient $h¯$ for circular pipes in cross-flow wind arrangement inspired by the work of Manohar and Ramroop [12]. The apparatus was designed to allow for multiple pipes of varying diameters to be positioned in a row. The testing rig was constructed using perforated angle iron, and bolted into shape. Triangular corner pieces were used to create additional stability, and the entire jig was bolted into place on a pallet to enable easy transportation. The dimensions of the jig were 110 cm (L) × 66 cm (W) × 100 cm (H) and the height of the horizontal section was adjustable to ensure direct air flow over the pipes. The pipes were insulated with Armaflex® AF-1, 10-mm thick insulation to better simulate real-life industry use, and to provide a smooth surface, avoiding local turbulence over the areas where the sensors were mounted. Details about the insulation can be found in Ref. [19]. The insulation has a rated thermal conductivity of 0.033 W/(m ⋅K). A drawing of the 50 mm insulated pipe with dimensions is found in Fig. 11. It should be noted that the uninsulated sections had a significant impact on the heat loss, and for future experiments, the entire pipe should either be insulated or uninsulated. The end caps for the pipes were designed in openscad and printed in extruded acrylonitrile butadiene styrene plastic using the three-dimensional printing laboratory at the University of Stavanger. Heating elements were used to create a constant heat flux from the pipes. The heating elements were secured to the end caps using fire retardant silicone sealant. The heating elements were obtained from RS Components, and have a nominal output of 1000 W at 240 V ⋅ AC. As this heat flux is much higher than expected in real-life applications, the power output of the heating elements was controlled using a variac. Figure 3 shows an overhead view of the rig as installed in the climate laboratory for testing. A description of the key components is found in Table 8. In order to minimize the effects the uninsulated end sections had on the recorded heat loss, the data obtained from the sensors located at the midsection (number 8 in Fig. 3) were used for the analysis.

###### Temperature Measurement.

The data logger used in the experiment is an Arduino Uno R3. The temperature sensors used for measuring the temperature of the pipe are of type Maxim Integrated DS18B20. These temperature sensors have a rated accuracy of ±0.5 °C for temperatures between −10 °C and 85 °C, and an overall range from −55 °C and 125 °C. The resolution is configured to be 0.0625 °C. Further information about the DS18B20 can be found in Ref. [20]. Six temperature sensors were strategically attached on the surface of each pipe as shown in Fig. 11. For measuring the ambient temperature and humidity, a DHT22 digital temperature and humidity sensor were used. Further information about the DHT22 sensor can found in Ref. [21]. In order to check for uniform surface temperature on the pipe and surface temperature stability, preliminary heating tests were carried out to verify the overall test arrangement. Equilibrium conditions were reached within 150 min of heating and were verified by monitoring the six temperature sensors at 30 s time interval for 24 h. The pipe was considered to have reached equilibrium when the variation in temperature over a 2.5 h period was less than ±0.5 °C.

###### Wind Measurement.

To measure the wind speed, the sensor installed in the climate laboratory was utilized. The sensor provided a voltage output, which was compared to the wind speed measured using a hand-held LCA6000 anemometer. Based on this, a relationship between the voltage output and the measured wind speed was established, and used for calculating the wind speed.

###### Testing Procedure.

The following testing procedure was utilized when rigging up for the experiments:

1. (1)Position the testing rig in the climate laboratory, directly in front of the wind tunnel. Adjust the height so that the pipes are in the middle of the air flow.
2. (2)Connect up the wind speed sensor to the gray junction box on the testing jig.
3. (3)Position the ambient temperature sensor and connect it up to the gray junction box.
4. (4)Select pipes according to schedule.
5. (5)Position the temperature sensors along the lines of the black markings on the pipe. one temperature sensor at the top and another at the bottom of the pipe. Secure the temperature sensor to the pipe with aluminum tape.
6. (6)Connect the temperature sensors to the gray junction box.
7. (7)Connect the power cables to the heating elements.
8. (8)Connect a multimeter in series with one of the leads connecting to the variac, and set it to measure the current.
9. (9)Connect a multimeter in parallel with the two leads connecting to the variac, and set it to measure the voltage.
10. (10)Connect the data cable from the gray junction box to the Arduino.
11. (11)Connect power to the Arduino.
12. (12)Verify that the logging has started. The light-emitting diodes work like a heartbeat sensor and will rapidly flash green when logging has started.
13. (13)Close the doors to the cooling room, and allow the temperature to settle down to −20 °C.
14. (14)Adjust the output voltage of the variac until the measured current is equal to 1 A per pipe connected. This equals ≈ 50 W with a resistance of 58.5 Ω.

