hx report

Contents

Executive Summary ........................................................................................................................ 1

Introduction ..................................................................................................................................... 2

Theoretical Background .................................................................................................................. 3

Equipment ....................................................................................................................................... 4

Experiment ...................................................................................................................................... 5

Results ............................................................................................................................................. 5

Discussion ....................................................................................................................................... 9

Conclusion .................................................................................................................................... 12

Nomenclature ................................................................................................................................ 13

References ..................................................................................................................................... 14

Error Analysis ............................................................................................................................... 15

Appendixes ................................................................................................................................... 16

Appendix A1 ............................................................................................................................. 16

Appendix A2 ............................................................................................................................. 28

Appendix A3 ............................................................................................................................. 30

Appendix A4 ............................................................................................................................. 32

Appendix A5 ............................................................................................................................. 33

Appendix A6 ............................................................................................................................. 35

Appendix A7 ............................................................................................................................. 37

CME2121: Heat Exchanger

Page 1

Executive Summary

The main objective of this experiment is to acquire hands-on in the operation of a bench top shell

and tube heat exchanger as well as to understand how various factors and parameters that can

eventually affect the rates of heat transfer. This will in turn, affect the performance and

efficiency of the heat exchanger. The experiments were conducted in both co-current flow and

counter-current flow setups with varying flow rates of hot and cold fluids into the equipment.

From the results obtained from the experiment, it can be perceived from the trend that an

increased in rate of heat transfer, Q is directly proportional with an increase in flow rate into the

heat exchanger. However, upon analyzing the Q values for both co-current flow and counter-

current flow configurations; the experimental results show that co-current flow has a better

performance with higher effectiveness, values as shown in Table 1 and Table 2. This therefore,

does not tally with the literature research from theoretical reasoning and estimation. This might

be due to the design of the heat exchanger, which has a length too short to obtain a distinct

temperature difference for hot and cold fluids in and out of the equipment. The size of the

equipment also resulted in a shorter residence therefore the difference in Q values of both flows

to be small. The equipment might not have yet reached steady state when the measurements were

taken therefore accounting for these discrepancies.

The results show that a higher Reynolds number, Re will give a higher heat transfer coefficient,

U. A higher Re is resulted by a higher velocity of fluid flowing in to equipment. As more fluid is

flowing into the equipment, the log mean temperature difference would also be increased which

would in turn increase the value of U. With several exceptions such as the value of U at 45oC is

higher from the rest of results obtained, which can be depicted from the trends are being

discussed.


Page 2

Introduction

Purpose of this report is to study on how a heat exchanger operation will be affected by the

varying flow rates, flow pattern and parameters. Heat exchangers are commonly used in the

chemical industry by removing or adding thermal energy from one fluid to another by making

use of waste heat from other processes. This will save energy cost and optimize plant energy

usage. By understanding operating parameters of the heat exchanger and factors that can affect

its efficiency, proper design and sizing can be done, to optimize the heat exchanger.

Heat exchanger operates on three modes of heat transfer, conduction, convection and radiation.

Conduction happens when there is a metal-to-metal contact in the exchanger, example baffles to

tubes in the exchanger. Convection is where transfer of heat from one place to another by the

movement of fluids, example fluid to tubing. Radiation heat transfers is more significant when

heat is transferred from a furnace to the boiler tubes to produce steam. For this experiment, the

major mode of heat transfer is conduction and convection.

Heat transfer is dependent mainly on the densities, specific heat capacities, thermal

conductivities, and dynamic viscosities of the fluids. In order for heat transfer to occur, the

difference of two flowing fluids temperature must he high. This will create a driving force for

heat to transfer from hot regions to cold regions.

Common applications of heat exchangers are using heat produced from the outlet of an

exothermic or endothermic reactor, to preheat the reactors feedstock. Using this method to

recycle heat, less energy is required to preheat the feed, and less energy to cool down the

products.


Page 3

Theoretical Background

For this experiment, a single-pass shell and tube heat exchanger is used. Two fluids at different

temperatures are passed through the heat exchanger. When there is a temperature difference, heat

transfer takes place from a high temperature region to a low temperature region by conduction.

The law of heat conduction, also known as Fourier's law, states that heat transfer through a

material is proportional to the negative gradient in the temperature and to the area, define by the

equation,

- (1)

Equation 1 is based on some assumptions: steady state heat transfer, one directional heat flow,

isotropic and homogenous material, bounding surfaces are isothermal, constant temperature

gradient and linear temperature profiles.

Hot fluid flows axially through the tubes while cold fluid flows through the shell side of the heat

exchanger, over the tubes. The cold fluid in the tube can flow in either co-current or counter-

current directions.

= (2 1) = (2 1) - (2)

= - (3)

According to equation 2, the heat transferred to the cold fluid must be equal to the heat

transferred from the hot fluid. This equation can be used to determine the performance and

efficiency of the heat exchanger. The higher the overall heat transfer coefficient (U), the better

the performance of the heat exchanger.

Two types of flow, either laminar or turbulent flow can exist in the heat exchanger. When

Reynolds number is low at less than 2100, laminar flow exists. If Reynolds number is greater

than 6000, flow is turbulent. Laminar flow depends on the thermal conductivity of the fluid for

heat transfer to occur from a stream to the heat exchanger walls. However for turbulent flow, it

has heat transfer efficiency is higher as it continuously mixes the fluid in the stream. The type of


Page 4

flow is important as it determines the pressure losses of the fluid as it flows through the heat

exchanger. The higher the pressure loss, the more pumping power the heat exchanger requires.

Equipment

A single-pass shell and tube heat exchanger is used for this experiment. The fluid through the

tubes can only flow in one direction, either co-current or counter-current. The shell side consists

of 2 baffles. The purpose of the baffles is to support the tubes and prevent any tubes failure,

which is caused by flow-induced vibration. It is also to increase the velocity of the fluid, forcing

the fluid to flow across the tubing in a traverse direction. The equipment consists of 4 pipes (1-

4), 2 of them (1 and 2) consist of hot fluid flowing through and the other 2 (3 and 4) consist

of cold fluid flowing through. The experiment is required to conduct both co-current and

counter-current flows of fluids in the tubes. For co-current flow, 1 is hot fluid out and 2 is hot

fluid into the equipment. For counter-current flow, 1 and 2 are switched therefore 1 would

then be hot fluid in and 2 would be hot fluid out of the equipment. 3 and 4 remain as cold

fluid in and cold fluid out of the equipment respectively for both co-current and counter-current

flows. A heater is used to heat up the fluid before it is pumped through the tube as hot fluid into

the equipment. Desired temperature of the hot fluid flowing into the equipment can be controlled

from the control panel. Temperature probes in the tubes measure the temperatures of 1, 2, 3

and 4. The reading of the measurements can be seen from the control panel by turning the knob

from 1 to 4. A stopwatch is used to measure the time-interval to record the readings of 1 to 4.

