Concentric Tube Heat Exchanger (1)

3"

Concentric Tube H

eat Exchanger H

eat transfer analysis in CTH

E for co-current and counter-current flow

s S

CH

MID

T 2: M

athew S

hum – P

roject Leader M

ichael Pearson

Siddharthan S

elvasekar C

hristopher Thornton V

ictor Vazquez

C

BE

MS

140A

Professor V

enugopalan H

enry Sam

ueli School of E

ngineering U

niversity of California, Irvine

Irvine, California

11/12/2014

CTHE – heat transfer analysis for co-current and counter-current flows "

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Abstract

The effectiveness of heat transfer through a single pass heat exchanger for counter-

current and parallel flow conditions were observed by examining the efficiency of heat transfer

between passing fluids. This was achieved experimentally with an Armfield concentric tube heat

exchanger by determining temperature profiles, power and temperature efficiencies, and overall

heat transfer coefficients for counter-current and parallel flows. It was observed that counter-

current flow was the most efficient method of heat transfer, as the rate of heat transfer occurred

more uniformly when compared to parallel flow. An increase in heat transfer efficiency from

25.00% to 28.21% was achieved between passing fluids by increasing the temperature of the

hot fluid from 50"°C to 60 °C. Additionally, increasing the flow rate of the hot fluid from 1000.00

cc/min to 4000.00 cc/min showed an increase in heat transfer efficiency from 20.59% to 38.24%

for the cold fluid.


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Table of Contents

1 Introduction to Concentric Tube Heat Exchangers .................................................................... 1

2 Objectives .................................................................................................................................. 1

3 Material and Methods ................................................................................................................ 2

3.1 Temperature Readings, Fluid Direction, and Stream Inlets and Outlets ........................ 2

3.2 Fluid Control, Temperature Control, Fluid Meters .......................................................... 4

4 Theory ........................................................................................................................................ 5

4.1 Temperature Profiles of Counter-Current and Parallel Flow ........................................... 5

4.2 Energy and Temperature Analysis ................................................................................. 6

4.2.1 Log-Mean Temperature Difference (LMTD) ......................................................... 7!

4.2.2 Determining Overall Heat Transfer Coefficient ..................................................... 7

4.3 Determining Power and Temperature Efficiencies ......................................................... 8

4.3.1 Power Efficiencies ................................................................................................ 8!

4.3.2 Temperature Efficiencies ...................................................................................... 8

5 Results and Discussion ............................................................................................................. 9

5.1 Parallel Flow ................................................................................................................... 9

5.2 Counter-Current Flow ................................................................................................... 10

5.3 Temperature Variation .................................................................................................. 11

5.4 Flow Rate Variation ...................................................................................................... 14

5.5 Error Analysis ............................................................................................................... 16


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6 Conclusions ............................................................................................................................. 17

7 References .............................................................................................................................. 18

Appendix A ................................................................................................................................ 19

Appendix B ................................................................................................................................ 22

Appendix C ................................................................................................................................ 24

Appendix D ................................................................................................................................ 24

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List of Figures

Figure 1 Overall set up of concentric heat exchanger ............................................................. 3

Figure 2 Cold current direction set up ...................................................................................... 3

Figure 3 Temperature control and supply ................................................................................ 4 Figure 4 Flow meters and control valves ................................................................................ 4

Figure 5 Temperature profiles for co-current and counter-current flow ................................... 5

Figure 6 Temperature profile for parallel flow ........................................................................ 10

Figure 7 Temperature profile for counter-current flow ........................................................... 11

Figure 8 Varying the temperature of the hot water stream .................................................... 13

Figure 9 Varying the flow rate of the hot water stream .......................................................... 16

Figure 10 Varying the flow rate of the hot water stream ............................................................ 2


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List of Tables

Table 1 Experimental temperature data for the hot stream while varying the

temperature of hot stream by 5°C ............................................................................. 12

Table 2 Experimental temperature data for the cold stream while varying the

temperature of hot stream by 5°C ............................................................................. 12

Table 3 Calculations…while varying the flow rate of the hot stream by

increments of 1000 !!!

!"# ............................................................................................. 15

Table A.1 Experimental temperature data for the hot stream for parallel flow ........................... 19

Table A.2 Experimental temperature data for the cold stream for parallel flow ........................ 19

Table A.3 Calculations for a single pass heat exchanger in parallel flow ................................. 19

Table A.4 Experimental temperature data for the hot stream for counter-current flow ............. 19

Table A.5 Experimental temperature data for the cold stream for counter-current flow ............ 20

Table A.6 Calculations for a single pass heat exchanger in counter-current flow ...................... 20

Table A.7 Calculations… while varying the flow rate of the hot stream

by increments by 5°C ................................................................................................ 20

Table A.8 Experimental temperature data for the hot stream while varying the

flow rate of the hot stream by increments of 1000 !!!