The testing was performed using different configurations of the pipes. The various configurations are shown in Table 9. Throughout the testing of the pipes, the temperature was kept at −20 °C. Each experiment was performed at four different wind speeds: 0, 5, 10, and 15 m ⋅ s−1, and repeated three times to confirm the findings. The temperature readings from the temperature sensors were monitored in real time using the serial output on the Arduino to a comma-separated values (CSV) file on a computer. This CSV file was connected to Microsoft Excel, where the data were automatically refreshed every minute to show key numbers and plots of the temperature readings. This spreadsheet was used to identify when all sensors had stabilized, that is, showed a temperature difference of less than 0.5 °C over a period of 10 min between the maximum and minimum value obtained in this period. After the sensors had stabilized, the test was concluded, and we proceeded to the next test. Between each run, the following procedure was followed:

1. (1)Confirm that the temperature logger is working, and logging the data.
2. (2)Cool the room down to −20 °C, set the wind to 7.5 m/s to cool down the pipes faster
3. (3)Once the pipes have stabilized at −20 °C, write down the time of start, activate the heating element inside, and wait for the pipe to stabilize at the higher temperature.
4. (4)Once the pipe has stabilized at higher temperature, write down the time in the experiment log, turn on the fan, and set it to 5 m/s wind speed.
5. (5)Wait for the temperature to settle again, write down the time in the experiment log, and increase the wind speed to 10 m/s
6. (6)Wait for the temperature to settle again, write down the time in the experiment log, and increase the wind speed to 15 m/s.
7. (7)After the temperature has stabilized again, write down the time in the experiment log, turn off the heating element, and set the wind to 7.5 m/s to cool down the pipe to −20 °C for the next run.

###### Experiment 1.

Experiment 1 was used as the baseline case for 50-mm insulated pipes, and is used for comparing the different surface coatings. This experiment is discussed in detail in Ref. [22].

###### Experiment 2.

In experiment 2, two insulated 50 mm pipes that were positioned in line were tested. The purpose of this experiment was to validate the effect of staggered flow. It is assumed that the pipe that was positioned directly in front of the wind nozzle will have the same heat loss as a single pipe, but the effect on the second pipe is unknown. This experiment is discussed in detail in Ref. [23].

###### Experiment 3.

Experiment 3 tested three insulated 50 mm pipes that were positioned in line. The purpose of this experiment was to validate the effect of staggered flow across pipes that were located in very close proximity. It is assumed that the pipe that was positioned directly in front of the wind nozzle will have the same heat loss as a single pipe, but the effect on the second and third pipe is unknown. This experiment is discussed in detail in Ref. [23].

###### Experiment 4.

Experiment 4 tested the effect of ice glazing on the exterior of the insulation. The goal was to see whether the increased roughness of the surface affected the overall heat transfer coefficient. The ice was applied using a spray bottle filled with fresh water. The water was applied in multiple steps, with five minutes between each spray. The resulting ice was very uneven and would simulate a pipe exposed to sea spray. A picture of the pipe at the start of the testing is shown in Fig. 4. The experiment was considered to be a partial success, and it should be noted that when the pipes were removed after the experiment, the ice glazing was no longer present. This experiment is discussed in detail in Ref. [22].

###### Experiment 5.

Experiment 5 tested the effect of an even layer of ice, or an ice coating on the exterior of the insulation. The goal was to see if a layer of ice would affect the overall heat transfer coefficient of the pipe. As the ice layer was even and smooth, it is assumed that this would primarily have an insulating effect. Experiment 5 was performed after experiment 4, and only one run was performed, as the ice in experiment 4 had disappeared during the experiment. After this run, the ice layer was still present on the pipe, but additional runs were not performed. This experiment is discussed in detail in Ref. [22].

###### Experiment 6.

As experiment 4 was not a complete success, it was decided to try another configuration where the surface roughness would not melt. For experiment 6, quartz particles ranging from 0.8 to 1.2 mm in size were adhered to the insulation of the pipe to simulate a pipe that had been exposed for a long period of time with no maintenance. A picture of the pipe is shown in Fig. 5. In hindsight, the method used to apply the quartz was far from ideal, and the glue and quartz appears to have added a layer of insulation that overpowered any effect of the increased surface roughness. For future experiments, a very thin layer of adhesive material should be applied directly to the pipe, and particles should be sprinkled across to give a more realistic scenario. This experiment is discussed in detail in Ref. [22].

