Study Of Heat Transfer Coefficient In A Double Pipe Heat Exchanger 1i6x4c

ChE 304 Chemical engineering laboratory - III Experiment No. 1

Group No. 03 (A2)

Name of the experiment:

Study of heat transfer coefficient in a double pipe heat exchanger Submitted by: Md. Hasib Al Mahbub Student Id: 0902045 Level: 3; Term: 2 Section: A2

Date of performance: 04/03/2014

Partners’ Student Id. 0902041

Date of submission: 14/03/2014

0902042 0902043 0902044

Department of Chemical Engineering. Bangladesh University of engineering and technology, Dhaka.

Summary The objectives of this experiment were to study a double pipe heat exchanger and hence to obtain individual and overall heat transfer coefficients. Also the variation of heat transfer coefficient with Reynolds number and fluid velocity and also the experimental and theoretical heat transfer coefficient was compared. In this experiment, steam was used as the hot fluid while water was used as the cold fluid. Water was ed through the pipe and steam was ed through the annulus. Steam pressure was controlled by the valve opening. The inlet and outlet water temperature was recorded. This same process was done for several steam pressures of 5, 10 and 15 psig and different flow rate of water. Then by proper mathematical operation, heat transfer coefficient was determined. In this experiment, the overall theoretical heat transfer coefficient was found to be varied from 674.1697 W/m2.oC to 1501.875 W/m2.oC while the experimental values varied from 763.644 W/m2.oC to 1644.788 W/m2.oC. And, the individual steam side heat transfer coefficient was in the range of 7979.871 W/m2.oC to 8377.854 W/m2.oC while waterside heat transfer coefficient was from 987.6382 W/m2.oC to 1981.433 W/m2.oC. Graph of Nusselt number vs. Reynolds number, heat transfer coefficient vs. velocity and Wilson plot was drawn. The possible discrepancies are discussed at the end of the report.

1

Experimental Setup Pressure Gauge Saturated steam inlet Outlet Temperature

Inlet Temperature

Water Outlet Water Inlet

Steam Trap

Figure 1: Experimental setup of a double pipe heat exchanger.

2

Observed data Tube Length = 7 feet 4 inch Inner Tube: Nominal Diameter – 1 inch; Schedule 40 Table 1: Observed data for double pipe heat exchanger. Steam

Obs.

Water temperature

Pressure,

No.

(˚C)

P (psig) 5

10

15

Water

Inlet

Outlet

01

28

61

1.0

02

28

59

03

28

04

Condensate

Volume(L) Time(s)

Weight(kg)

Time(s)

10.19

0.25

60

1.0

8.8

0.3

60

49

1.0

4.15

0.65

60

28

43

1.0

2.94

0.95

60

05

28

64

1.0

10.03

0.45

60

06

28

57

1.0

6.78

0.55

60

07

28

50

1.0

4.56

0.65

60

08

28

46

1.0

3.44

0.75

60

09

28

68

1.0

12.47

0.35

60

10

28

58

1.0

6.87

0.45

60

11

28

53.5

1.0

5.25

0.55

60

12

28

49.5

1.0

4.06

0.65

60

3

Calculated data Length of the pipe, L= 7 ft 4 inch = 7.33 ft. = 2.234184 m. Outer diameter of the pipe, Do=1.32 inch. = 0.033528 m. (Donald Q. Kern, ‘Process Heat Transfer’, page: 843.) Outside surface area, Ao = π×D0×L = 0.2344 m2. Table 2: Data for experimental overall heat transfer coefficients. Mass flow Steam Obs. No.

Pressure (psig)

Saturation

Heat of

temperature, condensation, TS (oC)

S (kJ/kg)

Wt. of

rate of

condensate,

condensate,

WC (kg)

Mc (kg/s)

1

0.25

0.0042

2

0.3

0.005

0.65

0.0108

4

0.95

0.0158

5

0.45

0.0075

6

0.55

0.0092

0.65

0.0108

8

0.75

0.0125

9

0.35

0.0058

10

0.45

0.0075

0.55

0.0092

0.65

0.0108

3

7

11 12

5

10

15

108.39

115.21

120.97

2234.347

2215.612

2199.242

4

Table 3: Data for properties of water at mean temperature.

Mean Obs.

temperature

No.

of water, TM (oC)

Tube wall temperature

Density,

on steam

M

side,Tw

(kg/m3)

(oC)

Mass Flow rate of Water (kg/s)

Viscosity,

Prandtl

M

No.

