Completed Heat Transfer Project 2 PDF

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Summary

Final report Vacari heat transfer...

Description

1

Table of Contents 1.

Introduction.......................................................................................................................................3

2.

Premises and Assumptions................................................................................................................3

3.

Results................................................................................................................................................4

4.

Discussion...........................................................................................................................................5

Appendix....................................................................................................................................................7 Appendix A ---- Equations..................................................................................................................7 Appendix B ---- Spreadsheets...............................................................................................................8 Appendix C ---- Program....................................................................................................................14

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1. Introduction 1.1 Charge Our group was charged with designing a shell-and-tube heat exchanger which cools Syltherm 800 coming out of some other process down to reenter the process. The Syltherm 800 is to be cooled with water. And, perhaps most importantly, the cost, both of yearly operation and initial cost, of the heat exchanger is to be minimized.

1.2 Scope To ensure cost was minimized, we wrote a Visual Basic program which ran the variables through a brute-force method of testing reasonable values of independent variables, and reporting which combination will give the lowest cost while still meeting the heat transfer specifications.

2. Premises and Assumptions 2.1 premises The premises of the problem dictate the 127,000 lbm/hr (15.5 kg/s) of Syltherm 800 need to be cooled from 550°F (287.8°C) down to 180°F (82.2°C) with water supplied at 65°F (18.3°C), which cannot exceed 120°F (48.9°C).

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2.2 Assumptions For the fouling resistances, since Syltherm 800 is essentially non-fouling1, a fouling resistance of 0 was used. And since the water is being recycled, we figured it would be reasonably clean, but we still chose a relatively conservative value of .0002 K*m2/W. The absolute roughness of the copper pipes was assumed to be 0.0000015 m.2 It was also assumed that no heat was lost to the surrounding air, because insulation can be added around the outside of the shell to essentially neutralize any heat transfer to the environment. For finding the Nusselt number in the shell, we created a polynomial best fit curve to interpolate within the table to find values of C and n between given ratios of the pitch and tube outer diameter.

3. Results 3.1 Design Specifications 

One shell



Pipes made of copper



Water runs through the shell, while the Syltherm 800 runs through the pipes



Inner diameter of the tubes = .080 m



Outer diameter of the tubes = .174 m



Inner diameter of the shell = 2.433 m



Pitch = .521 m



Number of pipes within the shell = 7 (with two passes through the shell for each)

1 http://dowac.custhelp.com/app/answers/detail/a_id/13040/~/httf-%E2%80%93-syltherm-recommended-foulingfactor 2 http://www.engineeringtoolbox.com/surface-roughness-ventilation-ducts-d_209.html

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

Baffle spacing within the shell = 2.120 m



Total length of each pipe = 53.668 m



Total length of the shell = 26.834 m



Mass flow rate of Syltherm: 127,000 lbm/hr (15.5 kg/s)



Mass flow rate of water: 388,000 lbm/hr (47.3 kg/s)



The initial cost was calculated from:

3.2 Costs

o

O

Cost=3.882∗C p

(A ) log 10 ¿ ¿ .1634 ¿ ( A ) +¿ O C p =4.3247−.303 log 10 ¿



With



And A is the internal area of the pipes



The initial cost was found to be $89750



Yearly running costs are: o Electricity for pumping water through the shell: $51 o Electricity for pumping Syltherm through the pipes: $346 o Cost of supplying the cooling water: $47580

4. Discussion 4.1 Time Assumption The cost minimization was based around the heat exchanger running 24/7 for 20 years, so there was some trade off on initial cost in order to minimize pump power costs.

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4.2 Cost of Cooling Water By far the most expensive aspect of the heat exchanger is the cost of supplying the cooling water. In order to have the lowest volumetric flow rate possible, we ensured the water went through the greatest temperature change possible within safety standards (see appendix for details). Finding some way to decrease the cost of supplying the water or increasing the maximum safe temperature of the water would hugely reduce the price of operating the heat exchanger.

4.3 Choice of Shell Number One shell was chosen over two shells because even though the correction factor was closer to one for two shells, the initial cost for the same amount of area was significantly lower for one shell. The slightly lower area from the higher correction factor did not make up for the higher cost per area of the two shell heat exchanger.

4.4 The Nusselt Number In calculating the Nusselt number on the shell side, the ratio between the pitch and the outer diameter of the pipes could not go beyond three because extrapolating too far from the given chart resulted in a negative value for C from our best fit polynomial, and thus for the Nusselt number, which is impossible. The calculated optimal pipe dimensions give us a relatively thick pipe. However, the flowrate of the Syltherm is large and there are sharp turnarounds within the shell, so a thick pipe ensures that it will stay contained.

