Heat and Mass Transfer in Tray Drying - Tiffany Robinson · Heat and Mass Transfer in Tray Drying...
Transcript of Heat and Mass Transfer in Tray Drying - Tiffany Robinson · Heat and Mass Transfer in Tray Drying...
10/8/2014 LOUISIANA STATE UNIVERSITY 1
Heat and Mass Transfer in Tray Drying
Group # 11: Sami Marchand (GL), Chase Kairdolf (WR),
Tiffany Robinson (OR)
Instructor: Dr. Wetzel
Objective: The objective of this experiment is to exhibit how
accurately the theory of heat and mass transfer matches the
practice of drying used coffee grounds in a tray dryer.
Heat Transfer
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Mass Transfer
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The Drying Process
Settling period
Constant rate
Falling rate
Time
Moisture
Content
[1] “Air Drying” available via http://www.nzifst.org.nz/unitoperations/drying5.htm [Retrieved 9-22-2014.]
[1]
• The exchange of energy between a surface
and an adjacent fluid. [5]
Forced convection- an external agent forces a
fluid to flow past a solid surface
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Heat Transfer
[5] Welty, J. R., C. E. Wicks, and R. E. Wilson, “Fundamentals of Momentum, Heat, and Mass Transfer.” Fifth
ed., Wiley, (2008).
Heat Transfer Theoretical Calculations
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[5] Welty, J. R., C. E. Wicks, and R. E. Wilson, “Fundamentals of Momentum, Heat, and Mass Transfer.” Fifth
ed., Wiley, (2008).
ℎ =𝑘
𝐿0.664𝑅𝑒1/2𝑃𝑟1/3
𝑁𝑢𝐿 =ℎ𝐿
𝑘= 0.664𝑅𝑒𝐿
1/2𝑃𝑟1/3 [5]
Heat Transfer Expectations
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ℎ =𝑘
𝐿0.664𝑅𝑒1/2𝑃𝑟1/3
[5]
[5] Welty, J. R., C. E. Wicks, and R. E. Wilson, “Fundamentals of Momentum, Heat, and Mass Transfer.” Fifth
ed., Wiley, (2008).
Heat Transfer Equation
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ℎ =𝑞
2𝐴Δ𝑇
ℎ= convective heat transfer coefficient in 𝑊
𝑚2𝐾
𝑞= rate of heat transfer in 𝑊
𝐴= heat transfer area in 𝑚2
Δ𝑇= temperature gradient between surface and fluid in 𝐾
[5] Welty, J. R., C. E. Wicks, and R. E. Wilson, “Fundamentals of Momentum, Heat, and Mass Transfer.” Fifth
ed., Wiley, (2008).
[5]
Heat Transfer Equation
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ℎ =𝑞
2𝐴Δ𝑇
ℎ= convective heat transfer coefficient in 𝑊
𝑚2𝐾
𝑞= rate of heat transfer in 𝑊
𝐴= heat transfer area in 𝑚2
Δ𝑇= temperature gradient between surface and fluid in 𝐾
𝑞 =Δ𝑚𝛌𝑣
𝑡
Δ𝑚= change in mass in 𝑔
𝛌𝑣= heat of vaporization in 𝐽
𝑔
𝑡= time in 𝑠
[5]
[5] Welty, J. R., C. E. Wicks, and R. E. Wilson, “Fundamentals of Momentum, Heat, and Mass Transfer.” Fifth
ed., Wiley, (2008).
• Convective mass transfer is the transport of
material between boundary surface and a
moving fluid. [5]
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Mass Transfer
[5] Welty, J. R., C. E. Wicks, and R. E. Wilson, “Fundamentals of Momentum, Heat, and Mass Transfer.” Fifth
ed., Wiley, (2008).
Mass Transfer Theoretical Calculations
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𝑘𝑐 = 0.664𝐷𝐴𝐵𝐿
𝑅𝑒1/2𝑆𝑐1/3
[5]
𝑆ℎ𝐿 =𝑘𝑐𝐿
𝐷𝐴𝐵= 0.664𝑅𝑒𝐿
1/2𝑆𝑐1/3
[5] Welty, J. R., C. E. Wicks, and R. E. Wilson, “Fundamentals of Momentum, Heat, and Mass Transfer.” Fifth
ed., Wiley, (2008).