###### Experiment 7.

Experiment 7 tested one insulated 25 mm pipe in front of an insulated 50 mm pipe. The purpose of this experiment was to validate the effect of staggered flow when the pipes are of different diameters. It is assumed that the pipe that was positioned directly in front of the wind nozzle will have the same heat loss as a single pipe, but the effect on the second pipe is unknown. This experiment is discussed in detail in Ref. [23].

###### Experiment 8.

Experiment 8 tested a single, insulated 25 mm pipe. The purpose of this experiment was to establish a second baseline experiment for comparison with the theoretical calculations. This experiment is discussed in detail in Ref. [22].

###### Experiment 9.

Experiment 9 tested two insulated 25 mm pipes positioned in line. The purpose of this experiment was to validate the effect of staggered flow, and see whether the effect on 25 mm pipes are different than the 50 mm pipes tested in experiment 2. This experiment is discussed in detail in Ref. [23].

###### Experiment 10.

Experiment 10 tested one insulated 50 mm pipe in front of an insulated 25 mm pipe. The purpose of this experiment was to validate the effect of staggered flow when the pipes are of different diameters. The 50 mm pipe is positioned in front of the 25 mm pipe, and should disturb the flow of air. This experiment is discussed in detail in Ref. [23].

###### Experiment 11.

Experiment 11 tested a single, uninsulated 50 mm pipe. The goal of this experiment was to establish how big a difference insulation makes to the heat loss of a pipe. This experiment is discussed in detail in Ref. [22].

## Results

###### Theoretical Calculations.

To compare the different correlations with the experimental results, theoretical calculations were performed based on the experimental data. The wind speed used in all the theoretical calculations is based on the wind speeds measured using the anemometer. The corrected wind speed measurements can be found in Table 10. As Sec. 2 of the pipes is believed to be the best candidate for comparison due to these sensors being the furthest away from the uninsulated ends, the measurements from Sec. 2 were consistently used throughout the comparison. Full experimental and theoretical results with detailed calculations can be found in Refs. [22] and [23].

###### Comparison of Experimental Results.

A comparison of the overall heat transfer coefficients calculated from the experiments performed can be found in Figs. 6 and 7.

###### Comparison of Theoretical and Experimental Results.

Theoretical calculations for experiment 1 were performed, and a comparison of the values with the experimental data can be found in Fig. 8. A table of the values can be found in Table 11. Theoretical calculations for experiment 8 were performed, and a comparison of the values with the experimental data can be found in Fig. 9. A table of the values can be found in Table 12. Theoretical calculations for experiment 11 were performed, and a comparison of the values with the experimental data can be found in Fig. 10. A table of the values can be found in Table 13. The minimum, average, and maximum deviations between the theoretical and experimental values obtained are given in Tables 14 and 15.

## Discussion

###### Comparison of Experimental and Theoretical Results.

Theoretical calculations were performed for the scenarios tested in experiments 1, 8, and 11. For the insulated, 50 mm pipe (experiment 1), the theoretical and experimental values are very close, and the deviation between the theoretical and experimental values is between 0.40 and 5.79% with an average of 1.74% depending on the correlation used. It can also be observed in Tables 1113 that the deviation between experimental and theoretical values decreases at higher wind speeds, but the Nusselt numbers calculated using Fand and Keswani [15] show values that are significantly higher than the other correlations. This is also visible in Fig. 8. For the insulated 25-mm pipe (experiment 8), the deviations are higher throughout, and the correlations consistently give a lower overall heat transfer coefficient. From Table 15, the deviation is found to range from −4.54% to −0.72%, with an average deviation of −2.91%. For the uninsulated 50-mm pipe (experiment 11), the deviations are considerably higher, as illustrated in Fig. 10. The Fand and Keswani [15] correlation has a very large deviation for this experiment. As the correlation shows fair numbers at 7.1 m/s wind speed, the reason for this deviation is believed to be that the Reynolds number exceeds 40,000 for wind speeds of 13.6 and 18.6 m/s, and this results in a new set of constants in the formulas. In Table 15, the experimental values are found to be 43% higher on average compared to the theoretical values. It is believed that this difference is caused by the way the temperature sensors were installed in the experiments, and not inaccuracy in the theoretical calculations. The sensors were installed on the exterior of the pipe, which made them directly exposed to the ambient conditions. This may have resulted in the sensors reporting temperatures closer to the ambient temperatures rather than the pipe wall temperature. Had the sensors been embedded in the pipe wall, this would likely have given different and more accurate results. For the cases of multiple pipe configuration, reference is made to Peechanatt [23].