(kg/m.s)

Pr

1

44.5

76.445

990.42447

0.097195728

0.000585

3.7295

2

43.5

75.945

990.83579

0.112594976

0.000596

3.8043

3

38.5

73.445

992.7838

0.239225012

0.000654

4.2178

4

35.5

71.945

993.8621

0.338048333

0.000694

4.5018

5

46

80.605

989.7944

0.09868339

0.00057

3.6217

6

42.5

78.855

991.24

0.14620059

0.000607

3.8816

7

39

77.105

992.5973

0.217674846

0.000648

4.1733

8

37

76.105

993.3316

0.288759186

0.000673

4.3561

9

48

84.485

988.9303

0.079304755

0.00055

3.4857

10

43

81.985

991.0388

0.144256012

0.000601

3.8426

11

40.75

80.86

991.93

0.188939048

0.000627

4.0232

12

38.75

79.86

992.6908

0.244505123

0.000651

4.1954

5

Table 4: Data for properties at mean temperature (Cont’d)

Velocity of Obs.No.

Water, V (m/s)

Reynolds

Nusselt

No.

No.

Re

Nu

Water side

Film

heat

temperature,

transfer

hio

Tf

coefficients,

(W/m2.oC)

(oC)

hi (W/m2.oC)

1

0.175932999

7.94E+03

46.99696

1124.823

893.8938

84.43125

2

0.203722416

9.03E+03

52.45477

1253.147

995.8725

84.05625

3

0.431989701

1.75E+04

92.06636

2178.535

1731.276

82.18125

4

0.609781381

2.33E+04

118.3597

2783.741

2212.231

81.05625

5

0.178739508

8.28E+03

48.12093

1154.83

917.74

89.25625

6

0.264418475

1.15E+04

64.13742

1529.407

1215.415

87.94375

7

0.393148522

1.61E+04

85.72424

2030.458

1613.599

86.63125

8

0.521150366

2.05E+04

105.6861

2493.319

1981.433

85.88125

9

0.143765618

6.89E+03

41.01053

987.6382

784.8731

93.60625

10

0.260954478

1.15E+04

63.70505

1520.507

1208.342

91.73125

11

0.341477573

1.44E+04

77.64805

1845.46

1466.581

90.8875

12

0.441565828

1.80E+04

93.88314

2222.617

1766.307

90.1375

6

Table 5: Data for properties at film temperature.

Obs. No.

Density, f

Viscosity, f×104

(kg/m3)

(kg/m.s)

Thermal conductivity, kf (W/m.oC)

Condensation heat transfer coefficients, ho (W/m2.oC)

1

968

3.28

0.67285

8377.854

2

969

3.29

0.67262

8334.933

3

970

3.37

0.67145

8130.011

4

971

3.42

0.67072

8013.865

5

965

3.10

0.67565

8323.548

6

966

3.14

0.67492

8187.492

7

967

3.19

0.67417

8057.763

8

967

3.22

0.67373

7986.179

9

962

2.95

0.67793

8308.74

10

963

3.01

0.67698

8126.193

11

964

3.04

0.67654

8047.844

12

964

3.07

0.67613

7979.871

7

Table 6: Data for experimental heat transfer coefficients. Experimental Rate of heat

Rate of heat

Mean rate of

Log mean

overall heat

Observation

taken-up by

given-up by

heat

temperature

transfer

No.

water,

steam,

transfer,

difference,

Coefficient,

Qw(J/s)

Qc (J/s)

Qm(J/s)

Tlm (oC)

UOE (W/m2 oC)

1

13044.73587

9309.779167

11177.25752

62.4434

763.6442362

2

14195.63681

11171.735

12683.6859

63.6365

850.318422

3

20431.4906

24205.42583

22318.45822

69.36097

1372.749895

4

20627.7093

35377.16083

28002.43507

72.63203

1644.788241

5

14444.87987

16617.09

15530.98493

67.62034

979.8600024

6

17243.33618

20309.77667

18776.55642

71.73568

1116.665483

7

19476.23921

24002.46333

21739.35127

75.67779

1225.520398

8

21144.10264

27695.15

24419.62632

77.86355

1337.972592

9

12898.12542

12828.91167

12863.51854

71.10465

771.7989638

10

17609.33134

16494.315

17051.82317

76.99841

944.7816707

11

19594.58522

20159.71833

19877.15178

79.5399

1066.133263

12

21384.90708

23825.12167

22605.01437

81.74934

1179.676555

8

Table 7: Data for calculation of theoretical heat transfer coefficients Theoretical Overall heat Obs. No.

