Heat Transfer Manual

Heat Transfer FilePage 1

Heat Transfer

Submitted by:Zeeshan ZakiMuzammil Ali

Submitted to:Sir Adnan

Index

No. Detail Page1. Dirt factor in double pipe heat exchanger (co current flow) 22. Dirt factor in double pipe heat exchanger (counter current flow) 113. Heat losses of insulation 204. Heat Transfer through bricks 235. Loading factor of cooling tower 256. Number of Turns of cooling coil 27


Experiment Number 1Object:

To determine the dirt factor of double-pipe heat exchanger when cooling water is flowing co-current

Formulae:1. Approach 12. Approach 2

3.

4.

5.

6. Range 17. Range 28.9.10.11.12.

13.

14. DQ Kern Process Heat Transfer (text) page 105

15. (Area of cylinder formula)

16. DQ Kern Process Heat Transfer page 105 equation 6.3

17.

18.

19.

Sieder–Tate equation for turbulent flow DQ Kern Process Heat Transfer page 103 equation 6.2 & Coulson & Richardson’s Chemical Engineering volume 1 page 369

20.

Prandl Number

21. ( in Poise)


Correlation for viscosity of water in Poise (P) for in Kelvin table 6, page 683 Coulson and Richardson Chemical Engineering, Volume 1, Fifth Edition

22.

(Rearranged formula for in Ns/m2 for T in Celsius)

23. where





Legend:T1 and T2 are called approach. THI, THO, TCI and TCO are the temperature at the hot inflow and outflow, cold inflow and outflow respectively.TCBM and THBM are the bulk mean temperature of cold and hot streamsTHOT = Temperature decrease of hot fluid TCOLD = Temperature increase of cold fluidTLMTD = Log mean temperature differenceCW, CP = heat capacity of water = 4.184 J/kg = 1 Btu/lb

= heat flow rates for heat loss, hot and cold water respectively = mass flow rate with subscripts for hot and cold water= pressure reading on the meter for the hot fluid in psi (lb/in2) or kg/cm2

AI, AO = Area of cross section of inner pipe and outer pipe/annulus respectivelyAIS = Internal Surface area of the pipe = Density of water taken as 1g/cc =1000kg/m3= 62.382 lb/ft3

D1 and D2 are the inner and outer diameter of inner pipe respectivelyD3 and D4 are the inner and outer diameter of outer pipe respectivelyDe is the equivalent diameter used for calculating Reynolds Number and heat transfer coefficient for hot fluid flow in the annulus v = Fluid velocity k = Thermal conductivity Re = Reynolds Numberh = Heat transfer coefficient or film coefficient (subscript “i" for inner coefficient, “o” for outer and “io” for inner biased on outer diameter)G = Mass flow rate per unit area (proportional to P’)UC = Clean Overall heat transfer coefficient UD = Dirty Overall heat transfer coefficientRD = Dirt Factor or resistance to heat flow in heat exchangers due to scalingD in Re and h is called characteristic diameter which is De for outer and D1 for inner pipe


Conversion factors between MKS and FPSLength: 1 in = 2.54 cm 1 ft = 0.3048 m (1)Area: 1 in2= 6.451 6 cm2 1 ft2= 0.0929 m2 (2)Volume: 1 ft3 = 28 316.85 dm3 (3)Mass: 1 lb = 453.9237 g (4)Viscosity dynamic: 1 dyn s/cm2 (poise P) = 0.1 Ns/m2 or Pa s (5)

1 lbm/ (ft h) = 4.133 789x10–4 Ns/m2 (6)1 lbm / (ft s) = 1.488 164 Ns/m2 (7)10 Poise P = 1 Pa. s = 1 Ns/m2 (8)1 cP (centi poise) = 1 mNs/m2 (9)

Velocity: 1 ft/s = 0.3048 m/s (10)Fluid velocity: 1 ml/s = 0.127133 ft3/h = 3.5315 x10–3 ft3/s (11)Thermal Conductivity: 1 Btu/ (h ft °F) = 1.730 735 W/ (m K) (12)Heat transfer Coefficient: 1 Btu/ (h ft2 °F) = 5.678 263 W/ (m2 K) (13)Pressure: 1 Psi (lb/in2) = 0.07035831 kg/cm2 (14)

1 kg/cm2 = 14.213 Psi (15)Density: 1 g/cm3 = 62.382 lb/ft3 (16)

Temperature: (17)

K = °C + 273.15 (18)

Table 1–4, page 1–4 to 1–10 Perry’s Chemical Engineer’s Handbook

Observations:Pipe Symbol Cm in ft m

Outer pipe

Outer diameter D4 4.84 1.906 0.159 0.0484

Inner diameter D3 4.10 1.616 0.135 0.0410

Inner Pipe

Outer diameter D2 2.09 0.823 0.069 0.0209

Inner diameter D1 1.54 0.605 0.050 0.0154

Equivalent diameter De 5.966 2.349 0.196 0.060Length L 560 220.472 18.373 5.60

Parameter cm2 in2 ft2 m2

AI 1.854 0.287 0.00200 1.85x10–4

AO 9.794 1.518 0.01054 9.79 x10–4

AIS 3677 570 3.958 0.368AI, AO, AIS, De were calculated by formulae 13, 14, 15, 16 respectively. The outer diameter of pipes was noted and standard thickness of schedule 40 pipes was subtracted to get inner diameter of the pipes. The inner pipe is called a ½ inch pipe and outer pipe is 1½ inch designation. The data for pipes can be obtained from Perry’s Chemical Engineer’s Handbook (7th edition) table 10–18 page 10–72, Plant Design and Economics for Chemical Engineers by Max S Peters (4th edition) table 13 page 888, Process Heat Transfer by Donald Q Kern table 11 page 844, Unit Operations for Chemical Engineers by McCabe Smith sixth edition appendix 3 page 1068.


Temperature for water streams (Celsius):Hot Cold THBM TCBM TCOLD THOT T1 T2 TLMTDInlet Outlet Inlet Outlet

50.00 46.00 29 35 48.0 32.0 6.0 4.0 21.00 11.00 15.4650.00 46.50 30 35.5 48.3 32.8 5.5 3.5 20.00 11.00 15.0550.00 46.25 30 34 48.1 32.0 4.0 3.8 20.00 12.25 15.8149.50 46.50 31 36 48.0 33.5 5.0 3.0 18.50 10.50 14.1248.50 46.00 31 35 47.3 33.0 4.0 2.5 17.50 11.00 14.0048.75 46.00 31 36 47.4 33.5 5.0 2.8 17.75 10.00 13.5147.50 45.00 31 36 46.3 33.5 5.0 2.5 16.50 9.00 12.3748.00 45.50 31 36 46.8 33.5 5.0 2.5 17.00 9.50 12.8947.75 45.50 31 36 46.6 33.5 5.0 2.3 16.75 9.50 12.78

Temperature for water streams (Fahrenheit):Hot Cold THBM TCBM TCOLD THOT T1 T2 TLMTDInlet Outlet Inlet Outlet