𝑘𝑐 = 0.664𝐷𝐴𝐵𝐿
𝑅𝑒1/2𝑆𝑐1/3
Mass Transfer Expectations
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[5]
[5] Welty, J. R., C. E. Wicks, and R. E. Wilson, “Fundamentals of Momentum, Heat, and Mass Transfer.” Fifth
ed., Wiley, (2008).
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𝑘𝑐 =𝑚
𝐴 𝐶𝐴𝑆 − 𝐶𝐴∞ 𝑘𝑐= convective mass transfer coefficient in
𝑚
𝑠
𝑚 = rate of mass transfer in 𝑘𝑔 𝐻2𝑂
𝑠
𝐴= mass transfer area in 𝑚2
𝐶𝐴𝑆= concentration of water at the surface in 𝑘𝑔 𝐻2𝑂
𝑚3
𝐶𝐴∞= concentration of water in the bulk stream in 𝑘𝑔 𝐻2𝑂
𝑚3
[5]
Mass Transfer Equation
[5] Welty, J. R., C. E. Wicks, and R. E. Wilson, “Fundamentals of Momentum, Heat, and Mass Transfer.” Fifth
ed., Wiley, (2008).
Mass Transfer Equation
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𝑘𝑐 =𝑚
𝐴 𝐶𝐴𝑆 − 𝐶𝐴∞ 𝑘𝑐= convective mass transfer coefficient in
𝑚
𝑠
𝑚 = rate of mass transfer in 𝑘𝑔 𝐻2𝑂
𝑠
𝐴= mass transfer area in 𝑚2
𝐶𝐴𝑆= concentration of water at the surface in 𝑘𝑔 𝐻2𝑂
𝑚3
𝐶𝐴∞= concentration of water in the bulk stream in 𝑘𝑔 𝐻2𝑂
𝑚3
[5]
𝐶𝐴𝑆 =𝑃𝐴𝑅𝑇
𝑃𝐴= vapor pressure of water in 𝑃𝑎
𝑅= gas constant in 𝑃𝑎∗𝑚3
𝑘𝑔 𝐻2𝑂∗𝐾
𝑇= temperature of water in 𝐾
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𝑘𝑐 =𝑚
𝐴 𝐶𝐴𝑆 − 𝐶𝐴∞ 𝑘𝑐= convective mass transfer coefficient in
𝑚
𝑠
𝑚 = rate of mass transfer in 𝑘𝑔 𝐻2𝑂
𝑠
𝐴= mass transfer area in 𝑚2
𝐶𝐴𝑆= concentration of water at the surface in 𝑘𝑔 𝐻2𝑂
𝑚3
𝐶𝐴∞= concentration of water in the bulk stream in 𝑘𝑔 𝐻2𝑂
𝑚3
[5]
𝐶𝐴𝑆 =𝑃𝐴𝑅𝑇
𝐶𝐴∞ = ℎ𝐴𝜌𝑎𝑖𝑟
ℎ𝐴= moisture content in 𝑘𝑔 𝐻2𝑂
𝑘𝑔 𝑑𝑟𝑦 𝑎𝑖𝑟
𝜌𝑎𝑖𝑟= density of air in 𝑘𝑔 𝑑𝑟𝑦 𝑎𝑖𝑟
𝑚3
𝑃𝐴= vapor pressure of water in 𝑃𝑎
𝑅= gas constant in 𝑃𝑎∗𝑚3
𝑘𝑔 𝐻2𝑂∗𝐾
𝑇= temperature of water in 𝐾
[2]
[2] Felder, R. M., and R. W. Rousseau, “Elementary Principles of Chemical Processes,” Third ed., Wiley,
(2005).