Figure 1: Shell and Tube Heat Exchanger


Page 5

Experiment

The experiment is conducted for both co-current and counter current setup. Schematic diagrams

for both setups can be found in the CME2121 laboratory manual. The heat exchanger is being

operated at co-current flow mode first. The fixed hot water flow rate for the respective

temperatures of 45oC, 52oC and 60oC are conducted with varying flow rates of cold water at 1, 2

and 3 L/min respectively. Three sets of intended stabilized readings are taken with every step

changes being made. (Refer to appendix for the experimental data). The above step is repeated

for counter current setup mode. The main idea is to keep the tube side water flow rate constant

and use 3 differing shell side water flow rates. Bearing in mind during the experiment that the

shell side flow is turbulent and the tube side flow is either turbulent or laminar. For Fhot

readings, flow meter is faulty, so a constant value of 1.5L/min is used in the data.

Results

Table 1: Results for Co-Current Flow

Reservoir

temp (C)

Fhot (L/min)

Fcold (L/min)

Qhot (W) Qcold (W) Uavg (W/m2.K)

Ucal (W/m2.K)

hot (%)

cold (%)

45 1.5 1.22

0.069

405.06

66.52

273.18

27.08

1574.59

4.63

1401.83

265.02

22.9

3.6

18.9

1.6

1.5

2.10

0.038

415.51

56.86

277.10

23.59

1609.89

4.36

1758.80

211.24

24.5

3.3

11.6

1.0

1.5

3.00

0.074

450.12

45.66

277.48

18.98

1673.98

3.35

2016.63

271.06

26.6

2.4

8.16

0.5

52 1.5

1.02

0.021

466.46

12.03

376.56

10.93

1394.10

0.68

1316.02

186.22

18.9

0.4

22.2

0.5

1.5

2.07

0.029

535.68

16.77

412.73

13.54

1516.44

0.88

1775.90

217.76

22.1

0.6

12.2

0.4

1.5

2.98

0.021

559.91

21.23

407.45

17.84

1540.40

1.26

2044.09

198.99

23.4

0.8

8.50

0.4

60 1.5

1.04

0.015

606.66

48.21

522.23

11.36

1405.81

1.70

1343.41

167.98

17.7

1.5

22.8

0.4

1.5

2.12

0.020

689.49

24.20

597.70

13.65

1530.84

0.94

1820.95

205.07

21.2

0.7

12.9

0.3

1.5

3.00

0.018

723.89

13.19

618.72

18.10

1553.88

0.64

2090.02

208.62

22.1

0.3

9.30

0.3


Page 6

Table 1: Results for Counter-Current Flow

Reservoir

temp (C)

Fhot (L/min)

Fcold

(L/min)

Qhot (W) Qcold (W) Uavg (W/m2 K)

Ucal (W/m2 K)

hot (%)

cold (%)

45 1.5

1.03

0.013

405.06

66.52

273.18

27.08

823.81

3.19

1303.58

138.51

3.80

2.5

26.3

1.9

1.5

1.97

0.018

415.51

56.86

277.10

23.59

845.27

10.30

1711.82

159.66

6.50

3.7

13.4

0.7

1.5

2.94

0.015

450.12

45.66

277.48

18.98

872.52

67.60

2001.29

161.47

8.80

1.4

8.30

0.6

52 1.5

1.08

0.021

466.46

12.03

376.56

10.93

737.07

0.91

1342.09

182.42

7.70

0.4

22.2

0.5

1.5

1.97

0.019

535.68

16.77

412.73

13.54

785.26

7.37

1737.19

175.94

10.4

1.1

13.2

0.4

1.5

2.90

0.073

559.91

21.23

407.45

17.84

819.29

6.42

2022.86

251.35

11.8

0.8

9.20

0.5

60 1.5

1.07

0.021

606.66

48.21

522.23

11.36

1001.47

0.91

1360.15

202.40

9.90

0.3

23.0

0.4

1.5

2.11

0.005

689.49

24.20

597.70

13.65

1155.97

17.99

1818.35

146.58

12.6

0.5

13.5

0.4

1.5 3.04

0.022

723.89

13.19

618.72

18.10

1207.12

2.91

2096.35

221.84

14.2

0.4

9.50

0.3

Table 3: and values for Co-Current flow

Reservoir temp (C)

45

1912.61 743.01 6669.28302.67

2649.26 429.98 6643.86254.38

3279.49 811.56 6650.39307.81

52

1732.75 249.36 7019.13293.34

2634.37 344.34 6983.70295.02

3273.71 290.28 6971.68286.15

60

1754.59 193.15 7437.14359.01

2672.14 258.38 7411.03355.51

3291.01 265.07 7428.41356.57


Page 7

Table 4: and values for Counter-Current flow

Reservoir temp (C)

45

1735.78178.64 6647.94227.92

2547.19235.02 6623.53226.18

3240.10239.46 6646.30227.20

52

1779.59247.70 6998.56281.73

2552.37235.20 6967.07276.81

3221.65803.99 6962.47276.30

60

1782.08252.90 7456.88355.62

2668.59162.59 7395.92357.61

3314.13301.51 7392.69344.55

Table 5: Heat Load (Q) values for Co-Current flow

Reservoir

temp (C)

T1 (C) T2 (C) T3 (C) T4 (C) Qhot (J/s) Qcold (J/s)

45 41.20

0.50

45.10

0.36

28.03

0.07

31.27

0.25

405.06

66.52

273.18

27.08

40.63

0.39

44.63

0.37

28.30

0.05

30.20

0.15

415.51

56.86

277.10

23.59

40.60

0.29

44.93

0.25

28.60

0.05

29.93

0.07

450.12

45.66

277.48

18.98

52 47.53

0.07

52.03

0.07

28.20

0.05

33.50

0.10

466.46

12.03

376.56

10.93

46.57

0.07

51.73

0.11

28.30

0.05

31.17

0.07

535.68

16.77

412.73

13.54

46.23

0.13

51.63

0.13

28.50

0.05

30.47

0.07

559.91

21.23

407.45

17.84

60 53.73

0.45

59.60

0.10

27.90

0.05

35.13

0.11

606.66

48.21

522.23

11.36

52.93

0.13

59.60

0.17

28.13

0.07

32.20

0.05

689.49

24.20

597.70

13.65

53.03

0.07

60.03

0.07

28.30

0.05

31.27

0.07

723.89

13.19

618.72

18.10


Page 8

Table 6: Heat Load (Q) values for Counter-Current flow

Reservoir

temp (C)

T1 (C) T2 (C) T3 (C) T4 (C) Qhot (J/s) Qcold (J/s)