## Conclusions

Extensive review of the available literature on heat transfer from horizontal pipes under cross-flow wind showed the availability of different heat transfer correlations, which have wide range of validity. This paper, while comparing experimental findings and theoretical calculations, shows that proper selection of heat transfer correlation is very critical. Usage of an improper correlation can give erroneous results and thus, proper guidance is essential for designers and engineers performing calculations for heat loss from horizontal pipes which are subjected to cross-flow wind. The test methodology developed for testing the heat transfer from the pipes gave reasonably good results conforming to theoretical calculation for the selected correlation. So, it is recommended for industrial usage to conduct experiments in order to validate the findings. The test apparatus designed for determination of the heat transfer coefficient was portable and sturdy; it was capable of accommodating multiple pipes of varying diameters, thus providing a wide range of applicability and worked on the principle of energy balance upon reaching equilibrium condition. The experiments performed using cross-flow wind of 5 m/s, 10 m/s, and 15 m/s blowing over multiple pipe configurations of diameter 25 mm and 50 mm insulated steel pipes yielded mostly consistent results. Heat transfer correlations such as those suggested by Hilpert, Fand and Keswani, Morgan, Žukauskas, Whitaker and Churchill–Bernstein were used to determine the heat transfer coefficients for horizontal pipes subjected to cross-flow wind and the results were compared with the experimental values. The comparison showed that the values of the heat transfer coefficients for the insulated pipes had minimal deviation; i.e., in the range of 0.5–2.82% in the case of diameter 50 mm insulated pipe and 12–14% in the case of diameter 25 mm insulated pipe. The most significant finding was the effect of insulation on the reduction of heat loss. Comparison of diameter 50 mm uninsulated and insulated pipes showed that the reduction in heat transfer coefficient is in the range of 400–4000% with the usage of 10 mm thick insulation made of elastomeric foam based on synthetic rubber. The Churchill–Bernstein correlation is suggested as the best method for use by the industry based on the governing criteria such as ease of use, range of validity, accuracy, and the experimental findings. Based on the experimental data, all of the tested heat transfer correlations used for cylinders are found to give accurate values for the overall transfer coefficient. For a 50-mm insulated pipe, the theoretical values are found to be in the range of 0.40–5.79% off the experimental values. For a 25-mm insulated pipe, the theoretical values are found to be in the range of −4.54% to −2.91% off the experimental values. For the uninsulated pipe, the experimental values are significantly higher than the theoretical values. This is likely due to the way the temperature sensors were installed. The overall heat transfer coefficient of an uninsulated pipe is found to increase significantly with increasing wind speeds. For an insulated pipe, the overall heat transfer coefficient also increases, but only by decimal points. Even at a very low wind speed of 0.05 m/s, the overall heat transfer coefficient of an uninsulated pipe is three times higher than that of an insulated pipe (for further details and results, the reader is directed to Refs. [22] and [23], where the full extent of the work is provided).

## Future Work

For piping on oil and gas processing facilities, a flow assurance analysis should be performed. A comparison should be performed between two facilities, one with insulated pipes and one with uninsulated pipes. A life cycle cost analysis should be performed to evaluate the costs associated with the use of insulated pipes versus uninsulated pipes. Insulated pipes will have a higher installation cost, but based on the findings in this thesis, the savings in power consumption should make this a worthwhile investment when operating in cold climate areas. A study should be performed on how cold climate affects the nozzles used in fire extinguishing systems. This paper only considers piping, and none of the subsystems, which are also required to maintain a working fire extinguishing system. The overall heat transfer is normally dominated by either convection on one side of the wall, or by conduction through insulating layers. The results presented in this paper show this very clearly; however, the conduction effects of the insulating layers have been our focus as we are considering situations with very cold temperatures. Further work could focus on the conductive versus the convective effects in more moderate climate conditions

## Acknowledgements

The lead author and first co-author would like to thank the University of Stavanger and GMC Maritime AS for providing the resources required prepare this project, and the University of Stavanger for providing the resources for preparing this paper.