122.00 114.80 84.2 95.0 118.4 89.6 10.8 7.2 37.80 19.80 27.84122.00 115.70 86.0 95.9 118.9 91.0 9.9 6.3 36.00 19.80 27.10122.00 115.25 86.0 93.2 118.6 89.6 7.2 6.8 36.00 22.05 28.46121.10 115.70 87.8 96.8 118.4 92.3 9.0 5.4 33.30 18.90 25.42119.30 114.80 87.8 95.0 117.1 91.4 7.2 4.5 31.50 19.80 25.20119.75 114.80 87.8 96.8 117.3 92.3 9.0 5.0 31.95 18.00 24.31117.50 113.00 87.8 96.8 115.3 92.3 9.0 4.5 29.70 16.20 22.27118.40 113.90 87.8 96.8 116.2 92.3 9.0 4.5 30.60 17.10 23.20117.95 113.90 87.8 96.8 115.9 92.3 9.0 4.1 30.15 17.10 23.01

T1, T2, TCBM, THBM, TLMTD, THOT, T COLD calculated by formulae 1, 2, 3, 4, 5, 6 & 7 respectively. Temperature converted to Fahrenheit by conversion relation number 17.

Flow Observation:

Hot ColdMKS FPS MKS FPS

P kg/cm2

mkg/s (ml/s)

mlb/s ft3/h

V ml

Time s

(ml/s)

mkg/s

mlb/s ft3/h

0.06 0.11122 111.22 0.245 14.14 1000 14.2 70.42 0.0704 0.1551 8.950.06 0.11122 111.22 0.245 14.14 1000 14.2 70.42 0.0704 0.1551 8.950.06 0.11122 111.22 0.245 14.14 1000 14.2 70.42 0.0704 0.1551 8.950.06 0.11122 111.22 0.245 14.14 1000 17.1 58.48 0.0585 0.1288 7.430.06 0.11122 111.22 0.245 14.14 1000 17.1 58.48 0.0585 0.1288 7.430.06 0.11122 111.22 0.245 14.14 1000 17.1 58.48 0.0585 0.1288 7.430.06 0.11122 111.22 0.245 14.14 1000 22.1 45.25 0.0452 0.0997 5.750.06 0.11122 111.22 0.245 14.14 1000 22.1 45.25 0.0452 0.0997 5.750.06 0.11122 111.22 0.245 14.14 1000 22.1 45.25 0.0452 0.0997 5.75

The values of m HOT, m COLD calculated by formulae 8 & 9 respectively. MKS values are converted to FPS by conversion relations 4 & 11.


Heat Loss Calculation:

MKSQ HOT Q COLD Q LOSS

m HOT

kg/s kJ/s m COLD

kg/s kJ/s kJ/s

0.11122 1861.37 0.0704 1767.89 93.490.11122 1628.70 0.0704 1620.56 8.140.11122 1745.04 0.0704 1178.59 566.450.11122 1396.03 0.0585 1223.39 172.640.11122 1163.36 0.0585 978.71 184.650.11122 1279.69 0.0585 1223.39 56.300.11122 1163.36 0.0452 946.61 216.750.11122 1163.36 0.0452 946.61 216.750.11122 1047.02 0.0452 946.61 100.42

FPSQ HOT Q COLD Q LOSS

m HOT

lb/s Btu/s Btu/h m COLD lb/s Btu/s Btu/h Btu/h

0.245 1.764 6350.88 0.1551 1.6755 6031.88 319.000.245 1.544 5557.02 0.1551 1.5359 5529.23 27.800.245 1.654 5953.95 0.1551 1.1170 4021.26 1932.700.245 1.323 4763.16 0.1288 1.1595 4174.11 589.050.245 1.103 3969.30 0.1288 0.9276 3339.29 630.010.245 1.213 4366.23 0.1288 1.1595 4174.11 192.120.245 1.103 3969.30 0.0997 0.8972 3229.74 739.560.245 1.103 3969.30 0.0997 0.8972 3229.74 739.560.245 0.992 3572.37 0.0997 0.8972 3229.74 342.63

Q HOT, Q COLD & Q LOSS calculated by formula 10, 11 and 12 respectively.

Overall Dirty Heat Transfer Coefficient:

AIS = 0.368 m2 = 3.958 ft2

MKS FPSUD

W/m2 KUD

Btu/(h ft2 °F)16.44 2.901.47 0.26

97.44 17.1633.24 5.8535.87 6.3211.34 2.0047.64 8.3945.74 8.0521.36 3.76

UD is calculated by formula 26.


Thermal Conductivity and Viscosity DATA:MKS FPS

T Kelvin T Celsius k W/m K T Fahrenheit k Btu/(h ft °F)303 30 0.616 85.73 0.356 333 60 0.659 139.73 0.381

The equations for linear interpolation using the above data are:Equation Range

30–60°C86–140°F

This data was obtained from Coulson and Richardson’s Chemical Engineering, Volume 1, Fifth Edition page 346. Data for thermal conductivity can also be obtained from Process Heat transfer by D Q Kern Table 4 page 800 and in detail from Plant Design and Economics for Chemical Engineers by Max S Peter and Timmerhaus (table 4 Page 876). Equations for linear interpolation are used and developed to give a routine and simple correlation rather than interpolating between different values from the references.

The Viscosity can be correlated by formula 22 and can be converted to FPS using conversion relation 6.

The thermal conductivity and viscosity will be calculated at the bulk mean temperatures.

Calculation:Thermal Conductivity Viscosity

K HOT

k COLD

k HOT

kCOLD

HOT

COLD

W/(m K) Btu/(h ft °F) Ns/m2 lbm/ft h Ns/m2 lbm/ft h0.6420 0.6191 0.3578 0.3711 0.000567 1.371 0.000766 1.8520.6424 0.6201 0.3584 0.3713 0.000564 1.365 0.000754 1.8240.6422 0.6191 0.3578 0.3712 0.000566 1.368 0.000766 1.8520.6420 0.6212 0.3590 0.3711 0.000567 1.371 0.000742 1.7960.6409 0.6205 0.3586 0.3705 0.000574 1.389 0.000750 1.8140.6411 0.6212 0.3590 0.3706 0.000573 1.386 0.000742 1.7960.6395 0.6212 0.3590 0.3697 0.000584 1.413 0.000742 1.7960.6402 0.6212 0.3590 0.3701 0.000579 1.401 0.000742 1.7960.6400 0.6212 0.3590 0.3700 0.000580 1.404 0.000742 1.796

Fluid Velocity:MKS FPS

v HOT v COLD v HOT v COLDm/s ft/s ft/h ft/s ft/h

0.6 0.072 1.969 7086.7 0.2359 849.30.6 0.072 1.969 7086.7 0.2359 849.30.6 0.072 1.969 7086.7 0.2359 849.30.6 0.060 1.969 7086.7 0.1959 705.20.6 0.060 1.969 7086.7 0.1959 705.20.6 0.060 1.969 7086.7 0.1959 705.20.6 0.046 1.969 7086.7 0.1516 545.70.6 0.046 1.969 7086.7 0.1516 545.70.6 0.046 1.969 7086.7 0.1516 545.7

Fluid Velocity is calculated by formula 17 and 18. Be careful in the units of volume and area! The units must match.