!"# .............................................. 21

Table A.9 Experimental temperature data for the hot stream while varying the

flow rate of the hot stream by increments of 1000 !!!

!"# .............................................. 21

Table B.1 Sample data taken from experiment B ...................................................................... 22

Table C.1 Specific heat and density values of water at respective log mean temperature……..24


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1 Introduction to Concentric Tube Heat Exchangers

The function of a heat exchanger is to transfer energy (heat) from one fluid to another.

Concentric tube heat exchangers involve a hot and cold fluid flowing concentrically, either in co-

current (parallel) flow or counter-current flow. For co-current flow, both fluids flow in the same

direction, whereas in counter-current flow, both fluids flow in the opposite direction. In the

Armfield heat exchanger, the hotter fluid flows through the inner tube to reduce heat loss, which

leaves the cold fluid in the outer tube to absorb the heat given off. Two modes of heat transfer

phenomena that can be analyzed are forced convective heat transfer, and conductive heat

transfer. Convective heat transfer occurs when heat transfers to the inner wall of the pipe, and

when heat transfers from the outer pipe wall to the cold fluid. Conductive heat transfer occurs

through the tube wall. By determining temperatures at the inlet, midpoint, and outlet within the

heat exchanger, heat transfer analysis can provide further information about power efficiency,

temperature efficiency, and the overall heat transfer coefficient for this system. Moreover,

concentric tube heat exchangers are ubiquitous in chemical engineering, and are commonly

encountered in manufacturing, chemical plants, petrochemical plants, natural gas processing,

refrigeration, and air conditioning. Moreover, heat exchangers are commonly used in companies

plating lines such as Dupont, Moog Inc., and Northrop Grumman. Therefore, heat transfer

analysis can be extremely useful in determining the optimal configuration for a heat exchanger.

2 Objectives

The objective of this experiment is to simulate conditions of parallel and counter-current

fluid flow in order to examine the power and temperature efficiencies and effectiveness of

concentric tube heat exchangers. The power efficiency is determined by taking the ratio of the

heat power absorbed to the heat power emitted, where the source of absorption is provided by

the heat given off from the hot fluid flow. By using flow and temperature profiles, log-mean


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temperature differences (LMTD), the overall heat transfer coefficients, and energy balances, the

heat power absorbed and emitted can be calculated. Additionally, by monitoring and recording

the inlet, midpoint, and outlet temperatures of the fluids flowing throughout the apparatus,

temperature profiles and LMTD values can be graphed and computed, respectively, which

visually highlight the direction of heat transfer between the passing fluids.

3 Material and Methods

The single pass heat exchanger is an Armfield machine with heat transmission area of

0.067m2. The Armfield machine has many controls and valves that will be explained further.

3.1 Temperature Readings, Fluid Direction and Stream Inlets and Outlets

The set up for this experiment is presented in Figure 1. A concentric heat exchanger in

the shape of an inverted U uses four valves to change the direction of the cold flow to create

conditions of co-current flow as well as countercurrent flow. Note that the hot flow always runs in

the inner pipe and always in the same direction indicated with the red arrows , inlet and

outlets are represented with the same arrows. This is done to avoid heat loss to the

environment, and ensure that the heat is transferred only to the outside pipe where the cold flow

appears. The inlet cold flow and outlet are denoted with blue arrows . The apparatus is

also equipped with valves to drain the fluid from any internal bubbles that might skew the flow

rate readings, and these are pointed out with black pointers . The thermometers reading the

temperature of the cold stream are indicated with blue pointers . The thermometers reading

the temperature of the hot stream are marked with red pointers .


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Depending on the configuration of the valves at the bottom of the apparatus the user can direct

the cold flow in either direction. The configuration presented in Figure 1 is used to make the flow

Figure 2 Flow Diagram

Figure 1 Overall set up of concentric heat exchanger

OUT$$


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Figure 3 Temperature control and supply

be parallel. However, counter flow is easily adjusted by changing the position of the knobs

presented in Figure 2.

3.2 Fluid Control, Temperature Control, and Fluid Meters

Figure 3 shows the temperature control panel (black

box) as well as the power switch for the hot stream pump

and heater. The hot water is stored on a tank on the back of

the overall set up where it is kept to the temperature set by

the “Temperature Control” knob. The ”Supply” switch turns

on the heater as well as the pump providing the hot stream

to the heat exchanger.

