Heat and Mass Transfer in Tray Drying

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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. 10/8/2014 LOUISIANA STATE UNIVERSITY 1

Heat Transfer Mass Transfer 10/8/2014 LOUISIANA STATE UNIVERSITY 2

The Drying Process [1] Moisture Content Settling period Constant rate Falling rate Time [1] Air Drying available via http://www.nzifst.org.nz/unitoperations/drying5.htm [Retrieved 9-22-2014.] 10/8/2014 LOUISIANA STATE UNIVERSITY 3

Heat Transfer 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 [5] Welty, J. R., C. E. Wicks, and R. E. Wilson, Fundamentals of Momentum, Heat, and Mass Transfer. Fifth ed., Wiley, (2008). 10/8/2014 LOUISIANA STATE UNIVERSITY 4

Heat Transfer Theoretical Calculations Nu L = hl k = 0.664Re L 1/2 Pr 1/3 [5] h = k L 0.664Re1/2 Pr 1/3 [5] Welty, J. R., C. E. Wicks, and R. E. Wilson, Fundamentals of Momentum, Heat, and Mass Transfer. Fifth ed., Wiley, (2008). 10/8/2014 LOUISIANA STATE UNIVERSITY 5

Heat Transfer Expectations h = k L 0.664Re1/2 Pr 1/3 [5] [5] Welty, J. R., C. E. Wicks, and R. E. Wilson, Fundamentals of Momentum, Heat, and Mass Transfer. Fifth ed., Wiley, (2008). 10/8/2014 LOUISIANA STATE UNIVERSITY 6

Heat Transfer Equation h = q 2AΔT [5] h= convective heat transfer coefficient in W m 2 K q= rate of heat transfer in W A= heat transfer area in m 2 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). 10/8/2014 LOUISIANA STATE UNIVERSITY 7

Heat Transfer Equation h = q 2AΔT [5] h= convective heat transfer coefficient in W m 2 K q= rate of heat transfer in W A= heat transfer area in m 2 ΔT= temperature gradient between surface and fluid in K q = Δmλ v t Δm= change in mass in g λ v = heat of vaporization in J g t= time in s [5] Welty, J. R., C. E. Wicks, and R. E. Wilson, Fundamentals of Momentum, Heat, and Mass Transfer. Fifth ed., Wiley, (2008). 10/8/2014 LOUISIANA STATE UNIVERSITY 8

Mass Transfer Convective mass transfer is the transport of material between boundary surface and a moving fluid. [5] [5] Welty, J. R., C. E. Wicks, and R. E. Wilson, Fundamentals of Momentum, Heat, and Mass Transfer. Fifth ed., Wiley, (2008). 10/8/2014 LOUISIANA STATE UNIVERSITY 9

Mass Transfer Theoretical Calculations Sh L = k cl D AB = 0.664Re L 1/2 Sc 1/3 [5] k c = 0.664 D AB L Re1/2 Sc 1/3 [5] Welty, J. R., C. E. Wicks, and R. E. Wilson, Fundamentals of Momentum, Heat, and Mass Transfer. Fifth ed., Wiley, (2008). 10/8/2014 LOUISIANA STATE UNIVERSITY 10

Mass Transfer Expectations k c = 0.664 D AB L Re1/2 Sc 1/3 [5] [5] Welty, J. R., C. E. Wicks, and R. E. Wilson, Fundamentals of Momentum, Heat, and Mass Transfer. Fifth ed., Wiley, (2008). 10/8/2014 LOUISIANA STATE UNIVERSITY 11

Mass Transfer Equation k c = m A C AS C A [5] k c = convective mass transfer coefficient in m= rate of mass transfer in kg H 2O s A= mass transfer area in m 2 C AS = concentration of water at the surface in kg H 2O m 3 C A = concentration of water in the bulk stream in kg H 2O m 3 m s [5] Welty, J. R., C. E. Wicks, and R. E. Wilson, Fundamentals of Momentum, Heat, and Mass Transfer. Fifth ed., Wiley, (2008). 10/8/2014 LOUISIANA STATE UNIVERSITY 12

Mass Transfer Equation k c = m A C AS C A [5] k c = convective mass transfer coefficient in m= rate of mass transfer in kg H 2O s A= mass transfer area in m 2 C AS = concentration of water at the surface in kg H 2O m 3 C A = concentration of water in the bulk stream in kg H 2O m 3 m s C AS = P A RT P A = vapor pressure of water in Pa Pa m 3 R= gas constant in kg H 2 O K T= temperature of water in K 10/8/2014 LOUISIANA STATE UNIVERSITY 13