Reynolds Number:MKS

HOT COLD

kg/m3v

m/s

Ns/m2D1 m Re

kg/m3

vm/s

Ns/m2

Dem Re

1000 0.60 0.000567 0.015 16260 1000 0.072 0.000766 0.060 56041000 0.60 0.000564 0.015 16330 1000 0.072 0.000754 0.060 56911000 0.60 0.000566 0.015 16295 1000 0.072 0.000766 0.060 56041000 0.60 0.000567 0.015 16260 1000 0.060 0.000742 0.060 47991000 0.60 0.000574 0.015 16052 1000 0.060 0.000750 0.060 47501000 0.60 0.000573 0.015 16087 1000 0.060 0.000742 0.060 47991000 0.60 0.000584 0.015 15776 1000 0.046 0.000742 0.060 37131000 0.60 0.000579 0.015 15914 1000 0.046 0.000742 0.060 37131000 0.60 0.000580 0.015 15880 1000 0.046 0.000742 0.060 3713

FPSHOT COLD

lb/ft3

vft/h

lb/ft h

D1

ft Re

lb/ft3v

ft/h

lb/ft hDeft Re

62.382 7086.7 1.371 0.050 16249 62.382 849.3 1.852 0.196 560062.382 7086.7 1.365 0.050 16318 62.382 849.3 1.824 0.196 568762.382 7086.7 1.368 0.050 16283 62.382 849.3 1.852 0.196 560062.382 7086.7 1.371 0.050 16249 62.382 705.2 1.796 0.196 479562.382 7086.7 1.389 0.050 16041 62.382 705.2 1.814 0.196 474762.382 7086.7 1.386 0.050 16075 62.382 705.2 1.796 0.196 479562.382 7086.7 1.413 0.050 15765 62.382 545.7 1.796 0.196 371062.382 7086.7 1.401 0.050 15903 62.382 545.7 1.796 0.196 371062.382 7086.7 1.404 0.050 15868 62.382 545.7 1.796 0.196 3710

Reynolds Number has been calculated by formula 23. The Reynolds number for MKS is very close to that of FPS this shows precision in calculation. The precision is lost because of recursive conversions and propagation of error. Reynolds Number is greater than 2100 showing that the flow is turbulent in both inner and outer tubes so that equation

Prandl Number:

MKSHOT COLD

CpJ/kg K

Ns/m2

kW/m K Pr Cp

J/kg K

Ns/m2k

W/m K Pr

4184 0.000567 0.6420 3.694 4184 0.000766 0.6191 5.1744184 0.000564 0.6424 3.677 4184 0.000754 0.6201 5.0864184 0.000566 0.6422 3.686 4184 0.000766 0.6191 5.1744184 0.000567 0.6420 3.694 4184 0.000742 0.6212 5.0004184 0.000574 0.6409 3.749 4184 0.000750 0.6205 5.0574184 0.000573 0.6411 3.739 4184 0.000742 0.6212 5.0004184 0.000584 0.6395 3.823 4184 0.000742 0.6212 5.0004184 0.000579 0.6402 3.785 4184 0.000742 0.6212 5.0004184 0.000580 0.6400 3.795 4184 0.000742 0.6212 5.000


FPSHOT COLD

CpBtu/lb

lb/ft h

kBtu/(h ft °F) Pr Cp

Btu/lb

lb/ft hk

Btu/(h ft °F) Pr

1 1.371 0.3578 3.833 1 1.852 0.3711 4.9901 1.365 0.3584 3.810 1 1.824 0.3713 4.9111 1.368 0.3578 3.825 1 1.852 0.3712 4.9881 1.371 0.3590 3.819 1 1.796 0.3711 4.8391 1.389 0.3586 3.873 1 1.814 0.3705 4.8971 1.386 0.3590 3.861 1 1.796 0.3706 4.8461 1.413 0.3590 3.937 1 1.796 0.3697 4.8581 1.401 0.3590 3.903 1 1.796 0.3701 4.8531 1.404 0.3590 3.911 1 1.796 0.3700 4.854

Heat transfer coefficient, overall Heat transfer coefficients:ID/OD = D1/D2= 0.735

Heat transfer coefficients MKS Dirt FactorHOT COLD Overall Clean Overall Dirtyhi hio ho UC UD RD

W/(m2 K) m2K/W4078 2998 483.2 416.12 16.44 0.05844088 3005 487.2 419.26 1.47 0.67784083 3001 483.2 416.19 97.44 0.00794078 2998 423.4 371.02 33.24 0.02744049 2977 421.1 368.91 35.87 0.02524054 2980 423.4 370.75 11.34 0.08554011 2948 344.9 308.75 47.64 0.01784030 2962 344.9 308.91 45.74 0.01864025 2959 344.9 308.87 21.36 0.0436

Heat transfer coefficients FPS Dirt FactorHOT COLD Overall Clean Overall Dirtyhi hio ho UC UD RD

Btu/(h ft2 °F) (h ft2 °F)/Btu701 515 87.2 74.56 2.90 0.3320703 517 87.8 75.08 0.26 3.8451702 516 87.2 74.59 17.16 0.0449703 516 76.2 66.42 5.85 0.1558698 513 75.8 66.02 6.32 0.1432699 514 76.1 66.32 2.00 0.4858693 509 61.9 55.20 8.39 0.1011696 511 62.0 55.27 8.05 0.1061695 511 62.0 55.25 3.76 0.2477

The values of hi and ho were calculated by formula 20 in which the characteristic diameter D was D1 for inner pipe and De for outer pipe. The value of hio and UC were calculated by formula 24 and 25 whereas values of UD were already calculated. The approximation of (/W) = 1, made in equation 20, is done because water is incompressible in the short temperature range.


Result:The mean value of dirt factor RD calculated when water was flowing co-current in the double pipe heat exchanger is found to be:

RD = 0.1069 m2K/WRD = 0.6068 (h ft2 °F)/Btu

Verification:1 m2K/W = 5.678 263 (h ft2 °F)/Btu (from conversion factor 13)

The value of RD FPS calculated by converting the value of RD MKS is found to be:RD CONVERTED = 0.1069 x 5.678 263 = 0.6070 (h ft2 °F)/Btu which is very close to the value of RD calculated [0.6068 (h ft2 °F)/Btu]. This shows that the calculation in the experiment has been consistent.



To determine the dirt factor of double-pipe heat exchanger when cooling water is flowing counter-current

Formulae:1. Approach 12. Approach 2

3.

4.

5.

6. Range 17. Range 28.9.10.11.12.

13.

14. DQ Kern Process Heat Transfer page 105

15. (Area of cylinder formula)


17.

18.

19.

Sieder–Tate equation for turbulent flow DQ Kern Process Heat Transfer page 103 equation 6.2 & Coulson & Richardson’s Chemical Engineering volume 1 page 369

20.

Prandl Number

21. ( in Poise)

Correlation for viscosity of water in Poise (P) for in Kelvin table 6, page 683 Coulson and Richardson Chemical Engineering, Volume 1, Fifth Edition


22.

