Heat Transfer File Page 1 Heat Transfer Submitted by: Zeeshan Zaki Muzammil Ali Submitted to: Sir Adnan Index No. Detail Page 1. Dirt factor in double pipe heat exchanger (co current flow) 2 2. Dirt factor in double pipe heat exchanger (counter current flow) 11 3. Heat losses of insulation 20
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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
Heat Transfer FilePage 2
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)
Heat Transfer FilePage 3
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
24. DQ Kern Process Heat Transfer page 105 equation 6.5
25. DQ Kern Process Heat Transfer page 106 equation 6.7
26. DQ Kern Process Heat Transfer page 107 equation 6.11
27. DQ Kern Process Heat Transfer page 108 equation 6.13
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
Heat Transfer FilePage 4
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)
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.
Heat Transfer FilePage 5
Temperature for water streams (Celsius):Hot Cold THBM TCBM TCOLD THOT T1 T2 TLMTDInlet Outlet Inlet Outlet
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.
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.
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
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.
Heat Transfer FilePage 10
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:
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.
Heat Transfer FilePage 11
Experiment Number 2Object:
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)
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
Heat Transfer FilePage 12
22.
(Rearranged formula for in Ns/m2 for T in Celsius)
23. where
24. DQ Kern Process Heat Transfer page 105 equation 6.5
25. DQ Kern Process Heat Transfer page 106 equation 6.7
26. DQ Kern Process Heat Transfer page 107 equation 6.11
27. DQ Kern Process Heat Transfer page 108 equation 6.13
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
Heat Transfer FilePage 13
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)
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.
Heat Transfer FilePage 14
Temperature for water streams (Celsius):Hot Cold THBM TCBM TCOLD THOT T1 T2 TLMTDInlet Outlet Inlet Outlet
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.
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.
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
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.
Heat Transfer FilePage 19
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:
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.
Heat Transfer FilePage 20
Experiment Number 3Object:
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
Heat Transfer FilePage 21
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.
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.
Heat Transfer FilePage 23
Experiment Number 4Object:
To determine the heat flow rate through different types of bricksData:
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:
Heat Transfer FilePage 24
The average heat flow across the bricks is as follows:
Detrolite: 35.677 WAlumina: 16.353 WFire-Brick: 74.088 W
Heat Transfer FilePage 25
Experiment Number 5Object:
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
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.
Heat Transfer FilePage 26
Basis: FPS system is used as psychrometric chart has data in FPS notation
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
Heat Transfer FilePage 27
Experiment Number 6Object:
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.
Heat Transfer FilePage 28
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:
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:
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.