Mass Transfer Equation
Experiment
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Velocity 0.5
𝑚
𝑠 (low)
1.45 𝑚
𝑠 (high)
Heat Supply 1000 𝑊 (low)
2500 𝑊 (high)
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Heat Transfer Results
• Experimental results 1.6
times larger than theory
• Uncertainty propagation
ranged from 35-55%
• Temperature not constant
over tray
Heat Transfer Results
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At a 95% confidence interval Nusselt and
Reynolds do not correlate
Flat Plate Correlation Experimental
Log(Nu) = -1.57 + 1.06*Log(Re)
Flat Plate Correlation Theoretical
Log(Nu) = -0.226 + 0.499*Log(Re)
Mass Transfer Results
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• Experimental results 1.2
times larger than theory
• Uncertainty propagation
ranged from 33-51%
• Temperature not constant
over tray
Mass Transfer Results
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At a 95% confidence interval Sherwood and
Reynolds do not correlate
Flat Plate Correlation Experimental
Log(Sh) = -0.858 + 0.737*Log(Re)
Flat Plate Correlation Theoretical
Log(Sh) = -0.190 + 0.4867*Log(Re)
Confidence Intervals
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Experimental
Theoretical
Corrections for Inconsistencies
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A B C D E
Top View
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jD = mass transfer
jH = heat transfer
Effect of Parameters
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Heat Transfer Mass Transfer
All parameters are significant
Conclusion The practice of drying used coffee grounds in a
convective tray dryer does not accurately adhere to the
theory of heat and mass transfer based on our results.
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References [1] “Air Drying” available via http://www.nzifst.org.nz/unitoperations/drying5.htm
[Retrieved 9-22-2014.]
[2] Felder, R. M., and R. W. Rousseau, “Elementary Principles of Chemical
Processes,” Third ed., Wiley, (2005).
[3] McCabe, W. L., J. C. Smith, and P. Harriott, “Unit Operations of Chemical
Engineering.” Seventh ed., McGraw-Hill, (2005).
[4] “The Performance of a Tray Dryer” available via http://www-
unix.ecs.umass.edu/~rlaurenc/che401/stations/dryer/drying.html [Retrieved 9-29-
2014.]
[5] Welty, J. R., C. E. Wicks, and R. E. Wilson, “Fundamentals of Momentum, Heat,
and Mass Transfer.” Fifth ed., Wiley, (2008).
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Appendix Contents • Appendix I
– Raw data (H/H, L/H, L/L, H/L)
• Appendix II
– Dimensionless groups
• Appendix III
– Design of experiment
• Appendix IV
– Values of constants
• Appendix V
– Values of heat/mass transfer coefficients
• Appendix VI
– Side by side confidence plots
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Appendix I Raw Data for High_High
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High/High 1.45 m/s 2500W
Time (min) Mass (g) T1(°C) T2(°C) T3(°C) T4(°C) T ∞ (°C) T wet bulb (°F)T dry bulb (°F)
0 1518.1 24.8 24.7 23.8 24.8 23.3
5 1512.3
10 1506.2 26.1 26.3 24.8 27.2
15 1501.1
20 1495.3 26.4 26.2 25.4 27.3
25 1489.7
30 1483.6 25.6 26.4 25.4 27.3 27.4 68 76
35 1477.4
40 1470.8 27.4 27.5 25.9 27.7
45 1465.6
50 1459.7 28.4 26.7 25.6 27
55 1453.4
60 1447.3 28.9 27.2 25.5 27.8 27.5
65 1440.3