(Rearranged formula for in Ns/m2 for T in Celsius)

23. where





Legend:T1 and T2 are called Approach. THI, THO, TCI and TCO are the temperature at the hot inflow and outflow, cold inflow and outflow respectively.TCBM and THBM are the bulk mean temperature of cold and hot streamsTHOT = Temperature decrease of hot fluid TCOLD = Temperature increase of cold fluidTLMTD = Log mean temperature differenceCW, CP = heat capacity of water = 4.184 J/kg = 1 Btu/lb

= heat flow rates for heat loss, hot and cold water respectively = mass flow rate with subscripts for hot and cold water= pressure reading on the meter for the hot fluid in psi (lb/in2) or kg/cm2

AI, AO = Area of cross section of inner pipe and outer pipe/annulus respectivelyAIS = Internal Surface area of the pipe = Density of water taken as 1g/cc =1000kg/m3= 62.382 lb/ft3

D1 and D2 are the inner and outer diameter of inner pipe respectivelyD3 and D4 are the inner and outer diameter of outer pipe respectivelyDe is the equivalent diameter used for calculating Reynolds Number and heat transfer coefficient for hot fluid flow in the annulus v = Fluid velocity k = Thermal conductivity Re = Reynolds Numberh = Heat transfer coefficient or film coefficient (subscript “i" for inner coefficient, “o” for outer and “io” for inner biased on outer diameter)G = Mass flow rate per unit area (proportional to P’)UC = Clean Overall heat transfer coefficient UD = Dirty Overall heat transfer coefficientRD = Dirt Factor or resistance to heat flow in heat exchangers due to scalingD in Re and h is called characteristic diameter which is De for outer and D1 for inner pipe


Conversion factors between MKS and FPSLength: 1 in = 2.54 cm 1 ft = 0.3048 m (1)Area: 1 in2= 6.451 6 cm2 1 ft2= 0.0929 m2 (2)Volume: 1 ft3 = 28 316.85 dm3 (3)Mass: 1 lb = 453.9237 g (4)Viscosity dynamic: 1 dyn s/cm2 (poise P) = 0.1 Ns/m2 or Pa s (5)

1 lbm/ (ft h) = 4.133 789x10–4 Ns/m2 (6)1 lbm / (ft s) = 1.488 164 Ns/m2 (7)10 Poise P = 1 Pa. s = 1 Ns/m2 (8)1 cP (centi poise) = 1 mNs/m2 (9)

Velocity: 1 ft/s = 0.3048 m/s (10)Fluid velocity: 1 ml/s = 0.127133 ft3/h = 3.5315 x10–3 ft3/s (11)Thermal Conductivity: 1 Btu/ (h ft °F) = 1.730 735 W/ (m K) (12)Heat transfer Coefficient: 1 Btu/ (h ft2 °F) = 5.678 263 W/ (m2 K) (13)Pressure: 1 Psi (lb/in2) = 0.07035831 kg/cm2 (14)

1 kg/cm2 = 14.213 Psi (15)Density: 1 g/cm3 = 62.382 lb/ft3 (16)

Temperature: (17)

K = °C + 273.15 (18)

Table 1–4, page 1–4 to 1–10 Perry’s Chemical Engineer’s Handbook

Observations:Pipe Symbol cm in ft m

Outer pipe

Outer diameter D4 4.84 1.906 0.159 0.0484

Inner diameter D3 4.10 1.616 0.135 0.0410

Inner Pipe

Outer diameter D2 2.09 0.823 0.069 0.0209

Inner diameter D1 1.54 0.605 0.050 0.0154

Equivalent diameter De 5.966 2.349 0.196 0.060Length L 560 220.472 18.373 5.60

Parameter cm2 in2 ft2 m2

AI 1.854 0.287 0.00200 1.85x10–4

AO 9.794 1.518 0.01054 9.79 x10–4

AIS 3677 570 3.958 0.368AI, AO, AIS, De were calculated by formulae 13, 14, 15, 16 respectively. The outer diameter of pipes was noted and standard thickness of schedule 40 pipes was subtracted to get inner diameter of the pipes. The inner pipe is called a ½ inch pipe and outer pipe is 1½ inch designation. The data for pipes can be obtained from Perry’s Chemical Engineer’s Handbook (7th edition) table 10–18 page 10–72, Plant Design and Economics for Chemical Engineers by Max S Peters (4th edition) table 13 page 888, Process Heat Transfer by Donald Q Kern table 11 page 844, Unit Operations for Chemical Engineers by McCabe Smith sixth edition appendix 3 page 1068.


Temperature for water streams (Celsius):Hot Cold THBM TCBM TCOLD THOT T1 T2 TLMTDInlet Outlet Inlet Outlet

42.00 41.00 32 35.5 41.5 33.8 3.5 1.0 6.50 9.00 7.6842.00 41.00 31.5 35 41.5 33.3 3.5 1.0 7.00 9.50 8.1942.00 41.00 31.5 35 41.5 33.3 3.5 1.0 7.00 9.50 8.1942.00 40.50 32 34 41.3 33.0 2.0 1.5 8.00 8.50 8.2541.50 40.00 32 34 40.8 33.0 2.0 1.5 7.50 8.00 7.7541.50 40.00 32 34 40.8 33.0 2.0 1.5 7.50 8.00 7.7540.50 39.50 32 34.5 40.0 33.3 2.5 1.0 6.00 7.50 6.7240.50 39.50 32 34.5 40.0 33.3 2.5 1.0 6.00 7.50 6.7240.00 39.00 32 34.5 39.5 33.3 2.5 1.0 5.50 7.00 6.22

Temperature for water streams (Fahrenheit):Hot Cold THBM TCBM TCOLD THOT T1 T2 TLMTDInlet Outlet Inlet Outlet

107.60 105.80 89.6 95.9 106.7 92.8 6.3 1.8 11.70 16.20 13.83107.60 105.80 88.7 95.0 106.7 91.9 6.3 1.8 12.60 17.10 14.74107.60 105.80 88.7 95.0 106.7 91.9 6.3 1.8 12.60 17.10 14.74107.60 104.90 89.6 93.2 106.3 91.4 3.6 2.7 14.40 15.30 14.85106.70 104.00 89.6 93.2 105.4 91.4 3.6 2.7 13.50 14.40 13.95106.70 104.00 89.6 93.2 105.4 91.4 3.6 2.7 13.50 14.40 13.95104.90 103.10 89.6 94.1 104.0 91.9 4.5 1.8 10.80 13.50 12.10104.90 103.10 89.6 94.1 104.0 91.9 4.5 1.8 10.80 13.50 12.10104.00 102.20 89.6 94.1 103.1 91.9 4.5 1.8 9.90 12.60 11.20

T1, T2, TCBM, THBM, TLMTD, THOT, T COLD calculated by formulae 1, 2, 3, 4, 5, 6 & 7 respectively. Temperature converted to Fahrenheit by conversion relation number 17. Note that the formula of T1 & T2 are different in co-current and counter current flow.