Figure 4 presents a picture of the flow meters as well

as the control valves. The flow meter shows the volumetric

flow rate going through the hot and cold stream

respectively. The flow meter for the hot stream is circled

red and the flow meter for the cold stream is circled blue.

The volumetric flow is measured by reading the marks

where the top of the weight sits when the flow is opened.

However, the tools used to regulate the flow rates are

control valves placed below the flow meters. These open

and close the circuit and can adjust the amount of flow

going through it as well. However, the tools used to

regulate the flow rates are control valves placed below the

flow meters. These open and close the circuit and can adjust the amount of flow going through it

as well.

Figure 4 Flow meters and control valves


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4 Theory

The fundamental aspects of determining temperature profiles, power and temperature

efficiencies, and the overall heat transfer coefficient for parallel and counter-current flow in

single pass heat exchangers is explained by the first law of thermodynamics, steady-state

conduction, forced convective heat transfer, and single-pass heat exchanger analysis.

4.1 Temperature Profiles of Counter-Current and Parallel Flow

Flow configurations in heat exchangers have significantly different impacts on

temperature profiles. The driving force in heat exchangers is expressed as the difference in

temperature from the hot stream to the cold stream at the same location in the heat exchanger.

In Figure 5 below, the counter-current flow temperature profile displays a larger heat transfer

per unit area in a single pass heat exchanger. Therefore in counter-current streams, the colder

stream is able to absorb more heat from the hot stream, where Tc,out can potentially reach Th,out

or even higher. Additionally, there is greater heat transfer for longer heat exchangers as the

driving force can be assumed to be constant for steady-state conditions. However in parallel

flow, Tc,out cannot reach Th,out as the driving force decreases along the length of a heat

exchanger. However, it is important to note that for co-current flows there is an initial driving

force that is greater than the initial driving force in counter-flow configurations. Ideally, it is very

useful to use co-current flows for smaller heat exchangers due to the large initial driving force,

whereas for larger heat exchangers, counter-current flow can be more efficient in transferring

Figure 5 Temperature profiles for co-current and counter-current flow in a single pass heat exchanger (WWW Pg. 339)


Page 6

heat due to the length of the heat exchanger.

4.2 Energy and Temperature Analysis

Energy can be neither created nor destroyed, as described by the first law of

thermodynamics. In order to find an overall energy balance for a single-pass concentric tube

heat exchanger, an energy balance must be performed for both the cold and hot streams, as

shown in Equations 1 and 2:

! = !!!(!!,! − !!,!) (1)

! = !!! !!,! − !!,! (2)

In Equations 1 and 2, 5 assumptions are made which consist of: mechanical energy,

potential energy, and kinetic energy are neglected. Next, heat transfer is neglected between the

heat exchanger and its surroundings; therefore the heat exchanger is perfectly insulated. Also,

the energy balance is assumed to be at steady state for each stream. The last assumption is

that there are constant conditions over the control surface of the heat exchanger. Here, ! is the

amount of heat transferred in terms of watts (W); ! is the mass flow rate in!!"!"#; !! is the specific

heat with units in !!"∗!; !!,! is the temperature of the cold stream coming out in !°!, !!,! is the inlet

temperature of the cold stream in terms degrees Celsius (°!), !!,! is the inlet temperature of the

hot stream in terms of degrees Celsius(°!), !!,! is the outlet temperature of the hot stream in

terms of °!. Additionally for an isolated system, the overall energy balance for the energy

exchanged between passing streams in the single pass heat exchanger can be written from

Equations 1 and 2 as:

! = !"∆! = !" !! − !! (3)

Here ! is the overall heat transferred from both the cold and hot streams in watts; ! is

the constant overall heat transfer coefficient which includes heat transfer from convection and


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conduction with units in !!!∗!, !! is the overall temperature of the hot stream in terms of !°!; and

!! is the overall temperature of the cold stream in terms of!°!.

4.2.1 Log-Mean Temperature Difference (LMTD)

The difference in temperature at each end of the heat exchanger between the hot and

cold streams is more easily evaluated using the logarithmic mean temperature difference

(LMTD) shown in Equation 4. This is due to the temperature profiles varying along the surface

area of the heat exchanger. Furthermore, depending on the LMTD, there is a corresponding

specific heat and density value for water presented in Appendix C

∆!!" = ∆!!!∆!!!"∆!!∆!!

(4)

Substituting Equation 4 into Equation 3, Equation 5 is a more pragmatic equation in

understanding heat transferring from the hot stream to the cold stream.