Mass Transfer Equation k c = m A C AS C A [5] k c = convective mass transfer coefficient in m= rate of mass transfer in kg H 2O s A= mass transfer area in m 2 C AS = concentration of water at the surface in kg H 2O m 3 C A = concentration of water in the bulk stream in kg H 2O m 3 m s C AS = P A RT P A = vapor pressure of water in Pa Pa m 3 R= gas constant in kg H 2 O K T= temperature of water in K C A = h A ρ air h A = moisture content in ρ air = density of air in kg H 2 O kg dry air kg dry air m 3 [2] [2] Felder, R. M., and R. W. Rousseau, Elementary Principles of Chemical Processes, Third ed., Wiley, (2005). 10/8/2014 LOUISIANA STATE UNIVERSITY 14

Experiment Velocity 0.5 m s (low) Heat Supply 1000 W (low) 2500 W (high) 1.45 m s (high) 10/8/2014 LOUISIANA STATE UNIVERSITY 15

Heat Transfer Results Experimental results 1.6 times larger than theory Temperature not constant over tray Uncertainty propagation ranged from 35-55% 10/8/2014 LOUISIANA STATE UNIVERSITY 16

Heat Transfer Results Flat Plate Correlation Experimental Flat Plate Correlation Theoretical Log(Nu) = -1.57 + 1.06*Log(Re) Log(Nu) = -0.226 + 0.499*Log(Re) At a 95% confidence interval Nusselt and Reynolds do not correlate 10/8/2014 LOUISIANA STATE UNIVERSITY 17

Mass Transfer Results Experimental results 1.2 times larger than theory Temperature not constant over tray Uncertainty propagation ranged from 33-51% 10/8/2014 LOUISIANA STATE UNIVERSITY 18

Mass Transfer Results Flat Plate Correlation Experimental Flat Plate Correlation Theoretical Log(Sh) = -0.858 + 0.737*Log(Re) Log(Sh) = -0.190 + 0.4867*Log(Re) At a 95% confidence interval Sherwood and Reynolds do not correlate 10/8/2014 LOUISIANA STATE UNIVERSITY 19

Confidence Intervals Experimental Theoretical 10/8/2014 LOUISIANA STATE UNIVERSITY 20

Corrections for Inconsistencies Top View A B C D E 10/8/2014 LOUISIANA STATE UNIVERSITY 21

j D = mass transfer j H = heat transfer 10/8/2014 LOUISIANA STATE UNIVERSITY 22

Effect of Parameters Heat Transfer Mass Transfer All parameters are significant 10/8/2014 LOUISIANA STATE UNIVERSITY 23

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. 10/8/2014 LOUISIANA STATE UNIVERSITY 24

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://wwwunix.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). 10/8/2014 LOUISIANA STATE UNIVERSITY 25

Appendix I Appendix Contents 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 10/8/2014 LOUISIANA STATE UNIVERSITY 26

High/High 1.45 m/s 2500W Appendix I Raw Data for High_High Appendix Contents Time (min) Mass (g) T1( C) T2( C) T3( C) T4( C) T ( C) T wet bulbt dry bulb 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 10/8/2014 LOUISIANA STATE UNIVERSITY 27

Appendix I Raw Data for High_High Continued Run 1 (1.45 m/s) 2500 W 1.45 2500 W Heat of Vaporization (J/g) 2435 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 Antoine's Vapor pressure water at 26.8C (Pascals) 3526.90851 T surface (average of constant drying) 26.81666667 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 Linear Interpolation 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 Slope of line 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 Appendix Contents 10/8/2014 LOUISIANA STATE UNIVERSITY 28

Appendix I Raw Data for High_High Continued Appendix Contents Heat and Mass Transfer Coefficients Theoretical Experimental Chilton-Colburn Analogy j D Theoretical 0.00353 0.003532 Experimental 0.090117 0.009263 j H Reynolds/Nusselt/Sherwood 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 10/8/2014 LOUISIANA STATE UNIVERSITY 29

Low/High 0.5m/s 2500W Appendix I Raw Data for Low_High Appendix Contents Time (min) Mass (g) T1( C) T2( C) T3( C) T4( C) T ( C) T wet bulbt dry bulb 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 10/8/2014 LOUISIANA STATE UNIVERSITY 30