Flow Observation:

Hot ColdMKS FPS MKS FPS

P kg/cm2

mkg/s (ml/s)

mlb/s ft3/h

V ml

Time s

(ml/s)

mkg/s

mlb/s ft3/h

0.06 0.11122 111.22 0.245 14.14 1000 35.81 27.93 0.0279 0.1551 3.550.06 0.11122 111.22 0.245 14.14 1000 35.81 27.93 0.0279 0.1551 3.550.06 0.11122 111.22 0.245 14.14 1000 35.81 27.93 0.0279 0.1551 3.550.06 0.11122 111.22 0.245 14.14 1000 12.03 83.13 0.0831 0.1288 10.570.06 0.11122 111.22 0.245 14.14 1000 12.03 83.13 0.0831 0.1288 10.570.06 0.11122 111.22 0.245 14.14 1000 12.03 83.13 0.0831 0.1288 10.570.06 0.11122 111.22 0.245 14.14 1000 26.00 38.46 0.0385 0.0997 4.890.06 0.11122 111.22 0.245 14.14 1000 26.00 38.46 0.0385 0.0997 4.890.06 0.11122 111.22 0.245 14.14 1000 26.00 38.46 0.0385 0.0997 4.89

The values of m HOT, m COLD calculated by formulae 8 & 9 respectively. MKS values are converted to FPS by conversion relations 4 & 11.


Heat Loss Calculation:

MKSQ HOT Q COLD Q LOSS

m HOT

kg/s kJ/s m COLD

kg/s kJ/s kJ/s

0.11122 465.34 0.0279 408.94 56.410.11122 465.34 0.0279 408.94 56.410.11122 465.34 0.0279 408.94 56.410.11122 698.02 0.0831 695.59 2.420.11122 698.02 0.0831 695.59 2.420.11122 698.02 0.0831 695.59 2.420.11122 465.34 0.0385 402.31 63.040.11122 465.34 0.0385 402.31 63.040.11122 465.34 0.0385 402.31 63.04

FPSQ HOT Q COLD Q LOSS

m HOT

lb/s Btu/s Btu/h m COLD lb/s Btu/s Btu/h Btu/h

0.245 0.441 1587.72 0.0615 0.3876 1395.26 192.470.245 0.441 1587.72 0.0615 0.3876 1395.26 192.470.245 0.441 1587.72 0.0615 0.3876 1395.26 192.470.245 0.662 2381.58 0.1831 0.6593 2373.31 8.270.245 0.662 2381.58 0.1831 0.6593 2373.31 8.270.245 0.662 2381.58 0.1831 0.6593 2373.31 8.270.245 0.441 1587.72 0.0847 0.3813 1372.64 215.080.245 0.441 1587.72 0.0847 0.3813 1372.64 215.080.245 0.441 1587.72 0.0847 0.3813 1372.64 215.08

Q HOT, Q COLD & Q LOSS calculated by formula 10, 11 and 12 respectively.

Overall Dirty Heat Transfer Coefficient:

AIS = 0.368 m2 = 3.958 ft2

MKS FPSUD

W/m2 KUD

Btu/(h ft2 °F)19.97 3.5218.74 3.3018.74 3.300.80 0.140.85 0.150.85 0.15

25.50 4.4925.50 4.4927.56 4.85

UD is calculated by formula 26.


Thermal Conductivity and Viscosity DATA:MKS FPS

T Kelvin T Celsius k W/m K T Fahrenheit k Btu/(h ft °F)303 30 0.616 85.73 0.356 333 60 0.659 139.73 0.381

The equations for linear interpolation using the above data are:Equation Range

30–60°C86–140°F

This data was obtained from Coulson and Richardson’s Chemical Engineering, Volume 1, Fifth Edition page 346. Data for thermal conductivity can also be obtained from Process Heat transfer by D Q Kern Table 4 page 800 and in detail from Plant Design and Economics for Chemical Engineers by Max S Peter and Timmerhaus (table 4 Page 876). Equations for linear interpolation are used and developed to give a routine and simple correlation rather than interpolating between different values from the references.

The Viscosity can be correlated by formula 22 and can be converted to FPS using conversion relation 6.

The thermal conductivity and viscosity will be calculated at the bulk mean temperatures.

Calculation:Thermal Conductivity Viscosity

K HOT

k COLD

k HOT

kCOLD

HOT

COLD

W/(m K) Btu/(h ft °F) Ns/m2 lbm/ft h Ns/m2 lbm/ft h0.6327 0.6216 0.3592 0.3657 0.000636 1.539 0.000739 1.7870.6327 0.6209 0.3588 0.3657 0.000636 1.539 0.000746 1.8050.6327 0.6209 0.3588 0.3657 0.000636 1.539 0.000746 1.8050.6323 0.6205 0.3586 0.3655 0.000639 1.546 0.000750 1.8140.6316 0.6205 0.3586 0.3651 0.000645 1.560 0.000750 1.8140.6316 0.6205 0.3586 0.3651 0.000645 1.560 0.000750 1.8140.6305 0.6209 0.3588 0.3645 0.000654 1.582 0.000746 1.8050.6305 0.6209 0.3588 0.3645 0.000654 1.582 0.000746 1.8050.6298 0.6209 0.3588 0.3640 0.000660 1.597 0.000746 1.805

Fluid Velocity:MKS FPS

v HOT v COLD v HOT v COLDm/s ft/s ft/h ft/s ft/h

0.6 0.029 1.969 7086.7 0.0935 336.80.6 0.029 1.969 7086.7 0.0935 336.80.6 0.029 1.969 7086.7 0.0935 336.80.6 0.085 1.969 7086.7 0.2785 1002.50.6 0.085 1.969 7086.7 0.2785 1002.50.6 0.085 1.969 7086.7 0.2785 1002.50.6 0.039 1.969 7086.7 0.1288 463.80.6 0.039 1.969 7086.7 0.1288 463.80.6 0.039 1.969 7086.7 0.1288 463.8

Fluid Velocity is calculated by formula 17 and 18. Be careful in the units of volume and area! The units must match.


Reynolds Number:MKS

HOT COLD

kg/m3v

m/s

Ns/m2D1 m Re

kg/m3

vm/s

Ns/m2

Dem Re

1000 0.60 0.000636 0.015 14490 1000 0.029 0.000739 0.060 23031000 0.60 0.000636 0.015 14490 1000 0.029 0.000746 0.060 22801000 0.60 0.000636 0.015 14490 1000 0.029 0.000746 0.060 22801000 0.60 0.000639 0.015 14423 1000 0.085 0.000750 0.060 67521000 0.60 0.000645 0.015 14290 1000 0.085 0.000750 0.060 67521000 0.60 0.000645 0.015 14290 1000 0.085 0.000750 0.060 67521000 0.60 0.000654 0.015 14092 1000 0.039 0.000746 0.060 31401000 0.60 0.000654 0.015 14092 1000 0.039 0.000746 0.060 31401000 0.60 0.000660 0.015 13960 1000 0.039 0.000746 0.060 3140