45 43.00

0.29

42.43

0.24

27.90

0.05

31.87

0.27

58.86

38.94

284.63

19.85

42.67

0.37

41.77

0.37

28.30

0.05

30.23

0.07

93.50

54.59

264.05

11.85

43.33

0.18

42.03

0.11

28.50

0.05

29.73

0.07

135.04

21.46

251.82

17.40

52 50.30

0.05

48.53

0.07

27.40

0.05

32.50

0.10

183.1

5 8.85

284.63

19.85

50.00

0.17

47.70

0.17

27.80

0.05

30.73

0.07

238.48

25.06

264.05

11.85

50.03

0.13

47.50

0.10

28.56

0.05

30.53

0.07

262.69

17.15

251.82

17.40

60 58.47

0.07

55.47

0.07

28.10

0.07

35.10

0.10

310.19

10.15

518.34

13.02

57.90

0.10

54.17

0.11

28.30

0.05

32.30

0.10

386.15

16.22

586.04

15.89

58.10

0.10

53.87

0.07

28.30

0.05

31.13

0.07

437.87

12.28

598.13

18.46

Figure 2: Overall Heat Transfer Coefficient vs. Reynolds Number in Co-Current Flow

3.14

3.15

3.16

3.17

3.18

3.19

3.2

3.21

3.22

3.23

2.80 2.90 3.00 3.10 3.20 3.30 3.40

Lo

g U

Log Re

Overall Heat Transfer Coefficient vs Reynolds number

45 deg C

52 deg C

60 deg C


Page 9

Figure 3: Overall Heat Transfer Coefficient vs. Reynolds Number in Counter-Current

Flow

Discussion

The temperature gradient of a co-current flow setup is maximum at entrance and decreases

towards the exit whereas that of the counter-current flow setup, the temperature gradient is fairly

constant over length of the heat exchanger. In counter-current flow setup, it is possible for

cooling fluid to leave at a higher temperature than heating fluid and able to extract higher heat

content from the heating fluid. For same terminal temperatures, it is known that the value of

LMTD obtained for counter-current flow is higher than that of co-current flow. Similarly, the

heat transfer area required for counter-current flow is lesser than that of co-current flow given

the same amount of heat load and terminal temperatures. In counter-current flow, temperature

difference will show less variation throughout the heat exchanger whereas in co-current flow, the

temperatures of 2 streams progressively approach each other which lead to more variation in

temperature difference throughout the exchanger. In theory, the Q value will be larger for a

counter-current configuration as compared to co-current configuration. However, the

experimental results shows otherwise. Several factors that lead to this deviation would be the

2.9

2.92

2.94

2.96

2.98

3

3.02

3.04

3.06

3.08

3.1

2.80 2.90 3.00 3.10 3.20 3.30 3.40

Lo

g U

Log Re

Overall Heat Transfer Coefficient vs Reynolds number

45 deg C

52 deg C

60 deg C


Page 10

length of the heat exchanger in the experimental setup which is too short for the distinct

difference in the temperature profile of the 2 differing configurations to be perceived. A small

heat exchanger used in the setup can lead to a shorter residence time which hence, depicts the

difference in the Q value of both flows to be small. Furthermore, the inlet temperature for the hot

stream in the counter-current flow is slightly lower than that of the co-current flow, therefore

accounting for these discrepancies.

From the results, the calculated Q values for the both hot and cold side of the heat exchanger,

doses not satisfy equation (2). Equation (2) is derived from thermodynamics whereby the energy

gain or loss is equal to the difference in temperature times by the mass and the heat capacity. The

equation assumes that the net heat loss by the hot fluid is equal to the net heat gain by the cold

fluid. From the calculated results, this equation does not hold true. Since all materials conduct

heat and heat travels from a high to low temperature, heat is loss to the surrounding via

conduction, convection and radiation, which thus, shows the difference in Q values for both the

hot and cold fluids.

For this experiment, the net heat loss to the surrounding is relative small due to the material of

the shell side; acrylic is not as conductive as stainless steel. (Acrylic, k = 0.2 W/m.K, Stainless

Steel, k = 16 W/m.K). The value of U is calculated based on averaging the Q of both hot and

cold fluid using equation (3).

The calculated Re values at the shell side is from 650-2000 and the Re values at tube side is from

8500-10000. At Re < 2100, the flow pattern is laminar, flow travels in a more layered and

orderly fashion, with no mixing within the flow. For Re > 4000, flow pattern is more chaotic,

mixing within the flow. The rate is heat transfer from the tube to the shell side behaves more of a

diffused manner, due to laminar flow at the shell side. There will be temperature gradient where

fluid is closer to the tubes compared to the fluid away from the tubes. To obtain a constant heat

transfer rate, temperature gradient must be constant. .

Both Figure 1 and Figure 2 show that with higher value of Re, the overall heat transfer

coefficient, U value obtained is higher. From Figure 1, U is higher when the fluid is at 45C

compared to the rest. This can be due configuration of the heat exchanger. For the co-current


Page 11

configuration, (Figure 2) at 45C, cold fluid is able to absorb the heat given out by the hot fluid

readily, denoted by the high U values. At higher temperature, the ability to absorb heat from the

hot fluid seems to be bottlenecked, U values for 52C and 60C is similar. Comparing with

figure 3, U increase steadily with increased temperature as the flow of fluid into the heat

exchanger is increased. At higher temperatures, co-current configuration has a limit on the

amount of heat it can transfer, as compared to counter-current configuration. Based on Figure 2

and Figure 3, as the experiment proceeds with higher temperatures, it is estimated that co-current

configuration will still have the same U value, whereas counter-current configuration U value

will increase proportion with temperature.

Theoretically, heat exchangers operating in counter-current configuration will have a better

efficiency as compared to co-current configurations. From the experimental results, it shows

otherwise. This can be explained by looking at the temperature difference of the co-current flow,

hot and cold inlet T and counter-current flow, hot inlet and cold outlet T. Looking at equation

(3), in order to have high Q value, T must be high, whereby U and A are constants. Looking

closed up on one tube, for a co-current configuration, at the instance when the hot and cold fluid

exchange heat at the inlet of the exchanger, the heat transfer from the hot tube side to the cold

shell side is the highest. Subsequently as fluid transverse down the exchanger, the rate of heat

transfer decreases as the T decreases. For a counter current configuration, both inlet and outlet

T is consistent, this means that where will be an even heat transfer from the hot tube side to

cold shell side. For this experiment, the heat exchanger efficiency is better for co-current

configuration is mainly due to the large temperature difference at the inlet of the exchanger and

the amount of heat transferred at the inlet of the exchanger, compared to counter-current.

Comparing theoretical value of U (ignoring the resistances caused by fouling) and experimental

U, resistance due to heat transfer can be calculated by taking the difference between the

theoretical and experimental values of U. Resistance is caused by fouling in the tubes which is

due to the presence of ions in the water. Water from Public Utilities Board (PUB), contains ions

such as, nitrates, sulfates, chlorides, and iron. Ions will get entrapped by the microscopic pores of

the stainless steel tubes. In the long run, as the concentration of the ions at the pores increases, it

will start to precipitate and form scales. These scales usually have a lower thermal conductivity


Page 12

compared with steel, hence a lower value of U. Other errors in the experiment might be due to

the equipment not being able to achieve thermal equilibrium and the existence of bubbles in the

water tubes.

Conclusion

In conclusion, the efficiency and performance of the heat exchanger is poor as the residence time

of the fluid is too short due to the length of benchtop heat exchanger setup. In order to increase

the maximum efficiency of the heat exchanger, the number of tubes and baffles can be increased.