## Nomenclature

• A =

surface area, m2

• cp =

specific heat capacity, J/(kg K)

• D =

characteristic length of the surface, m

• h =

convective heat transfer coefficient, W/(m2⋅K)

• h.t.c. =

heat transfer coefficient

• I =

electrical current, A

• k =

average thermal conductivity, W/(m⋅K)

• NuD =

Nusselt number, dimensionless

• Pr =

Prandtl number, dimensionless

• r =

• ReD =

Reynolds number, dimensionless

• Rex,c =

critical Reynolds number, 5 × 105

• tw =

wall thickness, m

• Ts =

surface temperature, K

• T =

ambient temperature, K

• U =

overall heat transfer coefficient, W/m2⋅K)

• u =

external/freestream temperature, m/s

• V =

electrical potential difference, voltage, V

• α =

thermal diffusivity, m2/s

• μ =

dynamic viscosity, kg/(s⋅m)

• ρ =

density, kg/m3

## References

Dubey, B. , 2012, “The Rise of Northern Sea Route,” Part of Course Material in FXMTOM900---Arctic Operations Course held at the University of Stavanger, p. 5.
Zolotukhin, A. , 2014, “ Oil and Gas Resources and Reserves With Emphasis on the Arctic,” Presentation at course AT-327, UNIS, p. 12.
Bird, K. J. , Charpentier, R. R. , Gautier, D. L. , Houseknecht, D. W. , Klett, T. R. , Pitman, J. K. , Moore, T. E. , Schenk, C. J. , Tennyson, M. E. , and Wandrey, C. J. , 2008, “ Circum-Arctic Resource Appraisal: Estimates of Undiscovered Oil and Gas North of the Arctic Circle,” United States Geological Survey, Reston, VA, Fact Sheet No. 2008-3049.
IAATO, 2007, “ IAATO Overview of Antarctic Tourism—2006–2007 Antarctic Season,” Information Paper 121, 30th Antarctic Treaty Consultative Meeting, International Association of Antarctic Tour Operators, South Kingston, RI.
IMO, 2016, “ International Code for Ships Operating in Polar Waters (Polar Code),” Regulation, International Maritime Organisation, London, Standard No. MEPC 68/21/Add.1.
Incropera, F. P. , DeWitt, D. P. , Bergman, T. L. , and Lavine, A. S. , 2006, “ Fundamentals of Heat and Mass Transfer,” Dekker Mechanical Engineering, 6th ed., Wiley, Hoboken, NJ.
Serth, R. W. , 2007, Process Heat Transfer: Principles and Applications, Elsevier Science & Technology Books, Amsterdam, The Netherlands.
Sutherland, W. , 1893, “ The Viscosity of Gases and Molecular Force,” Philos. Mag., 36(223), pp. 507–531.
Çengel, Y. A. , 2006, Heat and Mass Transfer: A Practical Approach, McGraw-Hill, Boston, MA.
Moran, M. J. , Shapiro, H. N. , Munson, B. R. , and DeWitt, D. P. , 2003, Introduction to Thermal Systems Engineering: Thermodynamics, Fluid Mechanics, and Heat Transfer, 1st ed., Wiley, Hoboken, NJ, pp. 405–467.
Morgan, V. T. , 1975, “ The Overall Convective Heat Transfer From Smooth Circular Cylinders,” Advances in Heat Transfer, Vol. 11, T. F. Irvine , and J. P. Hartnett , eds., Academic Press, New York, pp. 199–264.
Manohar, K. , and Ramroop, K. , 2010, “ A Comparison of Correlations for Heat Transfer From Inclined Pipes,” Int. J. Eng., 4(4), pp. 268–278.
Whitaker, S. , 1972, “ Forced Convection Heat Transfer Correlations for Flow in Pipes, past Flat Plates, Single Cylinders, Single Spheres, and for Flow in Packed Beds and Tube Bundles,” AIChE J., 18(2), pp. 361–371.
Hilpert, R. , 1933, “ Wärmeabgabe Von Geheizten Drähten Und Rohren im Luftstrom,” Forsch. Gebeite. Ingenieurwes., 4(5), pp. 215–224.
Fand, R. M. , and Keswani, K. K. , 1973, “ Recalculation of Hilpert's Constants,” ASME J. Heat Transfer, 95(2), p. 224.
Žukauskas, A. , 1972, “ Convective Heat Transfer in Cross Flow,” Advances in Heat Transfer, Vol. 8, J. P. Hartnett and T. F. J. Irvine , eds., Academic Press, New York, pp. 93–160.
Churchill, S. W. , and Bernstein, M. , 1977, “ A Correlating Equation for Forced Convection From Gases and Liquids to a Circular Cylinder in Crossflow,” ASME J. Heat Transfer, 99(2), pp. 300–306.
Theodore, L. , 2011, “ Heat Transfer Applications for the Practicing Engineer,” Heat Transfer Applications for the Practicing Engineer, 4th ed., Wiley, Hoboken, NJ.
Armacell Norway, 2016, “Tekniske Data—AF/Armaflex N,” Armacell Norway, Oslo, Norway.
Maxim Integrated, 2010, “DS18B20 Programmable Resolution 1-Wire Digital Thermometer,” Maxim Integrated, Sunnyvale, CA.
Aosong Electronics Co., 2010, “Digital-Output Relative Humidity and Temperature Sensor/Module DHT22,” Aosong Electronics Co., Renhe, China.
Kvamme, B. O. , 2016, “ Validation of Heat Transfer Coefficients: Single Pipes With Different Surface Treatments and Heated Deck Element,” M.S. thesis, University of Stavanger, Stavanger, Norway.
Peechanatt, J. , 2016, “ Validation of Heat Transfer Coefficients in Pipes and Deck Elements Without Ice Glazing,” M.S. thesis, University of Stavanger, Stavanger, Norway.
View article in PDF format.