FPSHOT COLD

lb/ft3

vft/h

lb/ft h

D1

ft Re

lb/ft3v

ft/h

lb/ft hDeft Re

62.382 7086.7 1.539 0.050 14479 62.382 336.8 1.787 0.196 230162.382 7086.7 1.539 0.050 14479 62.382 336.8 1.805 0.196 227862.382 7086.7 1.539 0.050 14479 62.382 336.8 1.805 0.196 227862.382 7086.7 1.546 0.050 14413 62.382 1002.5 1.814 0.196 674762.382 7086.7 1.560 0.050 14280 62.382 1002.5 1.814 0.196 674762.382 7086.7 1.560 0.050 14280 62.382 1002.5 1.814 0.196 674762.382 7086.7 1.582 0.050 14082 62.382 463.8 1.805 0.196 313862.382 7086.7 1.582 0.050 14082 62.382 463.8 1.805 0.196 313862.382 7086.7 1.597 0.050 13950 62.382 463.8 1.805 0.196 3138

Reynolds Number has been calculated by formula 23. The Reynolds number for MKS is very close to that of FPS this shows precision in calculation. The precision is lost because of recursive conversions and propagation of error. Reynolds Number is greater than 2100 showing that the flow is turbulent in both inner and outer tubes so that equation

Prandl Number:

MKSHOT COLD

CpJ/kg K

Ns/m2

kW/m K Pr Cp

J/kg K

Ns/m2k

W/m K Pr

4184 0.000636 0.6327 4.207 4184 0.000739 0.6216 4.9724184 0.000636 0.6327 4.207 4184 0.000746 0.6209 5.0284184 0.000636 0.6327 4.207 4184 0.000746 0.6209 5.0284184 0.000639 0.6323 4.229 4184 0.000750 0.6205 5.0574184 0.000645 0.6316 4.273 4184 0.000750 0.6205 5.0574184 0.000645 0.6316 4.273 4184 0.000750 0.6205 5.0574184 0.000654 0.6305 4.341 4184 0.000746 0.6209 5.0284184 0.000654 0.6305 4.341 4184 0.000746 0.6209 5.0284184 0.000660 0.6298 4.386 4184 0.000746 0.6209 5.028


FPSHOT COLD

CpBtu/lb

lb/ft h

kBtu/(h ft °F) Pr Cp

Btu/lb

lb/ft hk

Btu/(h ft °F) Pr

1 1.539 0.3592 4.284 1 1.787 0.3657 4.8861 1.539 0.3588 4.289 1 1.805 0.3657 4.9361 1.539 0.3588 4.289 1 1.805 0.3657 4.9361 1.546 0.3586 4.311 1 1.814 0.3655 4.9641 1.560 0.3586 4.351 1 1.814 0.3651 4.9691 1.560 0.3586 4.351 1 1.814 0.3651 4.9691 1.582 0.3588 4.410 1 1.805 0.3645 4.9531 1.582 0.3588 4.410 1 1.805 0.3645 4.9531 1.597 0.3588 4.451 1 1.805 0.3640 4.958

Heat transfer coefficient, overall Heat transfer coefficients:ID/OD = D1/D2= 0.735

Heat transfer coefficients MKS Dirt FactorHOT COLD Overall Clean Overall Dirtyhi hio ho UC UD RD

W/(m2 K) m2K/W3827 2813 235.0 216.93 19.97 0.04553827 2813 233.8 215.83 18.74 0.04873827 2813 233.8 215.83 18.74 0.04873818 2806 557.9 465.39 0.80 1.25063798 2792 557.9 464.99 0.85 1.17463798 2792 557.9 464.99 0.85 1.17463769 2771 302.0 272.31 25.50 0.03553769 2771 302.0 272.31 25.50 0.03553750 2756 302.0 272.17 27.56 0.0326

Heat transfer coefficients FPS Dirt FactorHOT COLD Overall Clean Overall Dirtyhi hio ho UC UD RD

Btu/(h ft2 °F) (h ft2 °F)/Btu666.0 489.6 41.9 38.58 3.52 0.2584665.5 489.2 41.7 38.41 3.30 0.2770665.5 489.2 41.7 38.41 3.30 0.2770663.8 487.9 99.5 82.64 0.14 7.0915660.9 485.8 99.4 82.53 0.15 6.6607660.9 485.8 99.4 82.53 0.15 6.6607656.9 482.9 53.7 48.35 4.49 0.2020656.9 482.9 53.7 48.35 4.49 0.2020654.0 480.7 53.7 48.29 4.85 0.1853

The values of hi and ho were calculated by formula 20 in which the characteristic diameter D was D1 for inner pipe and De for outer pipe. The value of hio and UC were calculated by formula 24 and 25 whereas values of UD were already calculated. The approximation of (/W) = 1, made in equation 20, is done because water is incompressible in the short temperature range.


Result:The mean value of dirt factor RD calculated when water was flowing counter-current in the double pipe heat exchanger is found to be:

RD = 0.4274 m2K/WRD = 2.4239 (h ft2 °F)/Btu

Verification:1 m2K/W = 5.678 263 (h ft2 °F)/Btu (from conversion factor 13)

The value of RD FPS calculated by converting the value of RD MKS is found to be:RD CONVERTED = 0.4274 x 5.678 263 = 2.4268 (h ft2 °F)/Btu which is very close to the value of RD calculated [2.4239 (h ft2 °F)/Btu]. This shows that the calculation in the experiment has been consistent.



To calculate and compare the heat losses of different insulationsFormulae:

1.

2.

3.4.

5.

6.

7.

8.

9. 30–60°C

10.

11.

12.

13.

14.

15.

Legend:THBM = Bulk mean temperature of hot water, THI, THO, TR are the temperature of inlet, outlet and the room. v HOT = fluid velocity of hot waterhi = internal film transfer coefficientk = thermal conductivity subscript “I" for insulation and “P” for pipeQP and QI are the heat losses through pipe and insulations.AIS = Internal surface area is the viscosityr1, r2, r3, r3’, are the inner, outer radius of pipe, and radius of glass wool and rock wool respectively. RT is the thermal resistances in K/W


Thermal Conductivity Data:Material k [Btu /(h ft °F)] k [W/(m K)]Steel Pipe 26.00 45.00Glass Wool 0.024 0.042Rock Wool 0.033 0.057

Data for thermal conductivity of Glass Wool and Steel Pipe was obtained from Coulson and Richardson Chemical Engineering Volume 1, table 9.1, page 346 and the thermal conductivity for Rock Wool was obtained from Example 2.5 page 19 Process Heat Transfer by DQ Kern.

Units Basis: MKS system will be usedPipe Symbol cm m Length

Insulation

Rock wooldiameter D3

” 9.27 0.0927 2.95 m

Glass wooldiameter D3 8.4 0.084 2.74 m

Inner Pipe

Outer diameter D2 3.34 0.0334

2.95 mInner diameter D1 2.64 0.0264

Area Parameter cm2 m2

AI 5.47 0.000547AIS 2446.67 0.2447

AI, AIS calculated by formula 6 and 7. The given pipes are of standard (schedule 40) 1-inch designation pipes.

