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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, π! (Β°C) 32.2 20
Outlet Temperature, π! (Β°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, π!,!, of
29.5Β°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 π!,! to range from 30-32Β°C.
After initial analysis, it was found that neither the range of power from the airβs server rack nor
the resulting power needed to pump the water varied greatly over design iterations; however, the
range for the air outlet temperature, π!,!, 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 π!,! 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 30Β°C for π!,! in the range 23-25Β°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 23-25Β°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, β, of a heat exchanger is the ratio of the actual heat transfer rate, π, to
the maximum possible heat transfer rate, π!"# ,
β = !!!"#
. (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
π = π!π!,!(π!,! β π!,!) = π!π!,!(π!,! β π!,!), (2)
where π is the mass flow rate, π! is the specific heat, π! is the fluid outlet temperature, π! 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
πΆ! = π!π!,!, (3.1)
πΆ! = π!π!,! . (3.2)
The maximum possible heat transfer rate referred to in Eq. (1) can then be defined as
π!"# = πΆ!"#(π!,! β π!,!), (4)
where πΆ!"# is equal to πΆ! or πΆ! , 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
!!"= !
(!!)!+ π ! +
!(!!)!
, (6)
where h is the convection coefficient for the fluid, A is the surface area over which the
convection takes place, and π ! 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
!!"= !
(!!!!!)!+ π ! +
!(!!!!!)!
, (7)
where π΄!is the total surface area with the addition of the fin, and π! is the overall fin efficiency
defined as
π! = 1β !!!!(1β π!), (8)
where π΄! and π! are the area and efficiency of the fin, respectively. Second, length, L, is
proportionally related to pump power through the pressure drop, Ξπ,
Ξπ = π !!!!!!
!, (9)
where f is the friction factor of the fluid, D is the pipe diameter, π is the fluid density, and π’! is
the fluidβs mean velocity. And since power, P, is
P = βΞπ, (10)
where β 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 π!,! to range from 30-32Β°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 airβs
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 (πΆ! β πΆ!), 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 (π!,! β π!,!), the heat exchanger would theoretically
have to be close to 100% effective. Substituting Eqs. (2-4) into Eq. (1) yields
β = !!(!!,!!!!,!)!!"#(!!,!!!!,!)
, (11)
which is approximately 1, since πΆ! β πΆ! and
π!,! β π!,! . Noting the starting value for the
y-axis scale of Fig. 8 emphasizes the
unusually large ratios for both β and πΆ! .
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 π!,! of 25Β°C only required 7.32m of piping, the minimum π!,! of 20Β°C needed
almost eight times more piping, totaling a
final length of 54.09m. Figure 9 shows how
constraining π!,! 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 β and πΆ! 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 30Β°C for π!,! in the range 23-25Β°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 π!,!(Β°C) 20.1 21 22 23 24 25 Water Outlet Temperature π!,! (Β°C) 20.1 25.9 28.7 30.2 31.1 31.6
Excluding π!,!=20.1Β° C, the average water outlet temperature for the 12m tube is 29.5Β°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 π!,! of 23Β°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 π!,! = 23Β°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 90Β° 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,
πΏ!"!#$ = 17 ππ·! + πΏ, (12)
where N is the number of 90Β° bends and π·! is the inner diameter of the water pipe.
Performance Evaluation:
The heat exchanger achieves an average water outlet temperature of 29.5Β°C over a
distance of 12m for water outlet temperatures ranging from 21-25Β°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 30Β°C
Air Outlet Temperature, π!,! 20.1Β°C 25Β°C Average π»π,π
Air Mass Flow Rate, π! (kg/s) 2.46 4.13 3.24 Air Heat Transfer Coefficient, β! (kW/m2K) 2.48 3.77 3.09 Water Mass Flow Rate, π! (kg/s) 0.718 0.718 0.718 Water Heat Transfer Coefficient, β! (MW/m2K) 1.09 1.65 1.36 Overall Fin Efficiency, π! 0.21 0.21 0.21 Overall Heat Transfer Coefficient, UA (W/K) 829.5 1.22E3 1.02E3 Effectiveness, π 0.83 0.82 0.82 Heat Capacity Ratio, πΆ! 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 π!,!=25Β°C were very similar
to that of the average, but drastically different from π!,!= 20.1Β°C. This supports the decision to
model the tube for the higher range of π!,! . 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 23Β°C in order to eliminate the dramatic increase in length and
power accompanying the low values of π!,!. 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 20Β°C air outlet temperature. A 29.5Β°C maximum water outlet temperature was
produced for an average of 8.13W of pump power.
References: [1] Go, David, 2015, βData Center Project Lecture,β 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, βWelded and Seamless Pressure Tubing Range of Sizes,β from http://www.webcotube.com/products/applications/heat-exchanger [4] Neutrium, 2012, βPressure Loss from Fittings- Equivalent Length Method,β from https://neutrium.net/fluid_flow/pressure-loss-from-fittings-equivalent-length-method/ [5] Jiang, Jess, 2011, βThe Price of Electricity in Your State,β from http://www.npr.org/blogs/money/2011/10/27/141766341/the-price-of-electricity-in-your-state [6] CDW Engineering, 2015, βAverage Life Expectancies,β 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
π =π
π!βπ
Calculate Heat Transfer Coefficient
Water
π π! =4ππππ·!
ππ’ = 0.023π π!!!ππ!.!
β =ππ’(π!)π·!
Air
π·! =4π΄!π
π π! =4πππππ·!
ππ’ = 0.023π π!!!ππ!.!
β =ππ’(π!)π·!
Fin Efficiency
π =2βππ‘
π! =tanh (ππΏ!)
ππΏ!
NTU Analysis
NTU =1
π! β 1ln (
π β 1ππ! β 1
)
πΏ =NTU(π!"#)
ππ΄ Power
π’! =π π π!π π·!
π = (0.79 ln π π! β 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
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