! = !"∆!!"! (5)

4.2.2 Determining Overall Heat Transfer Coefficient

The overall heat transfer coefficient is useful in understanding heat transfer through both

convection and conduction. By manipulating Equation 5, the overall heat transfer coefficient can

be determined as shown in Equation 6:

! = !!"#!!"#$%"&'!!"#!!"#$%&'%%'($!!"#!∗∆!!"

(6)

Alternatively, the overall heat coefficient (U) can also be calculated as the reciprocal of

the sum of a series of thermal resistances, where conduction and convection are each taken

into account independently.


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4.3 Determining Power and Temperature Efficiencies

Determining power and temperature efficiencies is crucial for understanding the

performance characteristics for heat exchangers.

4.3.1 Power Efficiencies

In order to determine the power efficiency, the heat power emitted and absorbed within

the heat exchanger must be calculated using Equations 7 and 8, respectively.

!"#$!!"#$%!!"#$$!% = !ℎ!!,ℎ!ℎ(!ℎ,! − !ℎ,!) (7)

!"#$!!"#$%!!"#$%"&' = !!!!,!!!(!!,! − !!,!) (8)

From Equations 7 and 8, two new terms introduced are density and volumetric flow rate

of the hot and cold streams (!ℎ, !!,!ℎ,!!) at the respective LMTD. Density is in terms of !"!!

while volumetric flow rate is in terms of !!

!"#. Power efficiencies can now be simply calculated by

dividing the heat power absorbed by the heat power emitted a shown in Equation 9. It is to be

noted that power efficiency is unit less. Also, heat exchanger’s power efficiencies are typically

less than 100%.

"! = !!"#!!"#$%!!"#$%"&'!!"#!!"#$%!!"!!!"# ∗ 100 (9)

4.3.2 Temperature Efficiencies

Similarly, temperature efficiencies can be found for both the hot stream and cold stream.

Both temperature efficiencies are found by dividing the temperature gradient in one stream by

the temperature gradient in the other stream as shown in Equations 8 and 9. Also, temperature

efficiencies are a clear indicator of the actual heat transfer occurring in the heat exchanger as a

percentage of the maximum possible heat transfer that would take place if an infinite surface


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area were available. Temperature efficiencies are also unit less like power efficiencies, and

below 100% temperature efficiency.

!!,! = !!,!"!!!,!"#!!,!"!!!,!"

∗ 100 (10)

!!,! = !!,!"#!!!,!"!!,!"!!!,!"

∗ 100! (11)

Furthermore, a mean efficiency of both the hot and cold temperature efficiencies can be

reported as shown in Equation 10:

!!"#$ = !!!!!! (12)

5 Results and Discussion

5.1 Co-Current Flow (A)

To begin, temperature data was collected from the inlet, midpoint, and outlet regions of the

apparatus while running a parallel fluid flow. The results were plotted in order to examine the

temperature profiles of the hot and cold streams, as shown below in Figure 6, which suggest

that the temperatures of both streams will eventually converge towards each other. From this

observation, it is possible to have fluids with different inlet temperatures to have similar outlet

temperatures by running parallel flow conditions within a heat exchanger. By utilizing Equations

7 and 8, it was shown that the power emitted from the hot stream and the power absorbed from

the cold stream was 835 W and 1114 W, respectively. From this data alone, it is clear that the

apparatus was not completely isolated, for a completely isolated system would not have

efficiency over 100%. Here, the efficiency was 133%, and thus it is assumed that the hot stream

gave energy to the cold stream and the surrounding environment. Additional calculations show

that the LMTD is 22.2 °C with an Overall Heat Transfer Coefficient (U) of 748.22 !!!°". These

calculations are summarized in Appendix A, tables A.1-3.


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Figure 6 Temperature profiles for parallel flow in a single pass heat exchanger obtained in experiment A.

5.2 Counter-Current Flow (B)

When examining the temperature profiles of counter-current conditions, it was obvious

that the temperatures of both streams did not converge, but instead created a larger separation

between the two, as shown in Figure 7. This implies that the temperature of the cold stream can

be brought relatively close to the inlet temperature of the hot stream. Additionally, heat transfer

is occurring more uniformly when compared to parallel flow, as demonstrated by the uniform

changes in temperatures of both streams.

The power emitted was calculated to be 833 W and the power absorbed was 1042 W,

which again implies that the system was not completely isolated form the surrounding

environment. As a result, the efficiency of heat transfer was 125% with a LMTD and U value of

23.3°C and 670.2 !!!°" respectively. These calculations are summarized in Appendix A, tables

A.4-6.

25.00"

30.00"

35.00"

40.00"

45.00"

50.00"

55.00"

60.00"

0.00" 0.10" 0.20" 0.30" 0.40" 0.50" 0.60" 0.70" 0.80" 0.90" 1.00" 1.10" 1.20" 1.30" 1.40" 1.50"

TEMPERATURE,!T!(°C)!

