Axial-Finned Counterflow Heat Exchanger

Katie Higgins 901 725 964

15 April 2015

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Executive Summary A heat exchanger was designed to preheat water for a minor league baseball park using

waste heat from a data center located inside Union Station as shown in Fig. 1.1 The goal was to

maximize the outlet temperature of the water and to minimize the energy required to pump the

water while subject to the design constraints summarized in Table 1.

Figure 1. Visual Summary of Design Constraints for Heat Exchanger

Table 1. Summary of Design Constraints for Heat Exchanger Fluid Hot Air Cold Water Inlet Temperature,  𝑇! (°C) 32.2 20

Outlet Temperature,  𝑇! (°C) 20-25 Maximize Power (kW) 28-32 Minimize

The final design, satisfying the majority of the design constraints and considering size

limitations and ease of manufacture, heats the water to an average outlet temperature, 𝑇!,!, of

29.5°C and requires an average water pump power of 8.13W. The heat exchanger models the

counterflow concentric aluminum tubes type with overall dimensions of 2.16m x 0.837m x

0.0381m. Cold water, flowing through the inner pipe with an outer diameter, OD, of 12.7mm, is

heated by warm air, which flows through a 38.1mm OD outer pipe enhanced with six axial fins.

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The overall serpentine configuration is shown in Fig. 2 with the cross-section of the pipe detailed

in Fig. 3.

Figure 2. Axial-Finned Counterflow Heat Exchanger

Figure 3. Cross-section of Concentric Tube

Since the purpose of the project was to heat the water, the design was chosen to produce a

minimum of 50% increase in water outlet temperature, requiring 𝑇!,! to range from 30-32°C.

After initial analysis, it was found that neither the range of power from the air’s server rack nor

the resulting power needed to pump the water varied greatly over design iterations; however, the

range for the air outlet temperature, 𝑇!,!, limited the model options merely to the counterflow in

concentric tubes, and drastically changed the required length of the tube. Figure 4 shows how

constraining 𝑇!,! to the upper half of the proposed range can reduce the required length by 77%.

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Figure 4. Air Outlet Temperature Effect on Required Pipe Length

Due to the size constraints of Union Station, the length of the pipe was limited to 12m

thus the water will only achieve a maximum of 30°C for 𝑇!,! in the range 23-25°C. Additionally

to make the design more practical, pipe dimensions were chosen from commonly manufactured

sizes for heat exchanger tubing.

Areas for improvement mainly focus on manipulating design constraints. Decreasing the

range of the air outlet temperature to 23-25°C would decrease length and power immensely. This

would also allow for a compact heat exchanger model to become applicable. Increasing the

difference between the fluid inlet temperatures would allow for greater heat rate transfer between

the fluids. And finally, an investigation into more complex patterns and geometries of fins could

be beneficial.

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Detailed Design A heat exchanger was designed implementing the counterflow concentric tubes model,

enhanced with six axial fins of thickness 0.001mm, which connect the 12.7mm OD inner pipe to

the 38.1mm OD outer pipe. The 12m long aluminum pipe was shaped into a serpentine pattern to

reduce the overall dimensions of the heat exchanger to 2.16m x 0.837m x 0.0381m.

Introduction:

Data centers store most of the computer hardware and technology equipment for big

establishments, such as companies and universities, in a centralized room or building. The

centers require cool-temperature environments to keep the equipment from overheating, and

need large amounts of electrical power to run all the equipment. Unfortunately, nearly 100 % of

the electrical power used to run such centers is dissipated as waste heat, thus it uses as much

power to cool the data centers as it does to run them in the first place.1

In recent years, an effort has been made to recycle this waste heat for other purposes. In

this project, the waste heat produced from Union Station Technology Center was used to preheat

water in the adjacent facility home to the South Bend Cubs minor league baseball team. The goal

was to maximize the outlet temperature of the water and to minimize the energy required to

pump the water while subject to design constraints including the water inlet temperature, the air

inlet and outlet temperature, and the energy output of the computer servers.