## References

Dubey, B. , 2012, “The Rise of Northern Sea Route,” Part of Course Material in FXMTOM900---Arctic Operations Course held at the University of Stavanger, p. 5.
Zolotukhin, A. , 2014, “ Oil and Gas Resources and Reserves With Emphasis on the Arctic,” Presentation at course AT-327, UNIS, p. 12.
Bird, K. J. , Charpentier, R. R. , Gautier, D. L. , Houseknecht, D. W. , Klett, T. R. , Pitman, J. K. , Moore, T. E. , Schenk, C. J. , Tennyson, M. E. , and Wandrey, C. J. , 2008, “ Circum-Arctic Resource Appraisal: Estimates of Undiscovered Oil and Gas North of the Arctic Circle,” United States Geological Survey, Reston, VA, Fact Sheet No. 2008-3049.
IAATO, 2007, “ IAATO Overview of Antarctic Tourism—2006–2007 Antarctic Season,” Information Paper 121, 30th Antarctic Treaty Consultative Meeting, International Association of Antarctic Tour Operators, South Kingston, RI.
IMO, 2016, “ International Code for Ships Operating in Polar Waters (Polar Code),” Regulation, International Maritime Organisation, London, Standard No. MEPC 68/21/Add.1.
Incropera, F. P. , DeWitt, D. P. , Bergman, T. L. , and Lavine, A. S. , 2006, “ Fundamentals of Heat and Mass Transfer,” Dekker Mechanical Engineering, 6th ed., Wiley, Hoboken, NJ.
Serth, R. W. , 2007, Process Heat Transfer: Principles and Applications, Elsevier Science & Technology Books, Amsterdam, The Netherlands.
Sutherland, W. , 1893, “ The Viscosity of Gases and Molecular Force,” Philos. Mag., 36(223), pp. 507–531.
Çengel, Y. A. , 2006, Heat and Mass Transfer: A Practical Approach, McGraw-Hill, Boston, MA.
Moran, M. J. , Shapiro, H. N. , Munson, B. R. , and DeWitt, D. P. , 2003, Introduction to Thermal Systems Engineering: Thermodynamics, Fluid Mechanics, and Heat Transfer, 1st ed., Wiley, Hoboken, NJ, pp. 405–467.
Morgan, V. T. , 1975, “ The Overall Convective Heat Transfer From Smooth Circular Cylinders,” Advances in Heat Transfer, Vol. 11, T. F. Irvine , and J. P. Hartnett , eds., Academic Press, New York, pp. 199–264.
Manohar, K. , and Ramroop, K. , 2010, “ A Comparison of Correlations for Heat Transfer From Inclined Pipes,” Int. J. Eng., 4(4), pp. 268–278.
Whitaker, S. , 1972, “ Forced Convection Heat Transfer Correlations for Flow in Pipes, past Flat Plates, Single Cylinders, Single Spheres, and for Flow in Packed Beds and Tube Bundles,” AIChE J., 18(2), pp. 361–371.
Hilpert, R. , 1933, “ Wärmeabgabe Von Geheizten Drähten Und Rohren im Luftstrom,” Forsch. Gebeite. Ingenieurwes., 4(5), pp. 215–224.
Fand, R. M. , and Keswani, K. K. , 1973, “ Recalculation of Hilpert's Constants,” ASME J. Heat Transfer, 95(2), p. 224.
Žukauskas, A. , 1972, “ Convective Heat Transfer in Cross Flow,” Advances in Heat Transfer, Vol. 8, J. P. Hartnett and T. F. J. Irvine , eds., Academic Press, New York, pp. 93–160.
Churchill, S. W. , and Bernstein, M. , 1977, “ A Correlating Equation for Forced Convection From Gases and Liquids to a Circular Cylinder in Crossflow,” ASME J. Heat Transfer, 99(2), pp. 300–306.
Theodore, L. , 2011, “ Heat Transfer Applications for the Practicing Engineer,” Heat Transfer Applications for the Practicing Engineer, 4th ed., Wiley, Hoboken, NJ.
Armacell Norway, 2016, “Tekniske Data—AF/Armaflex N,” Armacell Norway, Oslo, Norway.
Maxim Integrated, 2010, “DS18B20 Programmable Resolution 1-Wire Digital Thermometer,” Maxim Integrated, Sunnyvale, CA.
Aosong Electronics Co., 2010, “Digital-Output Relative Humidity and Temperature Sensor/Module DHT22,” Aosong Electronics Co., Renhe, China.
Kvamme, B. O. , 2016, “ Validation of Heat Transfer Coefficients: Single Pipes With Different Surface Treatments and Heated Deck Element,” M.S. thesis, University of Stavanger, Stavanger, Norway.
Peechanatt, J. , 2016, “ Validation of Heat Transfer Coefficients in Pipes and Deck Elements Without Ice Glazing,” M.S. thesis, University of Stavanger, Stavanger, Norway.