LENGTH!TRAVELED,!L!(METERS)!

Hot" Cold"


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Figure 7 Temperature profile for counter-current flow in a single pass heat exchanger obtained in experiment B.

"5.3 Temperature Variation (C)

As the concentric heat exchanger is further analyzed, it is important to examine the

temperature variations in the hot stream from 50oC to 65oC in increments of 5oC in order to

optimize the exchanger set up. One of the things that can be varied when cooling or heating a

certain fluid is the temperature of the stream used to do so. In this experiment the temperature

of the hot stream is altered in increments of 5oC to examine the corresponding efficiencies and

overall heat exchange for each trial. It is important to note that, similarly to the Experiment A

and B, this experiment also showcases efficiency in the energy transferred of over 100% that is

incorrect. It is possible that the water heater behind the heat exchanger set up was actually

transferring some of its heat to the cold stream in addition to the hot stream heating the cold

stream as well. Another possibility is that the valve used to change the stream direction might

have presented a mix of fluids since it was broken. However, if the broken valve was the issue,

the efficiency would actually be lowered instead of risen. In addition to those explanations, the

25.00"

30.00"

35.00"

40.00"

45.00"

50.00"

55.00"

60.00"

0.00" 0.10" 0.20" 0.30" 0.40" 0.50" 0.60" 0.70" 0.80" 0.90" 1.00" 1.10" 1.20" 1.30" 1.40" 1.50"

TEMPERATURE,!T!(°C)!

LENGTH!TRAVELED,!L!(METERS)!

Hot" Cold"


Page 12

readings of the thermometers could have been wrong due to poor thermometer calibration but

this is very unlikely since the thermometers were checked before the experiment and worked

fine.

Due to the lack of time to work with the heat exchanger, this lab does not provide a

conclusive reason to the high efficiency of the heat exchanger but instead provides likely

scenarios that could explain its error.

Table 1 Experimental temperature data for the hot stream for counter-current flow in a single pass heat exchanger while varying the temperature of hot stream by 5 °C

Counter-Counter Flow (Hot) Length (m) Temperature (oC) Location

0.00 50.00 55.00 60.00 65.00 in

0.75 47.00 53.00 55.00 58.00 mid

1.50 45.00 48.00 52.00 55.00 out

Table 2 Experimental temperature data for the cold stream for counter-current flow in a single pass heat exchanger while varying the temperature of hot stream by 5 °C

Counter-Current Flow (Cold) [Based Off the Inlet Hot Temp.]

Length (m) Temperature (oC) Location

0.00 33.00 35.00 36.00 38.00 out

0.75 29.00 30.00 30.00 31.00 mid

1.50 26.00 26.00 26.00 26.00 in

Table 1 and 2 present the results of the hot stream varied from 50oC to 65oC, in

increments of 5oC. The cold stream increases in outlet temperature as the inlet temperature

increases as well as expected while both streams are equal in volume being 2000 !"!

!"#.

Further analysis of this data yields the Power Emitted, Absorbed as well as the Power

Efficiency in Equations 7,8, and 9. This data is summarized in appendix A in Table A.9. It is very

significant to note that for this set up, the efficiency of the heat exchanger actually decreases as

the incoming hot stream temperature rises. With this in mind, one can design a heat exchanger

prioritizing either outlet temperature desired or overall efficiency. Also, despite the fact that the


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efficiency is over 100%, this data is still useful because the trend of lowering efficiency is

consistent as the inlet temperature increases.

Figure 8 Temperature profiles for counter-current flow in a single pass heat exchanger while varying the temperature of the hot water stream from 50, 55, 60, and 65 °C obtained in experiment C.

" Moreover from Appendix A, table A.9 summarizes the results for the Overall Heat

Transfer Coefficient (U) as well as the temperature efficiencies ηC, for the cold stream ηH for the

hot stream and ηmean for the mean temperature efficiency. These values show that unlike the

power efficiency, the temperature efficiencies stay mostly constant even with the change of inlet

temperature for the hot stream. However, the log mean temperature difference (LMTD) actually

increases. This data shows that the change of the incoming hot stream temperature to its outlet

temperature follow a constant pattern when its compared to the overall temperature difference

of the incoming temperature of the cold and hot stream. The cold stream follows this same

mode. This gives information about the pattern that the heat exchanger follows that can be used

to predict outlet temperatures as a function of the incoming temperatures of both streams.

Similarly, U also gives information about how energy is transferred across the heat exchanger.