70 1434.2 28.1 26.3 26.1 27.5 29
75 1428.9
55 66.4 Averages 27.46667 26.71667 25.65 27.43333 26.8 68 76
SLOPE 1.207273 Tray Ave. 26.81667
Appendix Contents
Appendix I Raw Data for High_High Continued
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Run 1 (1.45 m/s) 2500 W 1.45 2500 W Heat of Vaporization (J/g) 2435 1046.99
T wet (F/C) 68 20.00 80 1048.3
T dry (F/C) 76 24.44 85 1045.5
Vapor pressure water at 26.8C (mmHg) 26.45398932 T infinity (average of constant drying) 27.96666667 82.34
Vapor pressure water at 26.8C (Pascals) 3526.90851 T surface (average of constant drying) 26.81666667 80.27
Ca inf (kg mois/m^3) 0.01560 0.0133
Cas (kg mois/m^3)) 0.02546 P/RT Specific Heat, cp (J/kg K) 1006.356
300 1006.3
Density of air 1.173 301.1166667 320 1007.3
300 1.1769 dynamic viscosity (Pa s) 0.00001851576
320 1.1032 300 0.000018464
320 0.000019391
change in mass (g/min) 1.207272727 k conductivity (W/m K) 0.0263262625
constant drying region starts at 20 minutes 300 0.02624
320 0.027785
kinematic viscosity air (m^2/s) 0.00001579441 Prandtl number 0.708
300 0.000015689
320 0.000017577
301.1166667
Reynolds number 35344.776
Diffusivity (m2/s) 0.00002573818
Scmidt number 0.614
Linear Interpolation
Slope of line
Antoine's
Appendix Contents
Appendix I Raw Data for High_High Continued
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h k Re Nu Sh
7.60724 0.007092 Theoretical 35345 111.2496 106.0814
194.1814 0.0186 Experimental 35345 2839.743 278.2268
jH jD
Theoretical 0.00353 0.003532
Experimental 0.090117 0.009263
Chilton-Colburn Analogy
Heat and Mass Transfer Coefficients
Theoretical
Experimental
Reynolds/Nusselt/Sherwood
Appendix Contents
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Appendix I Raw Data for Low_High
Low/High 0.5m/s 2500W
Time (min) Mass (g) T1(°C) T2(°C) T3(°C) T4(°C) T ∞ (°C) T wet bulb (°F)T dry bulb (°F)
0 1428.9
5 1425.1 30.6 30.7 29.8 30.1 35.6 71 77
10 1421.4
15 1417.7 32.5 34 32 32.4 40.4
20 1413.3
25 1409.2 32.4 33.9 31.5 32.2 40.6
30 1405.5
35 1401.2 32.2 33.7 33 32.4 41.1 70 78
40 1396.4
45 1391.9 34.1 34.8 33.7 33.9 39.7
50 1387.3
55 1383.4 33.4 34.4 33.2 33.6 38.6
60 1377.4 68.5 77.5
65 1372.9 33.7 33.4 31.9 32.7 39
70 1368.1
75 1363.5 33.4 34.5 32.5 33.4 37.5
55 49.8 Averages 33.16 34.04 32.66 32.96 39.28571429 69.83333 77.5
SLOPE 0.905455 Tray Ave. 33.205
Appendix Contents
Appendix I Raw Data for Low_High Continued
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0.5 2500 W Heat of Vaporization (J/g) 2409
T wet (F/C) 69.83333333 21.02 80 1048.3
T dry (F/C) 77.5 25.28 85 1045.5
Vapor pressure water at 33.2C (mmHg) 38.1701561 T infinity (average of constant drying) 39.41666667
Vapor pressure water at 33.2C (Pascals) 5088.935614 T surface (average of constant drying) 33.205
Ca inf (kg mois/m^3) 0.01583 0.014
Cas (kg mois/m^3)) 0.03526 P/RT Specific Heat, cp (J/kg K) 1006.928
300 1006.3
Density of air 1.1306 312.5666667 320 1007.3
300 1.1769 dynamic viscosity (Pa s) 0.00001904647
320 1.1032 300 0.000018464
320 0.000019391
change in mass (g/min) 0.905454545 k conductivity (W/m K) 0.0272107750
constant drying region starts at 20 minutes 300 0.02624
320 0.027785
kinematic viscosity air (m^2/s) 0.00001687529 Prandtl number 0.705
300 0.000015689
320 0.000017577
312.5666667
Reynolds number 11407.209