In this report, after detailing the final design of the heat exchanger, heat exchanger theory

will be discussed, design constraints will be analyzed to support the choices for the final design,

and the overall performance of the heat exchanger will be evaluated.

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Final Design: Two concentric 12m long, aluminum pipes facilitate heat transfer from the hot air to the

cold water with a cross-section as shown in Fig. 5. The cold

water flows at a rate of 0.72 kg/s through a 12.7mm OD inner

pipe with 1.2mm thickness. The hot air flows at an average

rate of 3.24 kg/s in the opposite direction through a 38.1mm

OD inner pipe also with 1.2mm thickness. Air channels are

formed by six evenly-spaced, rectangular, aluminum fins that

span the distance between the two pipes, and extend along

the length of the tube with a 0.001mm thickness. Fig. 6

illustrates the serpentine pattern for the 12m long tubes,

which reduce the overall system size to 2.16m x 0.837m x 0.0381m.

Figure 6. Serpentine Pipe Layout

Heat Transfer Theory: A heat exchanger transfers heat from a warmer fluid to a colder fluid. There are three

main types of heat exchangers based on construction type: concentric tubes, cross flow heat

exchangers, and shell-and-tube heat exchangers. A subcategory of cross flow heat exchangers are

compact heat exchangers, which have dense arrays of finned tubes or plates in order to maximize

the heat transfer surface area per unit volume.2 Compact heat exchangers are ideal when one

Figure 5. Heat Exchanger Cross-section

0.837m

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fluid is a gas. Most air to water heat exchangers, like car radiators, fall in this category.

Unfortunately, due to the high effectiveness required by the design constraints, the most effective

model, which is concentric tubes with counterflow, was chosen over the preferred compact heat

exchanger model.

The effectiveness, ℇ, of a heat exchanger is the ratio of the actual heat transfer rate,  𝑞, to

the maximum possible heat transfer rate,  𝑞!"# ,

ℇ = !!!"#

. (1)

Since the heat lost by the hot fluid equals the heat gained by the cold fluid, the actual heat

transfer rate referred to in Eq. (1) is

𝑞 = 𝑚!𝑐!,!(𝑇!,! − 𝑇!,!) = 𝑚!𝑐!,!(𝑇!,! − 𝑇!,!), (2)

where 𝑚 is the mass flow rate, 𝑐! is the specific heat, 𝑇! is the fluid outlet temperature, 𝑇! is the

fluid inlet temperature, and the subscripts h and c denote the hot and cold fluids respectively. The

product of the mass flow rate and the specific heat can be combined into the hot and cold fluid

heat capacity rates as follows

𝐶! = 𝑚!𝑐!,!, (3.1)

𝐶! = 𝑚!𝑐!,! . (3.2)

The maximum possible heat transfer rate referred to in Eq. (1) can then be defined as

𝑞!"# = 𝐶!"#(𝑇!,! − 𝑇!,!), (4)

where 𝐶!"# is equal to 𝐶! or 𝐶! , whichever is smaller.

The Effectiveness-NTU Method allows the three construction types of heat exchangers to

be easily compared, because effectiveness is a merely a function of NTU and !!"#!!"#

as shown in

the graphs of effectiveness for different heat exchanger types in Appendix 1.2 NTU is related to

the overall heat transfer coefficient, UA, and to the minimum heat capacity rate by

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NTU = !"!!"#

. (5)

The overall heat transfer coefficient is the variable that can be optimized when designing heat

exchangers, and is expressed as

!!"= !

(!!)!+ 𝑅! +

!(!!)!

 , (6)

where h is the convection coefficient for the fluid, A is the surface area over which the

convection takes place, and 𝑅! is the conduction resistance through the pipe wall.

There are a few general trends and concerns that should be considered for all heat

exchanger designs. First, increasing the heat transfer surface area will reduce the necessary

length to achieve a desired fluid outlet temperature. This is achieved through the addition of fins,

which are small protrusions from the original geometry made from materials that have high rates

of heat conduction. Adding fins modifies the overall heat transfer coefficient to

!!"= !