Room Temperature: TR = 30°C

Pipe V ml T sec ml/sec State Temperatures

°C Mean

GlassWool

280 17 16.47Inlet 60.00 61.00 62.00 61.00

Outlet 58.00 57.00 58.50 57.83

570 17 33.53Inlet 62.00 62.00 61.50 61.83

Outlet 58.50 58.50 59.00 58.67

420 8 52.50Inlet 62.00 61.50 61.00 61.50

Outlet 58.50 59.50 59.50 59.17

Rock Wool

250 65 3.85Inlet 61.50 61.00 60.50 61.00

Outlet 48.50 49.00 49.50 49.00

265 14 18.93Inlet 60.00 60.50 61.00 60.50

Outlet 49.50 49.00 50.50 49.67

430 16 26.88Inlet 60.50 60.50 60.00 60.33

Outlet 52.50 54.00 55.00 53.83

BarePipe

235 38 6.18Inlet 59.00 59.00 58.50 58.83

Outlet 32.00 32.50 32.50 32.33

300 17 17.65Inlet 58.50 58.50 58.50 58.50

Outlet 34.50 41.00 46.00 40.50

570 20 28.50Inlet 58.50 58.00 58.00 58.17

Outlet 49.00 52.00 54.00 51.67


Material V ml/s T Inlet (mean)

T Outlet (mean)

T Bulk Mean T1 T2 LMTD

GlassWool

16.47 61.00 57.83 59.42 31.00 27.83 29.3933.53 61.83 58.67 60.25 31.83 28.67 30.2252.50 61.50 59.17 60.33 31.50 29.17 30.32

RockWool

3.85 61.00 49.00 55.00 31.00 19.00 24.5118.93 60.50 49.67 55.08 30.50 19.67 24.6926.88 60.33 53.83 57.08 30.33 23.83 26.95

Bare Pipe

6.18 58.83 32.33 45.58 28.83 2.33 10.5417.65 58.50 40.50 49.50 28.50 10.50 18.0328.50 58.17 51.67 54.92 28.17 21.67 24.77

Thermal resistances:Material RT K/W

Glass Wool 1.1979Rock Wool 0.9643

Bare Pipe 0.000282

Thermal resistances are calculated by formula 11 & 12Viscosity, Velocity, Thermal Conductivity and Film Coefficient:

Material THBMViscosity

Ns/m2K

W/(m K)Velocity

m/shi

W/(m2K)RT FILM

K/W

GlassWool

59.42 0.000472 0.6584 0.030 370.01 0.011060.25 0.000466 0.6596 0.061 658.05 0.006260.33 0.000465 0.6597 0.096 942.66 0.0043

RockWool

55.00 0.000505 0.6520 0.007 111.22 0.036755.08 0.000504 0.6522 0.035 398.28 0.010357.08 0.000489 0.6550 0.049 536.54 0.0076

Bare Pipe

45.58 0.000591 0.6385 0.011 149.04 0.027449.50 0.000553 0.6441 0.032 357.92 0.011454.92 0.000506 0.6519 0.052 551.74 0.0074

Viscosity, Velocity, Thermal Conductivity & Film Coefficient were calculated by formulae 9, 2, 10 & 11 respectively. Be careful in calculating fluid velocity as the units of volume flow rate should be in m3/s and internal area AI in m2. The film coefficient was calculated by formula 10 on the assumption that fluid flowing in all pipes at all temperature was turbulent. The Film resistance was calculated by formula 13. Heat Loss through Pipes:

Material Q LOSS (W) Mean Q LOSS (W)

Glass Wool24.304

24.870(1.45% of 1714.259)25.094

25.213

Rock Wool24.481

25.844(1.51% of 1714.259)25.326

27.724

Bare Pipe380.4

1714.2591540.63221.8

The heat losses were calculated by formulae 14 and 15.

Result:The results show 98.55% decrease in heat loss for glass wool and 98.49% decrease in heat loss for rock wool.



To determine the heat flow rate through different types of bricksData:

Brick Lengthcm

Widthcm

Thickness Area kW/(m K)cm m cm2 m2

Detrolite 19 9 4 0.04 171 0.0171 0.7Alumina 22 10 6 0.06 220 0.022 0.2

Fire Brick 21 10 5 0.05 210 0.021 1.4

Formula:

Legend:TH and TC are the temperature of hot face and cold face respectivelyx = Thickness of brickk = Thermal conductivity of brickA = Area exposed to heatQ = Heat flow across the brick

Observation:

Brick FurnaceTemperature

TemperatureHot face

TemperatureCold Face Q (W) Mean

Q (W)

Detrolite

100106 38 20.349

35.677

105 39 19.751102 40 18.554

200114 42 21.546156 44 33.516178 48 38.903

300255 61 58.055253 66 55.960252 70 54.464

Alumina

100110 35 8.250

16.353

108 36 7.920107 35 7.920

200196 48 16.280200 47 16.830204 47 17.270

300234 49 20.350283 50 25.630295 52 26.730

Fire Brick

100102 37 38.220

74.088

107 37 41.160104 37 39.396

200164 42 71.736167 41 74.088169 41 75.264

300243 63 105.840247 60 109.956248 59 111.132

Result:


The average heat flow across the bricks is as follows:

Detrolite: 35.677 WAlumina: 16.353 WFire-Brick: 74.088 W



To calculate the loading factor of cooling tower

Formula:1. T= TWI – TWO

2.

3.

4.

Page 584 equation 17.53 Process Heat Transfer By D Q KernLegend:T = temperature difference of water inlet and outlet TWI & TWO are the water inlet and outlet temperature respectivelyQ = heat lost by hot water per unit area of flow of cooling towerA = Internal ground area of the towerLO = flow rate of makeup water needed per unit area of flow of cooling tower TO = Room Temperature CW = Heat capacity of water taken as 1 Btu/ (lb °F)H1 and H2 are the enthalpy of entering and exiting airX1 and X2 are the values of humidity of exiting and entering airm W = mass flow rate, = density of water =1000kg/m3 =62.382 lb/ft3

Given:Internal ground area of cooling tower or area of flow = 715 in2 = 4.9653 ft2

Observations:Room temperature = 30°C = 86°F

ml/sec

Air Inlet temperature

Air Outlet temperature Water Temperature

DryBulb

WetBulb

DryBulb

WetBulb Inlet Outlet

116.729.5 28.5 29 27 61 4630.5 27.5 29 27 55 45.530 27 29 26 49 40.5

87.030 26.9 28.75 25.5 36 35

29.5 26.5 28 25 37 32.529 26.5 28 26 38 31.5

88.530 26.5 29 26 43.5 2930 29 29 26 43.75 2930 27 29 26 44 29

Correlations for humidity and enthalpy (75–90°F):1. (Btu/lb dry air)2. (lb water / lb air)

Here TWB and TDB are the wet bulb temperatures in degrees Fahrenheit. These correlations are developed using interpolation schemes from psychrometric charts. They have an expected error of less than 2% and can be verified by data from psychrometric chart. Range of application is 75–87°F for TDB.