Theoretically, Q will be larger for a counter-current flow configuration as compared to co-

current flow configuration. However, the experimental results show otherwise. Those

underlying reasons which lead to deviations are such that the length of exchanger in the

experimental setup is too short for the distinct difference in the temperature profile of the 2

differing configurations to be perceived. A small heat exchanger used in the setup can lead to a

lessen residence time which depicts the difference in Q of both flows are small. Furthermore, the

inlet temperature for the hot stream in the counter-current flow is slightly lower than that of the

co-current, therefore accounting for these discrepancies.

Generally, the higher the value of Re, the better the overall heat transfer coefficient as shown

from the trend lines of Figure 2 and Figure 3. This is because, as more fluid is flowing into the

equipment, the log mean temperature difference would also be increased which would in turn

increase the value of U. The existance of bubble in the water tubes, equipment not in thermal

equilibirum, scales along the tube wall might have lead the the deviations in the results obtained.

At higher temperatures, co-current flow configuration has a limit on the amount of heat it can

transfer, as compared to counter-current flow configuration. As the experiment proceeds with

higher temperatures, it is estimated that co-current flow configuration would still have the same

U value, whereas counter-current flow configuration U value will increase proportion with

temperature.


Page 13

Nomenclature

A heat transfer area (m2) xw Tube wall thickness (m)

D Tube diameter (m) Cp Specific heat capacity of fluid (J/kg.K)

F Correction Factor c subscript cold fluid

L Total tube length (m) h subscript hot fluid

heat exchanger effectiveess i subscript tube side (inside tubes)

mass flowrate of fluid (kgs-1) o subscript shell side (outside tubes)

Nu Nusselt number

Re Reynolds number

Fluid density (kgm-3)

Pr Prandtl number

Q Heat load (J/s)

Sw Area of baffle window (m2)

T Temperature (K)

T Difference in temperature (K)

Tlm Log mean temperature difference (K)

Tmax Maximum temperature difference (K)

Fluid viscosity (Pas)

U Overall heat transfer coefficient (Wm-2K-1)

h Film heat transfer coefficient for tube wall (Wm-2K-1)

k Fluid thermal conductivity (Wm-1K-1)

X Distance of heat transfer (m)

Cp Specific heat capacity of fluid (J/kg.K)

Cpmax Maximum specific heat capacity of fluid (J/kg.K)


Page 14

References

1. Thermal Conductivity of Some Common Materials and Gases [online].

Available from: http://www.engineeringtoolbox.com/thermal-conductivity-d_429.html

[Accessed on 6 February 2013]

2. Dean A. Bartlett, 1996, The Fundamentals of Heat Exchangers [online].

Available from: http://www.aip.org/tip/INPHFA/vol-2/iss-4/p18.pdf


3. Chemical Engineering Progress, 1996, Shell-and-Tube Heat Exchangers: Effectively

Design Shell-and-Tube Heat Exchangers [online].

Available from: http://www-

unix.ecs.umass.edu/~rlaurenc/Courses/che333/Reference/exchanger.pdf


4. Water Treatment [online].

Available from: http://www.pub.gov.sg/general/pages/watertreatment.aspx

[Assessed on 7 February 2013]

5. Heat Transfer [online].

Available from: http://ptumech.loremate.com/ht/node/7


6. Heat Transfer Flow [online].

Available from: http://www.ukessays.com/custom-essays/heat-transfer-flow.php



Page 15

Error Analysis

All the calculations obtained are the evidences of the importance of error analysing as a small

error may propagate causing a major error in the measurement readings.

There are two types of errors which were taken into account in our experiment namely, random

and systematic errors. These existent errors are inevitable to avoid in the conduct of experiments.

They are generally caused by human errors, electrical and instrumentation errors. They can be

calculated and analysed for when accounting for deviations from actual theoretical results.

Equations used in calculations,

= 2 +

2 - (4)

= (

)

2+ (

)

2 Where =

- (5)

Error arithmetic is used in the calculation, so as to know the propagation of errors during

processing. This will account for the uncertainly values for the final results.

Assumptions: Taking the average temperature to get physical properties of water intended

Detailed calculation of error shown in Appendix A7.


Page 16

Appendixes

Appendix A1

Table 7: Variable Values of Hot Fluid for Co-Current Flow

Fh

(L/min)

Fc

(L/min)

Th,ave

(oC)

h (kg/m3) (Pa.s) Cp,h (J/kg.K)

ks,h

(W/m.K)

kw,h

(W/m.K)

For 45 oC

1.5 1.22

0.069

43.15

0.62

990.40

0.033

0.0006997

5.99E-06

4194.78

0.33

14.79

0.0098

0.6316

0.00066

1.5 2.10

0.038

42.63

0.54

990.60

0.029

0.0007047

5.24E-06

4194.51

0.29

14.78

0.0086

0.6310

0.00058

1.5 3.00

0.074

42.77

0.38

990.54

0.021

0.0007034

3.74E-06

4194.58

0.20

14.78

0.0061

0.6311

0.00041

For 52 oC

1.5 1.02

0.021

49.78

0.10

987.63

0.005

0.0006351

9.47E-07

4198.25

0.05

14.90

0.0015

0.6387

0.00010

1.5 2.07

0.029

49.15

0.13

987.91

0.007

0.0006412

1.24E-06

4197.92

0.07

14.89

0.0020

0.6380

0.00014

1.5 2.98

0.021

48.93

0.19

988.00

0.010

0.0006433

1.85E-06

4197.81

0.10

14.88

0.0030

0.6378

0.00020

For 60 oC

1.5 1.04

0.015

56.67

0.46

984.40

0.025

0.0005680

4.50E-06

4201.85

0.25

15.01

0.0073

0.6462

0.00050

1.5 2.12

0.020

56.27

0.22

984.60

0.012

0.0005719

2.12E-06

4201.6

40.12

15.00

0.0034

0.6457

0.00024

1.5 3.00

0.018

56.53

0.10

984.47

0.005

0.0005693

9.47E-07

4201.78

0.05

15.00

0.0015

0.6460

0.00010


Page 17

Table 8: Variable Values of Cold Fluid for Co-Current Flow

Fh

(L/min)

Fc

(L/min)

Tc,ave

(oC)

c (kg/m3)

(Pa.s) Cp,c (J/kg.K)

ks,c

(W/m.K)

kw,c

(W/m.K)