transfer coefficients,

1 U OT

1 U OE

1 VM

0.8

UOT (W/m2.oC) 1

753.6054

0.001327

0.00131

4.015338

2

824.378

0.001213

0.001176

3.570828

3

1266.447

0.00079

0.000728

1.957137

4

1501.857

0.000666

0.000608

1.485459

5

770.0179

0.001299

0.001021

3.964821

6

967.2557

0.001034

0.000896

2.898455

7

1200.727

0.000833

0.000816

2.110351

8

1390.981

0.000719

0.000747

1.684339

9

674.1697

0.001483

0.001296

4.719282

10

961.9187

0.00104

0.001058

2.929194

11

1117.201

0.000895

0.000938

2.362165

12

1281.277

0.00078

0.000848

1.923108

9

Table 8: Data for the heat loss calculation and % of heat loss calculation. Rate of heat

Rate of heat

taken-up by

given-up by

Heat loss

water,

steam,

QL (J/s)

Qw(J/s)

Qc (J/s)

1

13044.73587

9309.779167

-3734.96

-40.11863911

2

14195.63681

11171.735

-3023.9

-27.06743229

3

20431.4906

24205.42583

3773.935

15.59127799

4

20627.7093

35377.16083

14749.45

41.69201594

5

14444.87987

16617.09

2172.21

13.07214518

6

17243.33618

20309.77667

3066.44

15.09834664

7

19476.23921

24002.46333

4526.224

18.85733166

8

21144.10264

27695.15

6551.047

23.65413208

9

12898.12542

12828.91167

-69.2138

-0.539513838

10

17609.33134

16494.315

-1115.02

-6.760003926

11

19594.58522

20159.71833

565.1331

2.803278816

12

21384.90708

23825.12167

2440.215

10.2421915

Observation No.

% of heat loss

10

Sample Calculation For observation No. 10: Inlet water temperature, T1 =28oC Outlet water temperature, T2 =58oC Volume of water collected, V1 =0.001m3 Time for water collection, tw = 6.87 s Weight of condensate collected, WC = 0.45 Kg Time for condensation, tc = 60s Density of water at 37 oC = 991.0388 Kg/m3 Weight of water collected, Ww = 0.001× 991.0388 = 0.9910388 Kg Mass flow rate of water, Mw = Ww/tw = (0.9910388÷6.87) Kg/s = 0.1442560116 Kg/s Mass flow rate of condensate, Mc = WC/tc = (0.45 ÷ 60) kg/s = 0.0075 kg/s Mean temperature of water, Tm = (T1+ T2)/2 = (58+28)/2 =43 oC Heat capacity of water at 43 oC, = 4069 J/kg. oC Rate of heat taken by water, Qw = Mw × × (T2-T1) =0.1442560116 × 4069× (58-28) = 17609.33134 J/s Heat of condensation of steam at 15 psig (29.7 psia), λs =2199.242 KJ/kg (Ref: Richard M. Felder, Ronald W. Rousseau, ‘Element Principles of Chemical Processes’, 3rd ed.) Rate of heat given by steam, QC = MC × λs = (0.0075 × 2199242) J/s =16494.315 J/s

Mean rate of heat flow, 17609.33134  16494.315 Qm = QW  QC = = 17051.82317 J/s 2 2

Saturation temperature of steam at 15 psig (29.7 psia), Ts = 120.97 oC (Ref: Richard M. Felder, Ronald W. Rousseau, ‘Element Principles of Chemical Processes’, 3rd ed.) 11

Temperature difference at inlet, ΔT1 = Ts - T1 = (120.97 – 28) oC = 92.97 oC Temperature difference at outlet, ΔT2 = Ts - T2 = (120.97 – 58) oC =62.97 oC Log mean temperature difference, ΔTlm =

92.97  62.97 o T1  T2 = C =77 oC 92.97 T1 ln ln 62.97 T2

The outside surface per linear feet = 0.344 ft2/ft Inside diameter (ID) of the pipe,

Di = 1.049 in. = 0.02665 m. (Donald Q. Kern, ‘Process

Heat Transfer’, page: 843.) Outside diameter (OD) of the pipe, Do = 1.32 in. = 0.033528 m. (Donald Q. Kern, ‘Process Heat Transfer’, page: 843.) Tube length = 7 ft. 4 in. = 88 in. = 7.33 ft. Outside area available for heat transfer, Ao = 0.344×7.33 ft2 = 0.2344 m2. Experimental overall heat transfer coefficient, UOE = =