Basis: FPS system is used as psychrometric chart has data in FPS notation

FPS values:

ft3/hr

Air Inlet temperature

Air Outlet temperature Water Temperature

DryBulb

WetBulb

DryBulb

WetBulb Inlet Outlet

7.2085.10 83.30 84.20 80.60 141.80 114.8086.90 81.50 84.20 80.60 131.00 113.9086.00 80.60 84.20 78.80 120.20 104.90

7.5086.00 80.42 83.75 77.90 96.80 95.0085.10 79.70 82.40 77.00 98.60 90.5084.20 79.70 82.40 78.80 100.40 88.70

6.6986.00 79.70 84.20 78.80 110.30 84.2086.00 84.20 84.20 78.80 110.75 84.2086.00 80.60 84.20 78.80 111.20 84.20

1 ml/s = 0.127133 ft3/h

mlb/hr

QBtu/(h ft2)

H1

Btu/lb dry air

H2

Btu/lb dry air

X1

lb water/lb dry air

X2

lb water/lb dry air

Loading Factor

LO

lb/(h ft2)

448.92440.9 47.4 44.5 0.02446 0.02207 2.1471545.9 45.5 44.5 0.02231 0.02207 0.3951383.2 44.5 42.6 0.02166 0.02034 0.993

467.9169.6 44.3 41.6 0.02148 0.01958 0.126763.3 43.6 40.6 0.02100 0.01903 0.5481102.6 43.6 42.6 0.02121 0.02076 0.532

702.12192.8 43.6 42.6 0.02079 0.02034 1.0572230.6 48.4 42.6 0.02511 0.02034 1.9622268.4 44.5 42.6 0.02166 0.02034 1.628

The value of Q is calculated by formula 2 and that of Lo by formula 4.

Result:The mean loading factor for the cooling tower is determined to be:

1.043 lb water /h ft2



To calculate the number of turns of coil in a helical coil agitator

Formula:

1.

2.3.4.

5.

6.

7.

8.

9.

10.

11. 30–60°C

12.

Chilton-Drew-Jebens correlation for outside film coefficient for agitated vessel in Coulson and Richardson’s Chemical Engineering Volume 1 page 497

13.

Chilton-Drew-Jebens correlation for outside film coefficient for agitated vessel in Process heat transfer by D Q Kern, page 722 equation 20.4

14.

Dittus Boelter equation for cooling water equation 9.54 page 367 Coulson and Richardson’s Chemical Engineering Volume 1 fifth edition (other editions have different page number and equation number)

15.

Jeschke Correction Factor page 426 Coulson and Richardson’s Chemical Engineering Volume 1 fifth edition & page 721 D Q Kern Process Heat Transfer

16.

17.


18.

19.

20.

Legend:AN = Surface area per turn of a helix by considering one turn of helix as a torus. The formula is for area of a torus with radius D2/2 rotated at a distance L from a fixed line or the axis of rotation. Look for formula at page 3-11 Perry’s Chemical Engineer’s Handbook, 7th Edition. W = Viscosity of water kW = thermal conductivity of water L = Paddle length, D1 = Inner diameter of helical tube DV = Inner diameter of tank. TWI and TWO are water inlet and outlet temperatures. For calculating the coefficients, the value of characteristic diameter will be D1 for inner coefficient and DV for external coefficients.Data given for 28° API oil at 80°C: = 4.04x10-4

lb/(ft/s) =0.0006012 Ns/m2

= 53.19 lb/ft3 = 852.6 kg/m3

k = 0.08 Btu/ (h ft °F) = 0.1385 W/ (m K)CP = 0.509 Btu/ (lb °F) = 2129.7 J/ (kg K)For apparatus:Inner diameter of coil = D1 = 0.018046 ft =0.00550 mOuter diameter of coil = D2 = 0.024476 ft = 0.00746 mLength of Paddle = L = 0.2875 ft = 0.08763 m Inner diameter of tank DV = 0.9625 ft = 0.29337 mOuter diameter of tank = DE = 1.000 ft = 0.3048 mNumber of Rotations = N = 720 rpm =12 rpsAI = 0.2376 cm2 (by formula 7)AN = 0.0129 m2 /turn (by formula 9)ID /OD = D1/D2 = 0.7373 (for use in formula 8)Observations:

ml/sec

Temperature Celsius MassKg/s

QLOSS

(W)Water Oil T WBM T1 T2 TLMTD TIn Out28.4 26 35 66 30.50 31.00 40.00 35.31 9 0.0284 1069.4328.4 26 34 59 30.00 25.00 33.00 28.82 8 0.0284 950.6028.4 26 31 54 28.50 23.00 28.00 25.42 5 0.0284 594.1322.2 26 40 76 33.00 36.00 50.00 42.62 14 0.0222 1300.3922.2 26 39 68 32.50 29.00 42.00 35.10 13 0.0222 1207.5022.2 26 38 62 32.00 24.00 36.00 29.60 12 0.0222 1114.6214.2 26 50 74 38.00 24.00 48.00 34.62 24 0.0142 1425.9114.2 26 44 68 35.00 24.00 42.00 32.16 18 0.0142 1069.4314.2 26 41 62 33.50 21.00 36.00 27.83 15 0.0142 891.19Mass is calculated by multiplying the volume by density. QLOSS is calculated by formula 17. TWBM, T1, T2, T, TLMTD are calculated by formula 1, 2, 3, 4, 5 respectively.

Calculated Physical properties of water:Velocity

m/sViscosity

Ns/m2k

W/(m K)hi pipe

W/(m2 K)hi coil

W/(m2 K)hio

W/(m2 K)1.1952 0.000790 0.6169 6177 7534 5555


1.1952 0.000798 0.6162 6142 7491 55231.1952 0.000824 0.6140 67036 7363 54280.9343 0.000750 0.6205 5216 6362 46910.9343 0.000758 0.6198 5187 6327 46650.9343 0.000766 0.6191 5159 6292 46390.5976 0.000679 0.6277 3850 4696 34620.5976 0.000720 0.6234 3729 4548 33530.5976 0.000742 0.6212 3669 4475 3299

The Jeschke correction factor has a value of 1.22. The values are calculated by using formulae 6, 10, 11, 14, 15 & 16 respectively. The value of CP taken is 4184 J/kg K, density = 1000 kg/m3, characteristic diameter = D1 = 0.0550 m. The value of viscosity and thermal conductivity are calculated at bulk mean temperature. The value of ho by using the values provided in formula number 12 is found to be:

ho = 1281 W/(m2 K)

UC

W/(m2 K)UD

W/(m2 K)Am2

AN

m2/turn Mean

1040.827 259.759 0.117 0.0129 9.0

9.9

1039.714 259.690 0.127 0.0129 9.81036.310 259.477 0.090 0.0129 7.01006.112 257.541 0.118 0.0129 9.21004.914 257.463 0.134 0.0129 10.41003.706 257.383 0.146 0.0129 11.3934.951 252.620 0.163 0.0129 12.6926.834 252.023 0.132 0.0129 10.2922.630 251.711 0.127 0.0129 9.9

The value of overall clean heat transfer and dirty heat transfer coefficient is calculated by formula 16 and 17. The value of area required for cooling is calculated by formula 19 and the number of turns by formula 20.

Result: The number of turns of cooling coils comes out to be 10.

Date post:	25-Nov-2014
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Heat Transfer Manual

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