Diffusivity (m2/s) 0.00002573818
Scmidt number 0.656
Antoine's
Linear
Interpolation
Slope of line
Appendix Contents
Appendix I Raw Data for Low_High Continued
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h k Re Nu Sh
4.460621 0.004119 Theoretical 11407 63.11246 61.60968
26.66517 0.007076 Experimental 11407 377.2804 105.8516
jH jD
Theoretical 0.006206 0.006217
Experimental 0.037101 0.010681
Theoretical
Experimental
Chilton-Colburn Analogy
Heat and Mass Transfer Coefficients Reynolds/Nusselt/Sherwood
Appendix Contents
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Appendix I Raw Data for Low_Low
Low/Low 0.5m/s 1000W
Time (min) Mass (g) T1(°C) T2(°C) T3(°C) T4(°C) T ∞ (°C) T wet bulb (°F)T dry bulb (°F)
0 1059.4 22.5 22.2 21.9 21.9 24.3
5 1057.6 69.8 77
10 1055.6 24.9 23.4 22.7 22.1 25.4
15 1053
20 1051.1 24.1 23.6 23 23.3 25.6
25 1049.1
30 1046.9 25.4 23.7 23.2 23.9 25.4
35 1044.5
40 1042.5 24.7 23.8 23.4 23.8 25.6
45 1040.5
50 1038.2 25.8 24.2 23.4 24 25.3
55 1036.1
60 1033.8 25.2 24.6 23.8 24.5 25.4
65 1031.3
70 1030.1 23.9 23.9 23.3 24.1 25.2
75 1028.6
55 22.5 Averages 24.85 23.96667 23.35 23.93333 25.275 69.8 77
SLOPE 0.409091 Tray Ave. 24.025
Appendix Contents
Appendix I Raw Data for Low_Low Continued
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0.5 1000W Heat of Vaporization (J/g) 2441
T wet (F/C) 69.8 21.00 75 1051.1
T dry (F/C) 77 25.00 80 1048.3
Vapor pressure water at 24C (mmHg) 22.409968 T infinity (average of constant drying) 25.41666667
Vapor pressure water at 24C (Pascals) 2987.75001 T surface (average of constant drying) 24.025
Ca inf (kg mois/m^3) 0.01680 0.0142
Cas (kg mois/m^3)) 0.02168 P/RT Specific Heat, cp (J/kg K) 1006.257
280 1005.7
Density of air 1.1830 298.5666667 300 1006.3
280 1.2614 dynamic viscosity (Pa s) 0.00001839884
300 1.1769 280 0.000017503
300 0.000018468
change in mass (g/min) 0.409090909 k conductivity (W/m K) 0.0261275550
constant drying region starts at 20 minutes 280 0.024671
300 0.02624
kinematic viscosity air (m^2/s) 0.00001555907 Prandtl number 0.709
280 0.000013876
300 0.000015689
298.5666667
Reynolds number 12372.206
Diffusivity (m2/s) 0.00002587639
Scmidt number 0.601
Antoine's
Linear
Interpolation
Slope of line
Appendix Contents
Appendix I Raw Data for Low_Low Continued
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h k Re Nu Sh
4.468515 0.00419 Theoretical 12372 65.84536 62.33782
54.50665 0.01274 Experimental 12372 803.1773 189.5438
jH jD
Theoretical0.005967 0.00597
Experimental0.07279 0.018151
Theoretical
Experimental
Chilton-Colburn Analogy
Heat and Mass Transfer Coefficients Reynolds/Nusselt/Sherwood
Appendix Contents
Appendix I Raw Data for High_Low
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High/Low 1.45 m/s 1000W
Time (min) Mass (g) T1(°C) T2(°C) T3(°C) T4(°C) T ∞ (°C) T wet bulb (°F)T dry bulb (°F)
0 1117.4
5 1111.8 23.4 22.9 22.6 23.4 24
10 1106.8
15 1103.9 22.4 22.7 22.3 22.8 24
20 1098.8 68 75.5
25 1095.1 22.5 22.2 21.8 22.5 24.1
30 1091
35 1087.2 22.8 22.7 21.7 22.5 23.9
40 1084.4
45 1080.6 23 22 21.5 22 23.8
50 1076.9
55 1073.3 22.1 21.9 21.4 21.9 23.9
60 1071.3
65 1067.7 22.9 22.2 21.5 22.1 23.9
70 1063.1
75 1059.4 22.5 22.2 21.9 21.9 24.3
55 39.4 Averages 22.66 22.2 21.58 22.2 23.94285714 68 75.5
SLOPE 0.716364 Tray Ave. 22.16
Appendix Contents