For 45 oC

1.5 1.22

0.069

29.65

0.67

994.96

0.036

0.000831

2.57E-06

4187.69

0.36

14.57

0.0107

0.6170

2.44E-05

1.5 2.10

0.038

29.25

0.56

995.08

0.031

0.000835

1.54E-06

4187.48

0.30

14.57

0.0090

0.6166

2.07E-05

1.5 3.00

0.074

29.27

0.39

995.07

0.021

0.000835

8.28E-07

4187.48

0.21

14.57

0.0063

0.6166

1.45E-05

For 52 oC

1.5 1.02

0.021

30.85

0.15

994.61

0.008

0.000820

1.05E-06

4188.32

0.08

14.59

0.0023

0.6183

5.09E-06

1.5 2.07

0.029

29.73

0.15

994.94

0.008

0.000830

8.28E-07

4187.73

0.08

14.58

0.0024

0.6171

5.55E-06

1.5 2.98

0.021

29.48

0.21

995.01

0.011

0.000833

8.28E-07

4187.60

0.11

14.57

0.0033

0.6168

7.63E-06

For 60 oC

1.5 1.04

0.015

31.52

0.48

994.41

0.026

0.000813

1.15E-06

4188.67

0.25

14.60

0.0076

0.6190

1.64E-05

1.5 2.12

0.020

30.17

0.23

994.81

0.013

0.000826

8.28E-07

4187.96

0.12

14.58

0.0037

0.6176

8.35E-06

1.5 3.00

0.018

29.78

0.13

994.92

0.007

0.000830

8.28E-07

4187.76

0.07

14.58

0.0021

0.6171

4.68E-06


Page 18

Table 9: Variable Values of Hot Fluid for Counter-Current Flow

Fh

(L/min)

Fc

(L/min)

Th,ave

(oC)

h (kg/m3)

(Pa.s) Cp,h (J/kg.K)

ks,h

(W/m.K)

kw,h

(W/m.K)

For 45 oC

1.5 1.03

0.013

42.72

0.38

990.56

0.020

0.000704

3.65E-06

4194.55

0.20

14.78

0.0060

0.6311

4.05E-04

1.5 1.97

0.018

42.22

0.53

990.76

0.029

0.000709

5.12E-06

4194.29

0.28

14.78

0.0084

0.6306

1.34E-05

1.5 2.94

0.015

42.68

0.21

990.58

0.011

0.000704

2.01E-06

4194.53

0.11

14.78

0.0033

0.6311

5.23E-06

For 52 oC

1.5 1.08

0.021

49.42

0.09

987.79

0.005

0.00063

8.28E-07

4198.06

0.05

14.89

0.0014

0.6384

1.86E-06

1.5 1.97

0.018

48.85

0.24

988.04

0.013

0.000644

2.35E-06

4197.77

0.13

14.88

0.0039

0.6378

5.34E-06

1.5 2.90

0.073

48.77

0.17

988.08

0.009

0.000645

1.61E-06

4197.72

0.09

14.88

0.0026

0.6377

3.65E-06

For 60 oC

1.5 1.07

0.021

56.97

0.10

984.25

0.005

0.000565

9.47E-07

4202.01

0.05

15.01

0.0016

0.6465

1.84E-06

1.5 2.11

0.005

56.03

0.14

984.71

0.008

0.000574

1.40E-06

4201.52

0.08

14.99

0.0023

0.6455

2.76E-06

1.5 3.04

0.022

55.98

0.12

984.74

0.006

0.000575

1.15E-06

4201.49

0.06

14.99

0.0019

0.6455

2.27E-06


Page 19

Table 10: Variable Values of Cold Fluid for Counter-Current Flow

Fh

(L/min)

Fc

(L/min)

Tc,ave

(oC)

c

(kg/m3)

(Pa.s) Cp,c

(J/kg.K)

ks,c

(W/m.K)

kw,c

(W/m.K)

For 45 oC

1.5 1.03

0.013

29.88

0.46

994.89

0.025

0.0008312

6.52E-06

4187.81

0.25

14.58

0.0074

0.6170

2.44E-05

1.5 1.97

0.018

29.27

0.53

995.07

0.029

0.0008351

5.46E-06

4187.48

0.28

14.57

0.0085

0.6166

2.07E-05

1.5 2.94

0.015

29.12

0.22

995.11

0.012

0.0008349

3.83E-06

4187.41

0.12

14.57

0.0036

0.6166

1.45E-05

For 52 oC

1.5 1.08

0.021

29.95

0.14

994.88

0.008

0.0008195

1.42E-06

4187.84

0.07

14.58

0.0022

0.6183

5.09E-06

1.5 1.97

0.018

29.27

0.26

995.07

0.014

0.0008304

1.49E-06

4187.48

0.14

14.57

0.0041

0.6171

5.55E-06

1.5 2.90

0.073

29.55

0.19

994.99

0.011

0.0008328

2.03E-06

4187.63

0.10

14.57

0.0031

0.6168

7.63E-06

For 60 oC

1.5 1.07

0.021

31.60

0.15

994.39

0.008

0.0008130

4.65E-06

4188.71

0.08

14.61

0.0023

0.6190

1.64E-05

1.5 2.11

0.005

30.30

0.18

994.77

0.010

0.0008261

2.27E-06

4188.03

0.10

14.58

0.0029

0.6176

8.35E-06

1.5 3.04

0.022

29.72

0.15

994.94

0.008

0.0008299

1.26E-06

4187.72

0.08

14.58

0.0023

0.6172

4.68E-06


Page 20

Table 11: Heat Load Values for Co-Current Flow

Fh (L/min) Fc (L/min) h (kg/s) Qh (J/s) c (kg/s) Qc (J/s) Qave (J/s)

For 45 oC

1.5 1.22

0.069

0.025

1.14E-03

405.06

66.56

0.020

1.13E-03

273.18

27.08

339.12

35.91

1.5 2.10

0.038

0.025

6.3E-04

415.51

56.90

0.035

6.2E-04

277.10

23.59

346.30

30.78

1.5 3.00

0.074

0.025

1.23E-03

450.12

45.71

0.050

1.23E-03

277.48

18.97

363.80

24.72

For 52 oC

1.5 1.02

0.021

0.025

3.5E-04

466.46

12.08

0.017

3.5E-04

376.56

10.92

421.51

8.31

1.5 2.07

0.029

0.025

4.8E-04

535.68

16.83

0.034

4.8 E-04

412.73

13.53

474.20

10.78

1.5 2.98

0.021

0.025

3.5E-04

559.91

21.30

0.049

3.5E-04

407.45

17.84

483.68

13.86

For 60 oC

1.5 1.04

0.015

0.025

2.7E-04

606.66

48.30

0.017

2.4E-04

522.23

11.36

564.45

24.76

1.5 2.12

0.020

0.025

3.3E-04

689.49

24.31

0.035

3.2E-04

597.70

13.65

643.59

13.89

1.5 3.00

0.018

0.025

2.9E-04

723.89

13.30

0.050

2.9E-04

618.72

18.09

671.30

11.20


Page 21

Table 12: Heat Load Values for Counter-Current Flow

Fh (L/min) Fc (L/min) h (kg/s) Qh (J/s) c (kg/s) Qc (J/s) Qave (J/s)