## Figures

Fig. 1

Temperature distribution through a cylinder with outer insulation

Fig. 2

Picture of the testing rig mounted on a pallet inside the climate laboratory

Fig. 3

Overhead view of the test rig, with key components marked

Fig. 4

Pipe with ice glazing as tested

Fig. 5

Insulated pipe with glued quartz particles compared to a normal, insulated pipe, experiment 6

Fig. 6

Comparison of overall heat transfer coefficients of single insulated 50 mm pipes

Fig. 7

Comparison of overall heat transfer coefficients of single uninsulated 50 mm pipes

Fig. 8

Exp. 1: Overall heat transfer coefficients compared to experimental data for single insulated 50 mm pipe

Fig. 9

Exp. 8: Overall heat transfer coefficients compared to experimental data for single insulated 25 mm pipe

Fig. 10

Exp. 11: Overall heat transfer coefficients compared to experimental data for single uninsulated 50 mm pipe

Fig. 11

Dimensions and measurements of pipes used for experimental testing

Fig. 12

Drawing of sensor locations and grouping of experimental measurements

Fig. 13

Drawing of wind nozzle and locations of wind speed measurements

## Tables

Table 1 Constants for use with Sutherland's law Eq. (14)
Table 2 Constants originally proposed by Hilpert [14]
Table 3 Updated constants for use with the Hilpert correlation [9,6,10]
Table 4 Reviewed values of C and m [15]
Table 5 Reviewed values of C and m [11]
Table 6 Values of n for different Prandtl numbers [16]
Table 7 Suggested values of C and m [16]
Table 8 Key components of testing rig
Table 9 Experiments performed
Table 10 Corrected wind speed measurements
Table 11 Deviations between theoretical and experimental heat transfer coefficients—Experiment 1
Table 12 Deviations between theoretical and experimental heat transfer coefficients—Experiment 8
Table 13 Deviations between theoretical and experimental heat transfer coefficients—Experiment 11
Table 14 Churchill–Bernstein, deviation from experimental values
Table 15 All correlations, deviation from experimental values

## Errata

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