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Appendix Appendix A ---- Equations

0.8

NuD =0.023 ℜ D Pr

0.4

for fluid being heated in internal forced convection

0.3 NuD =0.023 ℜ 0.8 for fluid being cooled in internal forced convection D Pr

ℜ D=

4m π Di μ

Nu=

ho D o =C ℜn Pr 1/ 3 for the Nusselt number in the shell k 2

π Do ) 4 (C p S − 4 De= π Do 2 n

G s=

ℜ=

m Sm

De Gs μ

U i=

1 1 = 1 A i ln( D o / D i) A i 1 1 D i ln (Do / D i) D i 1 + + + + D o ho k A o ho hi 2 πkL hi

R2 +1 1−P (√ ) )ln ( 1−PR R−1 F= 2 x + √ R +1 ) ln( 2 x−√ R +1 Q= mC p ∆ T =U i A i F ∆ T

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△Tm=

△ T 1− △ T 2 T1 ) ln(△ △T2

A=

Q Ui F∆ Tm

N=

A π Di L

f Fanning =

f Moody 4

The basic equations governing heat transfer in our heat exchanger are: ´ m ´ h∗c p ,h∗(T h , i−T h ,o ) = m ´ c∗c p , c∗(T c ,o −T c, i) Q= ´ Q=FUA ∆Tm m ´ h ,c p , h , T h ,i ,T h , o ,∧c p , c are set by the problem statement∧ physical properties .

´ c= Rearranging, we find : m

m ´ h∗c p , h∗( T h ,i−T h , o ) . Thus, the mass flow rate of the water can c p ,c∗( T c , o −T c ,i )

be reduced by increasing its temperature range. Appendix B ---- Spreadsheets Properties 560.9277778

K

355.3722222

K

density

679.5050239

density

882.5811059

specific heat

2065.794173

specific heat

1714.895153

viscosity

0.000512739

viscosity

0.003655072

conductivity

0.084618741

conductivity

0.123281646

Syltherm Average Temp (K)

Water Average 458.15

Temp (K)

306.7611111

density

785.8004877

density

993.6576983

specific heat

1890.368915

specific heat

4162.241085

8

viscosity

0.001232598

conductivity

0.1039578

Pr

22.4135713

291.4833333

viscosity

0.000738529

conductivity

0.622061912

Pr

4.941525664

322.0388889

density

997.8080901

density

988.2076345

specific heat

4146.087902

specific heat

4179.942771

viscosity

0.001041539

viscosity

0.000554266

conductivity

0.599935587

conductivity

0.640862022

Correction Factor Water in Tube

Water in Shell

ti

65

550

to

120

180

Ti

550

65

To

180

120

P

0.113402062

0.762886598

R

6.727272727

0.148648649

A B

9.909090909 8.086311257

1.472972973 1.202019241

F (1 Shell)

0.931081415

0.931081415

F (2 Shell)

0.984617084

0.984617084

Shell Pressure Cost

Tube OD(m)

0.17

Shell ID (m)

2.43

Baffle Space (m)

2.12

Clearance (m)

0.35

Pitch (m) 1/Roughness

0.52 116,226.22 Water

Flow rate (kg/s)

Syltherm 47.26

Water Equivalent Diameter

1.809370546

15.47 Syltherm

9

Re_shell

33732.16313

Cross-Flow Area

3.432323989

Gs (kg/(m^2*s))

13.76842015

f (Eq 8-24)

0.022759982

0.025767911

0.56341962

0.806610293

Power

0.026795851

0.015876892

Pump cost/hr ($)

0.005787904

0.003429409

Pressure Drop

Cooling Water cost/hr ($)

20211.10474

5.427578523

Viscosity Water

0.000738529

Syltherm

0.001232598

Density Water

993.6576983

Syltherm

785.8004877

Pipe Pressure Cost Pipe ID (m) 1/Roughness

0.08

Water

116,226.22

Length (m)

53.67

Number of Pipes

7.00

Water 47.26

Syltherm 15.46728244

29.61240852

12.25574933

Water 145213.2041

Syltherm 28476.95829

f_Moody

0.01661347

0.023692842

f_fanning

0.004153367

0.00592321

Pressure Drop (Pa)

24726.59225

4776.70955

Flow rate (kg/s) Velocity (m/s)

Re_Pipe

Syltherm

Density

993.6576983

785.8004877

Viscosity

0.000738529

0.001232598

10

Power/pipe

1175.979772

94.02223195

Total Power

8231.858402

658.1556236

Pump cost/hr ($)

0.493911504

0.039489337

Pipe Heat Transfer Shell Water

Syltherm

S Flow rate (kg/s)

47.26

15.47

Re

33732.16313

20211.10474

Nu

307.6171932

372.9744054

h_o

1097.612022

222.4030552

Pipe

(Note column switch) Syltherm

P Flow rate (kg/s)