(!!!!!)!+ 𝑅! +

!(!!!!!)!

 , (7)

where 𝐴!is the total surface area with the addition of the fin, and 𝜂! is the overall fin efficiency

defined as

𝜂! = 1−  !!!!(1− 𝜂!), (8)

where 𝐴! and 𝜂! are the area and efficiency of the fin, respectively. Second, length, L, is

proportionally related to pump power through the pressure drop, Δ𝑝,

Δ𝑝 = 𝑓 !!!!!!

!, (9)

where f is the friction factor of the fluid, D is the pipe diameter, 𝜌 is the fluid density, and 𝑢! is

the fluid’s mean velocity. And since power, P, is

P = ∀Δ𝑝, (10)

where ∀ is the volumetric flow rate, reducing the length would theoretically reduce the power.

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Finally, adding fins adds more resistance to flow, which raises the power, so the relationship

between pipe length, total surface area, and power must be optimized. Additional equations and

correlations used are found in Appendix 1.

Design Constraints and Analysis:

Design constraints included the given fluid inlet and outlet temperatures, required power,

size constraints and the ease of manufacturing and assembly. The design was optimized to

maximize water outlet temperature and minimize water pump power and pipe length. First, a

desired water outlet temperature was chosen. Since the purpose of the project was to heat the

water, the design was chosen to produce a minimum of 50% increase in water outlet temperature,

requiring 𝑇!,! to range from 30-32°C.

Next, the ranges for the server rack

heat rate and air outlet temperature were

investigated. While there was a 28-32kW

range for the heat rate supplied by air’s

server rack, the change in the mass flow rate

of air was not notable, which is displayed in

Fig. 7. As the mass flow rate did not change,

neither the length nor the pump power

varied much when the heat rate was changed from the maximum to minimum values. Thus,

calculations were carried out at an average heat rate of 30kW.

On the other hand, varying the range for the air outlet temperature had drastically

different results. Due to the server rack heat rate constraints, the product of the mass flow rate

Figure 7. Mass Flow Rate and Water Outlet Temperature for

Maximum and Minimum Heat Rate

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and specific heat of air equaled that of water (𝐶! ≅ 𝐶!), causing the heat capacity ratio, Cr, to be

about 1. Additionally, since the lower range of the air outlet temperature matched or nearly

matched the inlet temperature of the water (𝑇!,! ≅ 𝑇!,!), the heat exchanger would theoretically

have to be close to 100% effective. Substituting Eqs. (2-4) into Eq. (1) yields

ℇ = !!(!!,!!!!,!)!!"#(!!,!!!!,!)

, (11)

which is approximately 1, since 𝐶! ≅ 𝐶!  and

𝑇!,! ≅ 𝑇!,! . Noting the starting value for the

y-axis scale of Fig. 8 emphasizes the

unusually large ratios for both ℇ and 𝐶! .

Thus, concentric tubes in counterflow was

the only method that could achieve such

high effectiveness and heat capacity ratios as

shown by the effectiveness graphs in

Appendix 2.

Pipe length and pump power were also extremely dependent on the air outlet temperature.

While a maximum 𝑇!,! of 25°C only required 7.32m of piping, the minimum 𝑇!,! of 20°C needed

almost eight times more piping, totaling a

final length of 54.09m. Figure 9 shows how

constraining 𝑇!,! to the upper half of the

proposed range can reduce the required

length by 77%. Due to the size constraints of

Union Station, the length of the pipe was

Figure 8. Large ℇ and 𝐶! Ratios for Air Outlet Temperature

Figure 9. Air Outlet Temperature Effect

on Required Pipe Length

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limited to 12m thus the water will only achieve a maximum of 30°C for 𝑇!,! in the range 23-25°C.

Table 2 tabulates the water outlet temperature achieved for each air outlet temperature for 12m

of pipe.

Table 2. Water Outlet Temperature For a 12m Heat Exchanger for Varying Air Outlet Temperatures

Air Outlet Temperature 𝑇!,!(°C) 20.1 21 22 23 24 25 Water Outlet Temperature 𝑇!,! (°C) 20.1 25.9 28.7 30.2 31.1 31.6

Excluding 𝑇!,!=20.1° C, the average water outlet temperature for the 12m tube is 29.5°C.