For 45 oC

1.5 1.03

0.013

0.0247

2.21E-04

58.86

38.94

0.0171

2.22E-

04

284.63

19.85

171.75

21.86

1.5 1.97

0.018

0.0247

2.92E-04

93.50

54.60

0.033

2.93E-

04

264.05

11.85

178.78

27.93

1.5 2.94

0.015

0.0247

2.47E-04

135.04

21.52

0.049

2.48E-

04

251.82

17.40

193.43

13.83

For 52 oC

1.5 1.08

0.021

0.0246

3.48E-04

183.15

9.18

0.018

3.5E-04

365.95

25.53

274.55

13.51

1.5 1.97

0.018

0.0247

2.91E-04

238.48

25.20

0.033

2.93E-

04

400.63

17.98

319.56

15.42

1.5 2.90

0.073

0.0247

1.21E-03

262.69

21.39

0.048

1.22E-

03

401.55

27.75

332.12

16.31

For 60 oC

1.5 1.07

0.021

0.0246

3.46E-04

310.19

10.95

0.0180.0

00350

518.34

13.02

414.26

8.26

1.5 2.11

0.005

0.0246

8.21E-05

386.15

14.88

0.0358.2

8986E-05

586.04

15.89

486.09

11.35

1.5 3.04

0.022

0.0246

3.63E-04

437.87

13.80

0.0500.0

0036

598.13

18.46

518.00

11.09


Page 22

Table 13: Effectiveness of Heat Exchanger Values of Hot Fluids for Co-Current Flow

Fh

(L/min)

Fc

(L/min)

Tmax (T2-T3)

(oC)

Th (T2-T1)

(oC)

Cp,h (J/kg.K) h h (%)

For 45 oC

1.5 1.22

0.069

17.07 0.37 3.90 0.62 4194.780.14 0.229

0.036

22.93.64

1.5 2.10

0.038

16.33 0.37 4.00 0.54 4194.510.08 0.245

0.033

24.53.34

1.5 3.00

0.074

16.33 0.26 4.33 0.38 4194.580.05 0.266

0.024

26.62.39

For 52 oC

1.5 1.02

0.021

23.83 0.08 4.50 0.10 4198.250.06 0.189

0.004

18.90.41

1.5 2.07

0.029

23.43 0.12 5.17 0.13 4197.920.05 0.221

0.006

22.10.55

1.5 2.98

0.021

23.13 0.14 5.40 0.19 4197.810.05 0.234

0.008

23.40.83

For 60 oC

1.5 1.04

0.015

31.70 0.11 5.60 0.46 4201.920.06 0.177

0.015

17.71.46

1.5 2.12

0.020

31.47 0.18 6.67 0.21 4201.640.05 0.212

0.007

21.20.70

1.5 3.00

0.018

31.73 0.08 7.00 0.22 4201.780.05 0.221

0.003

22.10.31


Page 23

Table 14: Effectiveness of Heat Exchanger Values of Cold Fluids for Co-Current Flow

Fh

(L/min)

Fc

(L/min)

Tmax (T2-T3)

(oC)

Tc (T4-T3)

(oC)

Cp,c (J/kg.K) c c (%)

For 45 oC

1.5 1.22

0.069

17.070.37 3.230.26 4187.690.33 0.189

0.016

18.91.60

1.5 2.10

0.038

16.330.37 1.900.16 4187.480.29 0.116

0.010

11.61.00

1.5 3.00

0.074

16.330.26 1.330.08 4187.480.20 0.0816

0.082

8.160.54

For 52 oC

1.5 1.02

0.021

23.830.08 5.300.11 4188.320.05 0.222

0.005

22.20.46

1.5 2.07

0.029

23.430.12 2.870.08 4187.730.07 0.122

0.004

12.20.37

1.5 2.98

0.021

23.130.14 1.970.08 4187.600.10 0.085

0.004

8.500.37

For 60 oC

1.5 1.04

0.015

31.700.11 7.230.12 4188.670.25 0.228

0.004

22.80.38

1.5 2.12

0.020

31.470.18 4.070.08 4187.960.12 0.129

0.003

12.90.28

1.5 3.00

0.018

31.730.08 2.970.08 4187.760.05 0.093

0.003

9.300.27


Page 24

Table 15: Effectiveness of Heat Exchanger Values of Hot Fluids for Counter-Current Flow

Fh

(L/min)

Fc

(L/min)

Tmax (T1-T3)

(oC)

Th (T1-T2)

(oC)

Cp,h (J/kg.K) h h (%)

For 45 oC

1.5 1.03

0.013

15.100.29 0.570.37 4194.550.20 0.038

0.025

3.802.48

1.5 1.97

0.018

14.400.37 0.930.53 4194.300.28 0.065

0.037

6.503.66

1.5 2.94

0.015

14.830.18 1.300.21 4194.530.11 0.088

0.014

8.801.40

For 52 oC

1.5 1.08

0.021

22.900.07 1.770.08 4198.060.05 0.077

0.04

7.700.37

1.5 1.97

0.018

22.200.18 2.300.24 4197.770.13 0.104

0.011

10.41.09

1.5 2.90

0.073

21.470.15 2.530.16 4197.720.09 0.118

0.008

11.80.77

For 60 oC

1.5 1.07

0.021

30.370.08 3.000.10 4202.010.05 0.099

0.003

9.900.32

1.5 2.11

0.005

29.600.11 3.730.14 4201.520.08 0.126

0.005

12.60.49

1.5 3.04

0.022

29.800.11 4.230.12 4201.490.06 0.142

0.004

14.20.40


Page 25

Table 16: Effectiveness of Heat Exchanger Values of Cold Fluids for Counter-Current

Flow

Fh

(L/min)

Fc

(L/min)

Tmax (T1-T3)

(oC)

Tc (T4-T3)

(oC)

Cp,c (J/kg.K) c c (%)

For 45 oC

1.5 1.03

0.013

15.100.29 3.970.27 4187.810.14 0.263

0.019

26.31.87

1.5 1.97

0.018

14.400.37 1.930.08 4187.480.05 0.134

0.007

13.40.69

1.5 2.94

0.015

14.830.18 1.230.08 4187.40.05 0.083

0.006

8.300.58

For 52 oC

1.5 1.08

0.021

22.900.07 5.100.11 4187.840.06 0.222

0.005

22.20.48

1.5 1.97

0.018

22.200.18 2.930.08 4187.480.05 0.132

0.004

13.20.40

1.5 2.90

0.073

21.470.15 1.970.10 4187.630.05 0.092

0.005

9.200.46

For 60 oC

1.5 1.07

0.021

30.370.08 7.000.11 4188.710.06 0.230

0.004

23.00.36

1.5 2.11

0.005

29.600.11 4.000.11 4188.030.06 0.135

0.004

13.50.37

1.5 3.04

0.022

29.800.11 2.830.08 4187.720.05 0.095

0.003

9.500.29


Page 26

Table 17: Overall Heat Transfer Coefficient Values for Co-Current Flow

Fh

(L/min)

Fc

(L/min)

Tlm

(oC)

Qave

(J/s)

U (W/m2.K)

(experimental)

U (W/m2.K)

(theoretical)

Deviation from

theoretical value (%)