Qm Tlm .A0 17051.82317 W/m2.oC 77  0.2344

= 944.78167 W/m2.oC

Tube wall temperature on steam side, Tw = TS  Tm 2

o

C=

120.97  43 o C =81.985 oC 2

Properties at mean temperature, Tm= 43 oC Density of water, ρm =991.0338 kg/m3 Viscosity of water, μm =0.00060102 kg/m.s Prandtl no. of water,Pr = 3.8426 Thermal conductivity of water, km = 0.63608 W/m.oC (Ref: J P Holman, Suvik Bhattacharyya, ‘Heat Transfer’, page no.: 609) Inner flow area, Ai = 0.0005576 m2 Velocity of water, vm =

MW 0.1442560116 = m/s = 0.260954478 m/s  m  Ai 991.0338  0.0005576 12

Reynolds no. of water, Re =

Di . m .v m

=

m

0.02665  991.0338  0.260954478 = 11468.05 0.00060102

Water side heat transfer coefficient for turbulent flow Using Dittus-Boelter equation, hi = 0.023 × = 0.023×

km ×(Re)0.8 ×(Pr)1/3 Di

0.63608 × (11468.05)0.8× (3.8426)1/3 0.02665

= 1520.507 W/m2.oC Film temperature, Tf = Ts-0.75 × (Ts-Tw) = 120.97- 0.75× (120.97- 81.985) oC = 91.73125 °C Properties of condensate at film temperature, Tf = 97.73125 °C Density, ρf =963.21 kg/m3 Viscosity of condensate, μf = 0.00030103 kg/m.s Thermal conductivity of condensate, kf = 0.67698 W/m.oC (Ref: J P Holman, Suvik Bhattacharyya, ‘Heat Transfer’, page no.: 609) Steam side heat transfer coefficient using Nusselt equation for film type condensation, k f . f .g.S 3

ho = 0.725  [

2

D 0 (TS  TW )  f

= 0.725  [

]0.25

(0.67698) 3  (963.21) 2  9.81  2199.242 0.25 ] W/m2.oC 0.033528  (120.97  81.985)  0.00030103

= 8126.193 W/m2.oC

Now, xw= D0  Di  0.033528  0.02665  0.003439.m 2

2

Carbon-steel metal’s thermal conductivity, KM = 43 W/m.oC Log-mean diameter, Dlm =

0.033528  0.02665 D 0  Di  0.03.m = 0.033528 D0 ln ln 0.02665 Di

Theoretical overall heat transfer coefficient,

13

UOT = ( =(

D x .D 1  0  W 0 ) 1 h0 Di .hi K m .Dlm

1 0.033528 0.003439  0.033528 1   ) W/m2.oC 8126.193 0.02665  1520.507 43  0.03

= 961.9187 W/m2.oC Now,

1 1   0.001058 m2.oC/W U OE 944.78167

1 1   0.00104 m2.oC/W U OT 961.9187 1 1   2.929194 (s/m)0.8 0.8 v (0.2609544775) 0.8

Heat loss, QL = Qc-Qw = 1649.315- 17609.331341 = -1115.02 J/s % of heat loss = (Qc-Qw)*100/Qc = -6.76%

14

Graphs

Nusselt Number,Nu

1000

y = 0.019x0.8686

Power (10 psig)

100

10 7000

10 psig

Reynolds Number,Re

Figure 2: Log-log plot of Nusselt number vs. Reynolds number plot for 10 psig steam pressure.

1000

Nusselt Number,Nu

y = 0.0214x0.8569 100 5 psig Power (5 psig)

10 6000

Reynolds Number, Re Figure 3: Log-log plot of Nusselt number vs. Reynolds number for 5 psig steam pressure.

15

100

Nusselt Number,Nu

y = 0.0197x0.8646

15 psig Power (15 psig)

10 5000

Reynolds Number, Re Figure 4: Log-log plot of Nusselt number vs. Reynolds number for 15 psig pressure steam.

Water side heat transfer coefficient, hi W/m2.°C

10000

y = 3842.6x + 469.57

5 psig

1000

Linear (5 psig)

100 0.1

Velocity of water, v(m/s)

1

Figure 5: Log-log plot of water side head transfer coefficient vs. velocity for 5 psig steam pressure

16

10000

y = 3894.8x + 480.24

10 psig

1000

Linear (10 psig)

100 0.1

Velocity of water,v (m/s)

1

Figure 6: Log-log plot of water side head transfer coefficient vs. velocity for 10 psig steam pressure.