Water 15.47

47.26

Re

199338.708

1016492.429

Nu

1015.206677

2785.836195

h_i

1316.741803

21621.12392

Analysis Tube ID (m)

0.080151365

Approx Max number of pipes

Tube OD(m)

0.174339325

k_pipe

Shell ID (m)

2.120260935

Pitch (m)

0.521172748

Length (m)

W Flow rate (kg/s)

385.000

2.43253849

Baffle Space (m) Number of pipes

8.000

7 53.66815184

Celsius

ti

65.000

18.333

to

120.000

48.889

Ti

550.000

287.778

To

180.000

82.222

116226.217

Delta T1

430.000

238.889

Thickness (m)

0.094

Delta T2

115.000

63.889

Clearance (m)

0.347

1/Relative Roughness

47.258

Fahrenheit

11

S Flow rate (kg/s)

15.467

Ai

94.597

Ao

205.760

Ui_clean

573.220

Uo_clean

263.534

R_f (Syltherm) R_f (water (worst case))

LMTD

238.844

F (1 Shell)

0.931

F (2 Shell)

0.985

132.691

0.0000 0.0002

Ui_dirty

514.263

Uo_dirty

250.339

Qw C 6010212.149 Qsyl C 6010212.149 Q (F=1shell) UiAi (true)

48647

6010212

UoAo (true)

51510

6363829

Ai 1 shell Cp Initial Cost

Ao 1 shell 23117

31493

89745.97

122261

shell P water / hr

0.00578790

20 yrs

1011.82

shell P syl / hr

0.00342941

20 yrs

599.52

pipe P water/hr

0.4939115

20 yrs

86343.63

pipe P syl/hr

0.0394893

20yrs

6903.37

12

Water cost hr

5.43

20yrs

948827.57 4721.02

1046488.72

TOTAL COST Shell W

Shell Syl 7915.19

86943.15

shell P water / yr

50.591

shell P syl / yr

29.976

pipe P water/yr

4317.182

pipe P syl/yr

345.168

Water cost/yr

47441.378

Tube ID (m)

0.151618746

Approx Max number of pipes

Tube OD(m)

0.190177476

k_pipe

Shell ID (m)

2.065335354

Baffle Space (m)

2.696073765

Pitch (m)

0.386006085

Number of pipes Length (m)

10

385.000

Fahrenheit

Celsius

ti

65.000

18.333

to

120.000

48.889

Ti

550.000

287.778

To

180.000

82.222

126784.984

Delta T1

430.000

238.889

Thickness (m)

0.039

Delta T2

115.000

63.889

Clearance (m)

0.196 LMTD

238.844

132.691

W Flow rate (kg/s) 1/Relative Roughness

S Flow rate (kg/s)

24.53195266

11.000

47.258

15.467

Ai

116.852

Ao

146.569

F (1 Shell)

0.931

13

F (2 Shell)

Ui_clean

517.607

Uo_clean

412.661

R_f (Syltherm) R_f (water (worst case))

0.985

0.000 0.000

Ui_dirty

469.050

Uo_dirty

381.200

Qw C 6010212.149 Qsyl C 6010212.149 Q (F=2shell) UiAi (true) UoAo (true)

54809 55872

Ai 2 shell Cp Initial Cost

7160826 7299666

Ao 2 shell 19924

21279

154697

165218

shell P water / hr

0

20 yrs

1015

shell P syl / hr

0

20 yrs

601

pipe P water/hr

0

20 yrs

86591

pipe P syl/hr

0

20yrs

6923

14

Water cost hr

5

20yrs

951544

1114178

TOTAL COST Shell W

Shell Syl 7938

87192

Appendix C ---- Program All calculations were done on VBA / Microsoft Excel. Below is one rendition of the program which was used to find the minimum cost. After preliminary values were found, the program was tuned to find even more optimal values around them: Dim a, b, c, d, e, f, g, h As Integer Dim ID, OD, SID, BSp, P, L, Mw As Double Dim npipe As Double Dim Cost As Double Sub Cost_Minimizer() Cost = 1E+12 For a = 1 To 10 Range("B1").Value = 0.003 + a * 0.02 ID = Range("B1").Value For b = a To 10 Range("B2").Value = 0.01 + b * 0.03 OD = Range("B2").Value For c = b To 10 Range("B3").Value = 0.01 + c * 0.3 SID = Range("B3").Value \

For d = 1 To 10 Range("B4").Value = 0.1 + d * 0.1 BSp = Range("B4").Value For e = 1 To 3 * b Range("B5").Value = OD + e * 0.015 P = Range("B5").Value For f = 1 To 6 Range("B6").Value = (f - 1) * 100 + 1

15 npipe = Range("B6").Value For g = 1 To 10 Range("B7").Value = (g - 1) * 10 + 1 L = Range("B7").Value If Abs(Range("H4").Value - Range("J9").Value)...