Next, the dimensions of the concentric tubes were considered. The ideal inner diameter

for the water pipe for minimum pipe length

was calculated for an average 𝑇!,! of 23°C as

shown in Fig 10. In order to aid in ease of

manufacture and minimize cost, diameter

sizes were chosen from Webco Industries

Heat Exchanger Tubing Dimension List.3

The smallest tube available matched the

ideal diameter almost perfectly with an inner

diameter of 11.5mm and an outer diameter of 12.7mm. The same process was performed to find

the ideal air tube diameter and fin thickness. As for the amount of fins, increasing the number of

fins caused a huge increase in power usage for little reductions in length, so the number of fins

was kept to six.

Unfortunately pump power could not be optimized in the same way. Power, Eq. (10), was

plotted as a function of the two independent variables, pipe length and mass flow rate of water.

The results shown in Fig. 11 indicate an exponential increase in power with increasing length

and flow rate.

Figure 10. Optimization of Water Pipe Inner Diameter for

Required Length at 𝑇!,! = 23°C

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Figure 11. Pump Power Calculated for Various Pipe Lengths and Water Mass Flow Rates

Pump power was also a factor when creating the serpentine pattern to reduce the overall

heat exchanger size. There is an additional pressure drop for bends in pipes that can be estimated

by the Equivalent Length Method. For 90° Elbow Curved, Flanged/Welded pipe bends with a

curve radius to pipe diameter ratio of 2, the equivalent length to pipe diameter ratio is 17.4 Thus,

the total length used for pressure drop in Eq. (9) is the sum of the equivalent length plus the

calculated required length, L,

𝐿!"!#$ = 17 𝑁𝐷! + 𝐿, (12)

where N is the number of 90° bends and 𝐷! is the inner diameter of the water pipe.

Performance Evaluation:

The heat exchanger achieves an average water outlet temperature of 29.5°C over a

distance of 12m for water outlet temperatures ranging from 21-25°C. This increases the water

temperature by approximately 50%. The pump power ranges from 5.6-33.2W, with the average

around 8.13W. Assuming the water heater is used 8 hours per day and that Indiana costs 10 cents

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per kWh for electricity, it would cost approximately $1400.00 to preheat the water during

baseball season (April-September).5 Full results are listed in Table 3.

Table 3. Heat Exchanger Design Results for Average Heat Rate of 30kW and Water Outlet Temperature of 30°C

Air Outlet Temperature, 𝑇!,! 20.1°C 25°C Average 𝑻𝒉,𝒐

Air Mass Flow Rate, 𝑚! (kg/s) 2.46 4.13 3.24 Air Heat Transfer Coefficient, ℎ! (kW/m2K) 2.48 3.77 3.09 Water Mass Flow Rate, 𝑚! (kg/s) 0.718 0.718 0.718 Water Heat Transfer Coefficient, ℎ! (MW/m2K) 1.09 1.65 1.36 Overall Fin Efficiency, 𝜂! 0.21 0.21 0.21 Overall Heat Transfer Coefficient, UA (W/K) 829.5 1.22E3 1.02E3 Effectiveness, 𝜀 0.83 0.82 0.82 Heat Capacity Ratio, 𝐶! 0.99 0.72 0.920 NTU 17.8 2.93 3.87 Tube Length, L (m) 53.2 7.19 11.4 Pump Power (W) 33.2 5.60 8.13

There are two main things to note from Table 3. First, the results for 𝑇!,!=25°C were very similar

to that of the average, but drastically different from 𝑇!,!= 20.1°C. This supports the decision to

model the tube for the higher range of 𝑇!,! . Second, fins were added to augment the air heat

transfer coefficient since it was three orders of magnitude smaller that the water heat transfer

coefficient.