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Appendix I Raw Data for High_Low Continued
1.45 1000W Heat of Vaporization (J/g) 2445
T wet (F/C) 68 20.00 75 1051.1
T dry (F/C) 75.5 24.17 80 1048.3
Vapor pressure water at 24C (mmHg) 20.6368645 T infinity (average of constant drying) 23.98333333
Vapor pressure water at 24C (Pascals) 2751.355652 T surface (average of constant drying) 22.16
Ca inf (kg mois/m^3) 0.01546 0.013
Cas (kg mois/m^3)) 0.02003 P/RT Specific Heat, cp (J/kg K) 1006.214
280 1005.7
Density of air 1.1890 297.1333333 300 1006.3
280 1.2614 dynamic viscosity (Pa s) 0.00001832968
300 1.1769 280 0.000017503
300 0.000018468
change in mass (g/min) 0.716363636 k conductivity (W/m K) 0.0260151100
constant drying region starts at 20 minutes 280 0.024671
300 0.02624
kinematic viscosity air (m^2/s) 0.00001542914 Prandtl number 0.709
280 0.000013876
300 0.000015689
297.1333333
Reynolds number 36181.545
Diffusivity (m2/s) 0.00002587639
Scmidt number 0.596
Antoine's
Linear
Interpolation
Slope of line
Appendix Contents
Appendix I Raw Data for High_Low Continued
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h k Re Nu Sh
7.609973 0.007145 Theoretical 36182 112.6207 106.306
72.95075 0.023816 Experimental 36182 1079.605 354.3418
jH jD
Theoretical 0.003488 0.003491
Experimental 0.033435 0.011636
Heat and Mass Transfer Coefficients Reynolds/Nusselt/Sherwood
Theoretical
Experimental
Chilton-Colburn Analogy
Appendix Contents
Appendix II Dimensionless Groups
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𝑁𝑢 =𝐿ℎ
𝑘
𝑃𝑟 =𝑐𝑝𝜇
𝑘
𝑗𝐷 =𝑘𝑐𝑣∞
𝑆𝑐 2/3 𝑗𝐻 =ℎ
𝜌𝑣∞𝑐𝑝𝑃𝑟 2/3
𝑆ℎ = 𝑘𝑐𝐿
𝐷𝐴𝐵
𝑆𝑐 = 𝜇
𝐷𝐴𝐵𝜌
𝑅𝑒 =𝐷𝑉𝜌
𝜇
Appendix Contents
Appendix III Design of Experiment
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Heat DOE
Mass DOE
Velocity Heat Run Y1 Y2 Divisor Result Effects
- - 54.50665005 127.4574 348.3039 4 87.07598 AVE
+ - 72.95075269 220.8465 185.9603 2 92.98014 V
- + 26.66517397 18.4441 93.38913 2 46.69456 H
+ + 194.1813581 167.5162 149.0721 2 74.53604 VH
Velocity Heat Run Y1 Y2 Divisor Result Effects
- - 0.012739505 0.036555 0.062232 4 0.015558 AVE
+ - 0.023815814 0.025677 0.0226 2 0.0113 V
- + 0.007076433 0.011076 -0.01088 2 -0.00544 H
+ + 0.018600131 0.011524 0.000447 2 0.000224 VH
Appendix Contents
Appendix IV Values of Constants
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𝑅= 0.46189 in 𝑃𝑎∗𝑚3
𝑘𝑔 𝐻2𝑂∗𝐾
𝑙𝑜𝑔10 𝑃∗ = A −𝐵
𝑇 + 𝐶
Antoine Equation Constants
𝐴= 8.10765
𝐵= 1750.286
𝐶=235.000
Area of tray= 0.109725 𝑚2
Length= 0.385 𝑚2
Width= 0.285 𝑚2
8.314𝑃𝑎 ∗ 𝑚3
𝑚𝑜𝑙 ∗ 𝐾∗1
18
𝑚𝑜𝑙
𝑘𝑔 𝐻2𝑂
Appendix Contents
Appendix V Values of Heat/Mass Transfer Coefficients
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h k
7.607240069 0.007091797
194.1813581 0.018600131
High_High
Heat and Mass Transfer Coefficients
Theoretical
Experimental
h k
4.460620819 0.004118756
26.66517397 0.007076433
Low_High
Heat and Mass Transfer Coefficients
Theoretical
Experimental
h k
4.468515156 0.004189813
54.50665005 0.012739505
Low_Low
Experimental
Heat and Mass Transfer Coefficients
Theoretical
h k
7.609973067 0.007144973
72.95075269 0.023815814
High_Low
Heat and Mass Transfer Coefficients
Theoretical
Experimental
Appendix Contents
Appendix VI Side by Side of Confidence Intervals
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Mass Transfer Heat Transfer
Appendix Contents