For 45 oC

1.5 1.22

0.069

13.18

1.92

339.12

35.91

1574.59

4.63

1401.83

265.02

12.32

1.5 2.10

0.038

13.16

1.84

346.30

30.78

1609.89

4.36

1758.80

211.24

8.47

1.5 3.00

0.074

13.30

1.36

363.80

24.72

1673.98

3.35

2016.63

271.06

16.99

For 52 oC

1.5 1.02

0.021

18.50

0.42

421.51

8.31

1394.10

0.68

1316.02

186.22

5.93

1.5 2.07

0.029

19.14

0.52

474.20

10.78

1516.44

0.88

1775.90

217.76

14.61

1.5 2.98

0.021

19.22

0.79

483.68

13.86

1540.40

1.26

2044.09

198.99

24.64

For 60 oC

1.5 1.04

0.015

24.57

1.47

564.45

24.76

1405.81

1.70

1343.41

167.98

4.64

1.5 2.12

0.020

25.73

0.79

643.59

13.89

1530.84

0.94

1820.95

205.07

15.93

1.5 3.00

0.018

26.44

0.50

671.30

11.20

1553.88

0.64

2090.02

208.62

25.65


Page 27

Table 18: Overall Heat Transfer Coefficient Values for Counter-Current Flow

Fh

(L/min)

Fc

(L/min)

Tlm

(oC)

Qave

(J/s)

U (W/m2.K)

(experimental)

U (W/m2.K)

(theoretical)

Deviation from

theoretical value (%)

For 45 oC

1.5 1.03

0.013

12.76

2.55

171.75

21.86

823.81

3.19

1303.58

138.51

36.80

1.5 1.97

0.018

12.94

9.44

178.78

27.93

845.27

10.30

1711.82

159.66

50.62

1.5 2.94

0.015

13.57

64.32

193.43

13.83

872.52

67.60

2001.29

161.47

56.40

For 52 oC

1.5 1.08

0.021

19.42

1.15

274.55

13.51

865.20

1.09

1342.09

182.42

35.53

1.5 1.97

0.018

19.58

11.20

319.56

15.42

998.68

9.37

1737.19

175.94

42.51

1.5 2.90

0.073

19.22

9.17

332.12

16.31

1057.72

8.29

2022.86

251.35

47.71

For 60 oC

1.5 1.07

0.021

25.31

1.32

414.26

8.26

1001.47

0.91

1360.15

202.40

26.37

1.5 2.11

0.005

25.73

24.51

486.09

11.35

1155.97

17.99

1818.35

146.58

36.43

1.5 3.04

0.022

26.26

3.84

518.00

11.09

1207.12

2.91

2096.35

221.84

42.42


Page 28

Appendix A2

Part A) Sample Calculations to Find Heat Load

Co-Current Flow, Hot Fluid:

When Fhot =1.5L/min, Fcold=1.22L/min, Thot = 45oC

From equation (2):

Qh = h.Cph.(Thot,in Thot,out) = h.Cph.(T2-T1) - (4)

Thot,ave = Thot,in+Thot,out

2 =

T2 +T1

2

= 45.1 + 41.2

2= 43.15oC 0.62

Finding density of hot fluid:

hot = 1000 - 0.0543T - 0.0039T2 - (5)

Substituting in Thot,ave = 43.15oC into equation (5),

hot = 1000 - 0.0543(43.15) - 0.0039(43.15)2 = 990.40 kg/m3 0.21

hot = Fhot(

) x (

1

60)(

) x (

1

1000)(

3

) x (

3)

= 1.5.(1

60) x (

1

1000) x 990.4 = 0.0247 kg/s 0.00113

Finding heat capacity of hot fluid:

Cp,hot = 4172 + 0.5315T (8.31X10-5)T2 - (6)


Cp,hot = 4172 + 0.5315(43.15) (8.31X10-5)(43.15)2 = 4194.78J/K.kg 0.3269

With Cp,hot = 4194.78J/K.kg 0.3269, T1 = 41.20 oC, T2 = 45.10 oC,

Using equation (4):


Page 29

Qh = 0.0247 x 4194.78 x (45.10 41.20) = 405.06 J/s 66.52

Co-Current Flow, Cold Fluid:

When Fhot =1.5L/min, Fcold=1.22L/min, Thot = 45oC

From equaation (2):

Qc = c.Cpc.(Tcold,out Tcold,in) = c.Cpc.(T4-T3) - (7)

Tcold,ave = Tcold,out+Tcold,in

2 =

T4+T3

2

= 31.27 + 28.03

2= 29.65oC 0.26

Finding density of cold fluid:

Substituting in Tcold,ave = 29.65oC into equation (5),

cold = 1000 - 0.0543(29.65) - 0.0039(29.65)2 = 994.96 kg/m3 0.06

cold = Fhot(

) x (

1

60)(

) x (

1

1000)(

3

) x (

3)

= 1.22.(1

60) x (

1

1000) x 994.96 = 0.0201 kg/s 0.00114

Finding heat capacity of cold fluid:

Substituting in Tcold,ave = 29.65oC into equation (6),

Cp,cold = 4172 + 0.5315(29.65) (8.31X10-5)(29.65)2 = 4187.69J/K.kg 0.14

With Cp,cold = 4187.69J/K.kg 0.14, T3 = 28.03 oC, T4 = 31.27 oC,

Using equation (7):

Qc = 0.0201 x 4187.69 x (31.27-28.03) = 273.18 J/s 27.08


Page 30

Appendix A3

Part A) Sample Calculations to Find Heat Exchanger Effectiveness,

Using equation: = Q

Qmax =

(cp)(T)

(cpmax)(Tmax) - (8)

For Co-Current Flow:

Fhot = 1.5 L/min, Fcold, ave = 1.22 L/min, Thot = 45oC

Tmax, ave = T2+T3

2 =

45.1+28.03

2 = 36.57 0.38 = T

Using equation (6),

Cpmax = 4172 + 0.5315(36.57) 0.0000831(36.57)2 = 4191.32 0.33J/K.kg

Hot Fluids:

From equation (8):

hot = cph(T2T1)

cpmax(T2T3) =

(4194.78)(45.141.2)

(4191.32)(45.128.033) = 0.229 0.036

hot (%) = 0.229 X 100% = 22.9 3.64%

Cold Fluids:

From equation (8):

cold = cpc(T4T3)

cpmax(T2T3) =

(4187.69)(31.2728.03)

(4191.32)(45.128.03) = 0.189 0.016

cold (%) = 0.189 X 100% = 18.9 1.60%


Page 31

For Counter-Current Flow:

Fhot = 1.5 L/min, Fcold, ave = 1.0 L/min, Thot = 45C

Tmax,ave = T1+T3

2 =

43+28.033

2 = 35.45 0.30 = T

Using equation (4),

Cpmax = 4172 + 0.5315(35.45) 0.0000831(35.45)2 = 4190.74 0.14 J/K.kg

Hot Fluids:

From equation (9):

hot = cph(T1T2)

cpmax(T1T3) =

(4194.55)(43.042.43)

(4190.74)(43.027.9) = 0.0376 0.025

hot (%) = 0.0376 X 100% = 3.76 2.48 %

Cold Fluids:

From equation (9):

hot = cpc(T4T3)

cpmax(T1T3) =

(4187.81)(31.86727.9)

(4190.74)(43.027.9) = 0.263 0.019

hot (%) = 0.263 X 100% = 26.3 1.87%


Page 32

Appendix A4

Part A) Sample Calculations to Find Overall Heat Transfer Coefficient, U

From equation (3): Q = UATlmF

U = Q

ATlmF - (9)

A = DiL= (0.00515)(1.01) = 0.0163m2

F = 1 (Equipment used is a single-pass shell and tube heat exchanger)


Fhot = 1.5L/min, Fcold,ave = 1.22L/min, Thot = 45C

Tlm = flow into HX flow out of HX

ln(flow into HX

flow out of HX)

= (T2T3)(T1T4)

ln(T2T3

T1T4)

= 13.18C 1.92

Qave = Qhot+ Qcold

2 =

405.063+273.181

2 = 339.122J/s 35.91

From equation (9):

U = 339.122

(0.0163)(13.18)(1) = 1574.387J s-1m-2 K-1 4.63


Fhot = 1.5 L/min, Fcold, ave = 1.0 L/min, Thot = 45C

Tlm = (Thot in Tcold out) (Thot out Tcold in)

ln(Thot in Tcold outThot out Tcold in

) =

(T1T4)(T2T3)

ln(T1T4

T2T3)

= 12.76C 2.55

Q = Qhot+ Qcold

2 =

58.86+284.63

2 = 171.75J/s 21.86

From equation (9):

U = 171.75

(0.0163)(12.76)(1) = 823.81J s-1m-2 K-1 3.19


Page 33

Appendix A5

Part A) Sample Calculations to Find Reynolds Number, Re

Reynolds Number for Tube Side, Retube = (

) - (10)

Reynolds Number for Shell Side, Reshell = (

) - (11)



i = hot = 990.40 kg/m3 0.06, Di = 0.00515m

ui = (

3

)

(2) =

0.000025

0.00021 = 1.2m/s 0.055

i = hot = 0.00112 (9.74 X 10-6)T - (12)


h = 0.00112 (9.74 X 10-6)(43.15) = 0.000699 Pa.s 0.00000599

Using equation (10),

Retube = (990.40 1.2 0.00515

0.000699) = 8748.38 407.38

o = 0.000831 Pa.s 0.00000257

Go = - (13)

Gc =

- (14)

Gb =

- (15)

Sc = PDS (1 -

) - (16)

Using equation (16) with P = 0.047m, Ds = 0.04m, Do = 0.00635m, p = 0.009m,

Sc = (0.047)(0.04)(1 0.0635

0.009) = 0.000554m2


Page 34


Gc = 0.0202

0.000554 = 36.45kg/m2s 2.06

Sb = Sw = 0.0000654m2


Gb = 0.0202

0.0000654 = 308.5kg/m2s 17.41


Go = (36.45)(308.5) = 106.04kg/m2s 4.23


Reshell = (0.00635)(106.04)

0.000831 = 810.07 32.42


Page 35

Appendix A6

Part B) Sample Calculation to find an estimated value for shell side flim coefficient using the

Donohue equation

Film heat transfer coefficient, ho & hi

Shell film side coefficient, ho

Sw = Nb = 0 as there are no tubes along baffles window

Sw = Area of baffle window = [ 2 + 2 + 21]

- (17)

where r is the radius of the shell and L is the height of the window.

Sb = Sw = 6.54 x 10-5 m2



Using equation (15), Gb =

=

1.71 x 102

6.54 x 105 = 262.0 kg/m2.s 3.41

Sc = 0.000554m2

Using equation (14), Gc =

= 2.02 x 102

5.54 x 104 = 30.95 kg/m2.s 0.40

Using equation (13), Go= 262.0 30.95 = 90.05 kg/m2.s 0.83

kh = 0.585 + 1.08 X 10-3T - (18)


kh = 0.585 + 1.08 X 10-3(43.15) = 0.6316 W/m.K 0.0006643

Finding thermal conductivity of stainless steel:

ks = 14.1 + 0.016T - (19)



Page 36

ks = 14.1 + 0.016(43.15) = 14.79 W/m.K 0.009841

Assume =

Shell side film coefficient, = 0.2

(

)

0.6(

)

0.33(

)

0.14 - (20)

= 0.2 0.62

0.00635(

0.00635 90.05

8.29 104)

0.6(

4187.69 8.31 104

0.62)0.33=1912.61 W/m2.oC 743.01

Tube side film coefficient, hi = 0.023

(

)

0.8(

)0.33 - (21)

Substituting values into equation (21) gives hi = 6669.28 W/m2 oC 302.67

Overall heat transfer coefficient, Ucal

1

=

1

+

+

1

- (22)

Substituting values into equation (22) gives Ucal =1401.83 W/m2.OC 265.02


Page 37

Appendix A7

Sample Calculations for Error Analysis

Random Error, and Systematic Error,

Table 19: Errors Propogation for T1 Readings at different Fcold values for Co-Counter Flow

Fcold (L/min) T1 (C) Random Error, System Error, Combined Error,

1.22 41.20 0.608 0.05 0.50

2.10 40.63 0.473 0.05 0.39

3.00 40.60 0.346 0.05 0.29

1.02 47.53 0.057 0.05 0.07

2.07 46.57 0.057 0.05 0.07

2.98 46.23 0.153 0.05 0.13

1.04 53.73 0.100 0.05 0.45

2.12 52.93 0.153 0.05 0.13

3.00 53.03 0.021 0.05 0.07

Measured value = =1

=1

= 1

3(41.6 + 40.5 + 41.5) = 41.2C

= = 1

( )2

=1

= 1

3[(41.6 41.2)2 + (40.5 41.2)2 + (41.5 41.2)2

= 0.608C

Systematic error = = 0.05C

Using equation (4):

Combined Error, = 0.6082 + 0.052

= 0.5 C


Page 38

Error Arithmetic:

For Co-Current Flow, when Fhot = 1.5L/min, Fcold = 1.22L/min

= 0.0247 kg/s 0.00114, Cp= 4194.78 J/K.kg 0.3269

T = (T2-T1) = (45.10 - 41.20) = 3.9oC

At T1 = 41.20 oC, = 0.5oC

At T2 = 45.10oC, = 0.36oC

Hence, combined error for T is = (0.362) + (0.502) = 0.616oC

Therefore T = 3.9oC 0.616

Error arises from computing the heat transferred is a combination of error in mass flowrate and

error in T.

Combining equation (2), Qh = .Cp.T and equation (5),

= (

)

2+ (

)

2

Qh = .Cp.T x (0.00114/0.0247)2 + (0.3269/4194.78)2 + (0.616/3.9)2

Qh = 405.6 J/s 66.5

For the list of tabulated errors and calculation of the data, refer to Appendix A1.

hx report

Documents

appendix a1

appendix a2

appendix a3

appendix a4

appendix a5

appendix a6

appendix a7

heat exchanger page