Concerning the design, concentric tubes produce turbulent flow at low mass flow rates,

which increase the heat transfer coefficient, and therefore the rate of heat transfer. The major

disadvantage is often the impractical lengths required to achieve the desired heat transfer.

Considering the facility is a transformed train station, it has the space to hold a 2.16m x 0.837m

x 0.0381m heat exchanger. Due to the extremely small height, the heat exchanger could be

attached to the ceiling of the data center.

Life expectancy of a standard indoor heat exchanger ranges from 20-25 years, and

degrading performance is mostly due to fouling, or film build up on the heat transfer surface

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area.6 Including the fouling factors for air and water increases the overall heat transfer coefficient

by 5 W/K, which is not a big issue when UA is on the magnitude of 103.

The main area for improvement would be manipulating the server input heat rate and

constraining the minimum air outlet temperature so that it would be effective to apply the

compact heat exchanger model. It would be beneficial to look into ways to raise the minimum air

outlet temperature to greater than 23°C in order to eliminate the dramatic increase in length and

power accompanying the low values of 𝑇!,!. Also, manipulating the inlet temperatures of the

fluids to maximize the difference between them would be beneficial as the greater the

temperature difference between the two fluids, the greater the heat transfer between them. Other

minor areas for improvement include, factoring in the surface roughness of the tubes and

experimenting with different fin patterns and geometries to maximize heat transfer surface area.

In conclusion, the heat exchanger design satisfies the design constraints with the

exception of a 20°C air outlet temperature. A 29.5°C maximum water outlet temperature was

produced for an average of 8.13W of pump power.

References: [1] Go, David, 2015, “Data Center Project Lecture,” from https://sakailogin.nd.edu/access/content/group/SP15-AME-30334-01/Design%20Project/AME30334_S15_lecture_project.pdf [2] Incropera, Frank P., and David P. DeWitt, 1990, Fundamentals of Heat and Mass Transfer, Wiley, New York, Chap. 3-11. [3] Webco Industries, 2014, “Welded and Seamless Pressure Tubing Range of Sizes,” from http://www.webcotube.com/products/applications/heat-exchanger [4] Neutrium, 2012, “Pressure Loss from Fittings- Equivalent Length Method,” from https://neutrium.net/fluid_flow/pressure-loss-from-fittings-equivalent-length-method/ [5] Jiang, Jess, 2011, “The Price of Electricity in Your State,” from http://www.npr.org/blogs/money/2011/10/27/141766341/the-price-of-electricity-in-your-state [6] CDW Engineering, 2015, “Average Life Expectancies,” from http://www.cdwengineering.com/2013/02/07/average-life-expectancies/

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Appendices: Appendix 1 Additional Correlations and Equations Used in Calculations Calculate Mass Flow Rate

𝑚 =𝑄

𝑐!∆𝑇

Calculate Heat Transfer Coefficient

Water

𝑅𝑒! =4𝑚𝜇𝜋𝐷!

𝑁𝑢 = 0.023𝑅𝑒!!!𝑃𝑟!.!

ℎ =𝑁𝑢(𝑘!)𝐷!

Air

𝐷! =4𝐴!𝑃

𝑅𝑒! =4𝑚𝑁𝜇𝜋𝐷!

𝑁𝑢 = 0.023𝑅𝑒!!!𝑃𝑟!.!

ℎ =𝑁𝑢(𝑘!)𝐷!

Fin Efficiency

𝑚 =2ℎ𝑘𝑡

𝜂! =tanh  (𝑚𝐿!)

𝑚𝐿!

NTU Analysis

NTU =1

𝑐! − 1ln  (

𝜀 − 1𝜀𝑐! − 1

)

𝐿 =NTU(𝑐!"#)

𝑈𝐴 Power

𝑢! =𝜇  𝑅𝑒!𝜌  𝐷!  

𝑓 = (0.79 ln 𝑅𝑒! − 1.64)!!

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Appendix 2 Graphs of Effectiveness for Heat Exchangers for Different Heat Capacity Ratios [1] As seen below, the counterflow concentric tube is the most effective heat exchanger for heat capacity ratios, Cr, close to 1.2