In this case the calculated U’s give a relative wide range of values that fall within the error

margins. This is as expected because the overall heat transfer coefficient shouldn’t fluctuate too

25.00"30.00"35.00"40.00"45.00"50.00"55.00"60.00"65.00"

0.00" 0.10" 0.20" 0.30" 0.40" 0.50" 0.60" 0.70" 0.80" 0.90" 1.00" 1.10" 1.20" 1.30" 1.40" 1.50"

TEMPERATURE,!T!(°C)"

LENGTH!TRAVELED,!L!(METERS)"

HOT(50)" COLD(50)" HOT(55)" HOT(60)"HOT(65)" COLD(55)" COLD(60)" COLD(65)"


Page 14

much due to temperature changes this small. Here ΔT1 and ΔT2 represent the difference in

temperature between the hot inlet and cold outlet temperature and the difference between the

hot outlet and cold inlet temperatures respectively.

All streams from the four trials with different incoming hot stream temperatures are

shown on Figure 8 above. The graph further represents how the hot temperatures follow an

almost parallel pattern in terms of the amount of temperature decrease over the length of the

heat exchanger. It is also clear that the cold stream does in fact reach a higher temperature as it

comes through its outlet when the inlet hot stream temperature is higher. However, it is obvious

that the difference between trials is not as significant on the cold stream. This fits with the

original finding of decreasing efficiency as the inlet temperature for the hot stream is increased.

"5.4 Flow Rate Variation (D)

Under hot water flow rate variations in increments of 1000 !"!

!"#, the fastest hot water

stream at 4000 !"!

!"# lost the least amount of energy compared to the slowest hot water stream

shown in Figure 9. This is mainly due to new hot water being introduced into the heat exchanger

system at a faster flow rate. In contrast, the slowest hot water stream lost the most energy due

to the smaller volume of water going through the heat exchanger. As a result, the cold stream

when passing the fastest hot water stream absorbed the most energy in the single pass heat

exchanger. Consequently, if more hot water is being introduced into a heat exchanger, then

more energy can be given off to the cold stream.

The power emitted was greatest in the fastest hot water stream at 1,389W compared to

the 833W emitted in the slowest hot water stream. The power absorbed in the cold water

streams while the hot water stream was fastest was -1806W, while the power absorbed for the

slowest hot water stream was -972W as presented in table 3.


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Table 3 Calculations for a single pass heat exchanger in counter-current flow while varying the flow rate of the hot stream by increments of 1000 !!

!

!"#

Calculations

QC (m3/sec) QH (cm3/min)

Power Emitted (W) Power Absorbed (W) Power lost

(W) Power Efficiency (%)

1000 1000 833.78 -972.74 -138.96 116.67 1000 2000 1111.70 -1389.63 -277.93 125.00 1000 3000 1250.66 -1667.55 -416.89 133.33 1000 4000 1389.63 -1806.51 -416.89 130.00

ΔTm (°C) U (W/m2*°C) LMTD ΔT1 (°C) ΔT2 (°C) Heat Transmission Area

(m2) 24.41 594.66 24.41 27.00 22.00 0.07 24.99 830.07 24.99 24.00 26.00 0.07 24.88 1000.37 24.88 22.00 28.00 0.07 24.79 1087.86 24.79 21.00 29.00 0.07

ηcold (%) Ηhot (%) ηmean (%)

20.59 35.29 27.94 29.41 23.53 26.47 35.29 17.65 26.47 38.24 14.71 26.47

Again, the power efficiencies are above 100% where the fastest hot stream had a power

efficiency of 130%, while the slowest hot stream had a power efficiency of ~116%. Therefore,

power efficiencies are higher in streams that have higher hot water flow rates. The overall heat

transfer coefficient is 594 !!!°" in the slowest hot water stream as compared to 1087 !

!!°" in the

fastest hot water stream. Therefore, a higher overall heat transfer coefficient allows for greater

heat transfer between two passing streams. Furthermore, the temperature efficiency in the hot

stream decreases as the flow rate increases up to 4000!!!

!!"#. In contrast, the temperature

efficiency of the cold streams increases as the flow rate increases up to 4000!!!

!!"#. Again, the

decrease in the hot stream’s temperature efficiency is mainly due to new hot water constantly

being introduced to the system; however the increase in the cold stream’s temperature

efficiency balances out the losses from the hot streams temperature efficiency. Therefore, the

average of the temperature efficiencies remains similar in all trials despite increasing the flow

rate by 1000!!!

!!"#. Lastly, the LMTD is nearly identical around ~24°C for all hot water streams."


Page 16

Figure 9 Temperature profiles for counter-current flow in a single pass heat exchanger while varying the flow rate

of the hot water stream from 1000, 2000, 3000, and 4000 !!!