Appendix I Raw Data for Low_High Continued 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 Antoine's 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 Linear dynamic viscosity (Pa s) 0.00001904647 320 1.1032 Interpolation 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 Slope of line 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 Appendix Contents 10/8/2014 LOUISIANA STATE UNIVERSITY 31

Heat and Mass Transfer Coefficients Theoretical Experimental Appendix I Raw Data for Low_High Continued Appendix Contents Reynolds/Nusselt/Sherwood 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 Chilton-Colburn Analogy j D Theoretical 0.006206 0.006217 Experimental 0.037101 0.010681 j H 10/8/2014 LOUISIANA STATE UNIVERSITY 32

Low/Low 0.5m/s 1000W Appendix I Raw Data for Low_Low Appendix Contents Time (min) Mass (g) T1( C) T2( C) T3( C) T4( C) T ( C) T wet bulbt dry bulb 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 10/8/2014 LOUISIANA STATE UNIVERSITY 33

Appendix I Raw Data for Low_Low Continued 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 Antoine's 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 Linear dynamic viscosity (Pa s) 0.00001839884 300 1.1769 Interpolation 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 Slope of line 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 Appendix Contents 10/8/2014 LOUISIANA STATE UNIVERSITY 34

Heat and Mass Transfer Coefficients Theoretical Experimental Appendix I Raw Data for Low_Low Continued Appendix Contents Reynolds/Nusselt/Sherwood h k Re Nu Sh 4.468515 0.00419 Theoretica 12372 65.84536 62.33782 54.50665 0.01274 Experimen 12372 803.1773 189.5438 Chilton-Colburn Analogy j H j D Theoretica 0.005967 0.00597 Experimen 0.07279 0.018151 10/8/2014 LOUISIANA STATE UNIVERSITY 35

Appendix I Raw Data for High_Low Appendix Contents High/Low 1.45 m/s 1000W Time (min) Mass (g) T1( C) T2( C) T3( C) T4( C) T ( C) T wet bulbt dry bulb 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 10/8/2014 LOUISIANA STATE UNIVERSITY 36

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 Antoine's 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 Linear dynamic viscosity (Pa s) 0.00001832968 300 1.1769 Interpolation 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 Slope of line 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 Appendix Contents 10/8/2014 LOUISIANA STATE UNIVERSITY 37

Heat and Mass Transfer Coefficients Theoretical Experimental Appendix I Raw Data for High_Low Continued Appendix Contents Reynolds/Nusselt/Sherwood 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 Chilton-Colburn Analogy j D Theoretical 0.003488 0.003491 Experimental 0.033435 0.011636 j H 10/8/2014 LOUISIANA STATE UNIVERSITY 38

Appendix II Dimensionless Groups Appendix Contents j H = h ρv c p Pr 2/3 j D = k c v Sc 2/3 Nu = Lh k Pr = c pμ k Re = DVρ μ Sh = k cl D AB Sc = μ D AB ρ 10/8/2014 LOUISIANA STATE UNIVERSITY 39

Heat DOE Appendix III Design of Experiment Appendix Contents 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 Mass DOE 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 10/8/2014 LOUISIANA STATE UNIVERSITY 40

Appendix IV Values of Constants Appendix Contents R= 0.46189 in 8.314 Pa m 3 kg H 2 O K Pa m3 mol K 1 18 mol kg H 2 O log 10 P = A B T + C Antoine Equation Constants A= 8.10765 B= 1750.286 C=235.000 Area of tray= 0.109725 m 2 Length= 0.385 m 2 Width= 0.285 m 2 10/8/2014 LOUISIANA STATE UNIVERSITY 41

Appendix V Values of Heat/Mass Transfer Coefficients Appendix Contents High_High Heat and Mass Transfer Coefficients h k Theoretical 7.607240069 0.007091797 Experimental 194.1813581 0.018600131 Low_Low Heat and Mass Transfer Coefficients h k Theoretical 4.468515156 0.004189813 Experimental 54.50665005 0.012739505 Low_High Heat and Mass Transfer Coefficients h k Theoretical 4.460620819 0.004118756 Experimental 26.66517397 0.007076433 High_Low Heat and Mass Transfer Coefficients h k Theoretical 7.609973067 0.007144973 Experimental 72.95075269 0.023815814 10/8/2014 LOUISIANA STATE UNIVERSITY 42

Appendix VI Side by Side of Confidence Intervals Appendix Contents Mass Transfer Heat Transfer 10/8/2014 LOUISIANA STATE UNIVERSITY 43

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