Water side heat transfer coefficient,hi (W/m2.˚C)

10000

y = 4147x + 412.63

15 psig

1000

Linear (15 psig)

100 0.1

Velocity of water,v (m/s)

1

Figure 7: Log-log plot of water side head transfer coefficient vs. velocity for 15 psig steam pressure.

17

0.0014

Dirt factor = 0.0006658- 0.000608 = 0.0000578 0.0011

1/U

Experimental Theoretical Power (Experimental) 0.0008

Power (Theoretical)

0.0005 1.48

2.184

2.888

3.592

4.296

5

1/v.8 Figure 8: (1/U) vs. (1/V)0.8 plot for Wilson plot at 5 psig steam pressure. 0.0015

Dirt Factor = 0.000747-0.000719 = 0.000028

1/U

0.0012

Experimental

0.0009

Theoretical Power (Experimental) Power (Theoretical) 0.0006 1.68

2.344

3.008

3.672

4.336

5

1/v0.8 Figure 9: (1/U) vs. (1/V)0.8 plot for Wilson plot at 10 psig steam pressure.

18

0.0018

1/U

0.0015

Dirt Factor =0.000848-0.00078 = 0.000068

0.0012

Experimental 0.0009

Theoretical Power (Experimental) Power (Theoretical)

0.0006 1.92

2.536

3.152

3.768

4.384

5

1/v0.8 Figure 10: (1/U) vs. (1/V)0.8 plot for Wilson plot at 15 psig steam pressure.

19

Results and Discussions Range of the Theoretical Overall Heat Transfer Coefficient (UOT), 674.1697 W/m2.oC to 1501.875 W/m2.oC Range of the Experimental Overall Heat Transfer Coefficient (UOE), 763.644 W/m2.oC to 1644.788 W/m2.oC Ranges of individual steam side heat transfer coefficient - 7979.871 W/m2.oC to 8377.854 W/m2.oC Ranges of waterside heat transfer coefficient - 987.6382 W/m2.oC to 1981.433 W/m2.oC Slope of the straight line ‘Nusselt number Vs. Reynolds number’ Plots areFor 5 psig pressure

-

0.8569

For 10 psig pressure

-

0.8686

For 15 psig pressure

-

0.8646

The theoretical value of ‘Nusselt number Vs. Reynolds number’ Plots are 0.8 When the values of Nusselt no. is plotted against the values of corresponding Reynolds no. in a logarithmic plot a straight line with a slope of 0.8569 ≈ 0.8686 is obtained. According to Dittus-Boelter equation, the slope should be 0.8. This curve also conforms to Dittus-Boelter equation. Therefore, this finding is highly satisfactory. The dirt factor from the 1/U vs. 1/v0.8 plot ranges from 0.000028 to 0.000068. Nusselt no. vs. Reynolds and water side heat transfer coefficient (hi) vs. velocity (v) plots for different pressure shows straight lines in log-log coordinate. But 1/U vs. 1/v0.8 plots for different pressure for both theoretical and experimental overall heat transfer coefficients show straight lines in normal coordinate. As the experimental findings of overall heat transfer coefficients were generally lower than the theoretical ones, the 1/U curve for theoretical values was in below the curve for experimental values. The possible reasons of the discrepancies of theoretical and experimental values are mentioned bellow –  At the times of calculating the theoretical overall heat transfer coefficients the resistance due to the formation of scale or dirt was not taken into consideration. Hence, 20

Fouling or other factors are left from the calculation. In reality, the performance and efficiency of any heat exchanger are subject to these factors and this is why industrial exchangers are dismantled routinely after operating a certain period for cleaning dirts that are deposited on the wall. The double pipe heat exchanger used in this experiment is very old and may not undergo overhauling for a long period. The scale deposited in the meantime is sufficient to deviate the theoretical values from the experimental ones especially when dirt formation is neglected in calculation.  Malfunctioning of the stream trap is one of the reason for the heat loss becoming negative.  The steam pressure was considered constant during the experiment. But in practical it was not constant throughout the experiment.  Heat lost during the experiment due to convection and conduction were not considered.  Could be the unsteady nature of condensate flow caused some error in the determination of corresponding condensate for a given flow of water.  Some assumptions were made in determination of steam side heat transfer coefficient determination; such as the vapor pressure was neglected and the condensation was considered to be laminar and film type. But in practical could not satisfy those assumptions.

21