!"# obtained in experiment D.

"5.5 Error Analysis

While recording flow rate and temperature readings, there is an error of +/-0.1L/min, and

+/- 1°C, respectively. Additionally, the Armfield heat exchanger had three probable causes of

error that include: the cold water flow meter being jammed, leakage within pipes, and valves not

being fully closed. Additionally, presented in Appendix D is a photo of the Armfield heat

exchanger with a wrench attached in order to turn the valve. Due to these malfunctions or other

unknown sources of error, power efficiencies are reported above 100%.

25.00"

30.00"

35.00"

40.00"

45.00"

50.00"

55.00"

60.00"

0.00" 0.10" 0.20" 0.30" 0.40" 0.50" 0.60" 0.70" 0.80" 0.90" 1.00" 1.10" 1.20" 1.30" 1.40" 1.50"

TEMPERATURE,!T!(°C)"

LENGTH!TRAVELED,!L!(METERS)"

HOT(1000)" HOT(2000)" HOT(3000)" HOT(4000)"COLD(1000)" COLD(2000)" COLD(3000)" COLD(4000)"


Page 17

6 Conclusions

" Utilizing energy balances, heat transfer coefficients, and temperature profiles throughout

these experiments allowed for key characteristic properties of concentric tube heat exchangers

running parallel and counter current flows to be determined and examined. For instance, parallel

flow was shown to be best used when requiring two fluids of different input temperatures to

have similar output temperatures, as heat transfer occurs non-uniformly. On the other hand,

counter current flow can be used to bring the inlet temperature of a cold fluid to the inlet

temperature of a hot fluid with a uniform rate of heat transfer, and thus is the most efficient

choice of heat transfer when compared to parallel flow. Additionally, it was found that increasing

the temperature and flow rate of the hot fluid increased the efficiency of heat transfer between

passing fluids. It is important to note, however, that efficiencies throughout each experiment

were over 100%, which was believed to be caused by the heat transfer apparatus being not fully

insulated.


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7 References Welty, James R., Charles E. Wicks, and Robert E. Wilson. Fundamentals of Momentum, Heat,

and Mass Transfer. New York: Wiley, 1984. Print.


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Appendix A - Experimental Data Table A.1 Experimental temperature data for the hot stream for parallel flow in a single pass heat exchanger

Parallel Flow (Hot) Length (m) Temperature (oC) Location

0.00 60.00 in 0.75 55.00 mid 1.50 54.00 out

Table A.2 Experimental temperature data for the cold stream for parallel flow in a single pass heat exchanger

Parallel Flow (Cold) Length (m) Temperature (oC) Location

0.00 25.00 in 0.75 34.00 mid 1.50 41.00 out

Table A.3 Calculations for a single pass heat exchanger in parallel flow

Calculations

Power Emitted (W) Power Absorbed (W) Power lost (W) Efficiency (%) ΔTm (°C)

835.18 -1113.57 -278.39 133.33 22.21

U (W/m2*°C) Heat Transmission Area (m2) LMTD ΔT1 (°C) ΔT2 (°C)

748.22 0.07 22.21 35.00 13.00

Table A.4 Experimental temperature data for the hot stream for counter-current flow in a single pass heat exchanger

Counter-Current Flow (Hot)


0.00 60.00 in

0.75 56.00 mid

1.50 54.00 out


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Table A.5 Experimental temperature data for the cold stream for counter-current flow in a single pass heat exchanger

Counter-Current Flow (Cold)


0.00 41.00 out

0.75 33.00 mid

1.50 26.00 in

Table A.6 Calculations for a single pass heat exchanger in counter-current flow

Calculations Power Emitted (W) Power Absorbed (W) Power Lost (W) Efficiency (%) ΔTm (°C)

833.78 -1042.22 -208.44 125.00 23.21

U (W/m2*°C) LMTD ΔT1 (°C) ΔT2 (°C) Heat Transmission Area (m2)

670.21 23.21 19.00 28.00 0.07

Table A.7 Calculations for a single pass heat exchanger in counter-current flow while varying the temperature of hot stream by 5 °C

Calculations

Temperature (°C) Power Emitted (W) Power Absorbed (W) Power Lost (W) Efficiency (%)

50.00 697.03 -975.84 -278.81 140.00 55.00 974.37 -1252.77 -278.39 128.57 60.00 1111.70 -1389.63 -277.93 125.00

65.00 1389.63 -1667.55 -277.93 120.00

ΔTm (°C) U (W/m2*°C) ηC (%) ηH (%) ηmean (%)

17.31 841.29 29.17 20.83 25.00 19.94 937.64 31.03 24.14 27.59 23.88 868.54 29.41 23.53 26.47 26.49 939.38 30.77 25.64 28.21

LMTD ΔT1 (°C) ΔT2 (°C) Heat Transmission Area (m2) LMTD (reference)

17.31 24.00 12.00 0.07 15.00

19.94 29.00 13.00 0.07 20.00

23.88 34.00 16.00 0.07 25.00 26.49 39.00 17.00 0.07 25.00


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Table A.8 Experimental temperature data for the hot stream for counter-current flow in a single pass heat exchanger while varying the flow rate of the hot stream by increments of 1000 !!

!

!"#

Counter-Current Flow (Hot) Flow Rate (cc/min)

1000.00 2000.00 3000.00 4000.00


0.00 60.00 60.00 60.00 60.00 in

0.75 50.00 55.00 55.00 56.00 mid

1.50 48.00 52.00 54.00 55.00 out

Table A.9 Experimental temperature data for the cold stream for counter-current flow in a single pass heat exchanger while varying the flow rate of the hot stream by increments of 1000 !!

!

!"#

Counter-Current Flow (Cold) Flow Rate (cc/min)

1000.00 2000.00 3000.00 4000.00 Length (m) Temperature (oC) Location

0.00 33.00 36.00 38.00 39.00 out 0.75 29.00 30.00 32.00 32.00 mid 1.50 26.00 26.00 26.00 26.00 in


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Appendix B Sample Calculations: For a Counter-Current Single Pass Heat Exchanger Step 1: Record temperatures at the inlet, midpoint, and outlet for both the hot and cold stream.

(Make sure to record the location where the temperatures are taken relative to the flow

direction) Here point 1 refers to the left axis of Figure 7, and point 2 refers to the right axis of

Figure 7.

Table B.1 Sample data taken from experiment B

TH,in (°C) TH,mid (°C) TH,out (°C) TC,in (°C) TC,mid (°C) TC,out (°C)

60 56 54 26 33 41

at point 1 at point 2 at point 2 at point 1

Step 2: Create a temperature profile with the experimental data (Refer to Figure 7)

Step 3: Determine logarithmic-mean temperature difference to find the gradient between the hot

stream and cold stream using Equation 4:

∆!!" = ∆!!!∆!!!"∆!!∆!!

= ! !"!!" !(!"!!")!"!( !"!!"!"!!" )

= ! !!!"(!!.!") = 23.2 °C#

##

Step 4: Find the corresponding specific heat and density of water for the LMTD. Here the

specific heat and density of water for water at 25°C is 4.181 !!°", and 997.1 !"!!

Step 5: Now, power emitted can be found using Equation 7 and 8:

!"#$!!"#$%!!"#$$!% = !!!!,!!! !!,! − !!,! = 1000 !!

!"# ∗ 4.181!!°" 997.1

!"!! ∗(60°C -54°C) = 835W

!"#$!!"#$%!!"#$%"&' = !!!!,!!! !!,! − !!,! = 1000 !

!

!"# ∗ 4.181!!°" 997.1

!"!! ∗(26°C -41°C)

= -1113W

Note: dimensional analysis is used to convert the answer to Watts

Step 6: Through Equation 9, power efficiency can be calculated:

! = ℎ!"#!!"#$%!!"#$%"&'ℎ!"#!!"#$%!!"##$!% ∗ 100 = ! 835W!1113W ∗ 100 = 133.3%


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Step 7: From Equation 10 and 11, temperature efficiencies can be calculated:

!!,! = !!,!"!!!,!"#!!,!"!!!,!"

∗ 100 = ! !"!!"!"!!" ∗ 100 = !!" ∗ 100 = 17.6%

!!,! = !!,!"#!!!,!"

!!,!"!!!,!"∗ 100 = ! !"!!"!"!!" ∗ 100 = ! !"!" ∗ 100 = 44.1%!

Step 8 : From Equation,12, mean temperature efficiency can be calculated:

!!"#$ =!! + !!

2 = !17.6 + 44.12 = 30.9%


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APPENDIX C Table C.1 Specific heat and density values of water at respective log mean temperature

Temperature (°C) Cp: (J/g°C) Density:(g/m3)

20.00 4.18 998300.00

25.00 4.18 997100.00

30.00 4.18 995700.00

35.00 4.18 994100.00

40.00 4.18 992300.00

45.00 4.18 990200.00

50.00 4.18 988000.00

55.00 4.18 986000.00

60.00 4.19 983000.00

65.00 4.19 980000.00

APPENDIX D

Figure 10 Wrench clipped to Armfield Heat Exchanger due to broken valve piece

Concentric Tube Heat Exchanger (1)

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