Heat and Mass Transfer in Tray Drying

Transcription

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. 10/8/2014 LOUISIANA STATE UNIVERSITY 1

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

3 The Drying Process [1] Moisture Content Settling period Constant rate Falling rate Time [1] Air Drying available via [Retrieved ] 10/8/2014 LOUISIANA STATE UNIVERSITY 3

4 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

5 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

6 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

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 [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

8 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

9 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

10 Mass Transfer Theoretical Calculations Sh L = k cl D AB = 0.664Re L 1/2 Sc 1/3 [5] k c = 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

11 Mass Transfer Expectations k c = 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

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 [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

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 10/8/2014 LOUISIANA STATE UNIVERSITY 13

14 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

15 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

16 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

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

18 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

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

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

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

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

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

24 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

25 References [1] Air Drying available via [Retrieved ] [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 [Retrieved ] [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

26 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

27 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 Averages SLOPE Tray Ave /8/2014 LOUISIANA STATE UNIVERSITY 27

28 Appendix I Raw Data for High_High Continued Run 1 (1.45 m/s) 2500 W W Heat of Vaporization (J/g) 2435 T wet (F/C) T dry (F/C) Vapor pressure water at 26.8C (mmhg) T infinity (average of constant drying) Antoine's Vapor pressure water at 26.8C (Pascals) T surface (average of constant drying) Ca inf (kg mois/m^3) Cas (kg mois/m^3)) P/RT Specific Heat, cp (J/kg K) Density of air dynamic viscosity (Pa s) Linear Interpolation change in mass (g/min) k conductivity (W/m K) constant drying region starts at 20 minutes Slope of line kinematic viscosity air (m^2/s) Prandtl number Reynolds number Diffusivity (m2/s) Scmidt number Appendix Contents 10/8/2014 LOUISIANA STATE UNIVERSITY 28

29 Appendix I Raw Data for High_High Continued Appendix Contents Heat and Mass Transfer Coefficients Theoretical Experimental Chilton-Colburn Analogy j D Theoretical Experimental j H Reynolds/Nusselt/Sherwood h k Re Nu Sh Theoretical Experimental /8/2014 LOUISIANA STATE UNIVERSITY 29

30 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 Averages SLOPE Tray Ave /8/2014 LOUISIANA STATE UNIVERSITY 30

31 Appendix I Raw Data for Low_High Continued W Heat of Vaporization (J/g) 2409 T wet (F/C) T dry (F/C) Vapor pressure water at 33.2C (mmhg) T infinity (average of constant drying) Antoine's Vapor pressure water at 33.2C (Pascals) T surface (average of constant drying) Ca inf (kg mois/m^3) Cas (kg mois/m^3)) P/RT Specific Heat, cp (J/kg K) Density of air Linear dynamic viscosity (Pa s) Interpolation change in mass (g/min) k conductivity (W/m K) constant drying region starts at 20 minutes Slope of line kinematic viscosity air (m^2/s) Prandtl number Reynolds number Diffusivity (m2/s) Scmidt number Appendix Contents 10/8/2014 LOUISIANA STATE UNIVERSITY 31

32 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 Theoretical Experimental Chilton-Colburn Analogy j D Theoretical Experimental j H 10/8/2014 LOUISIANA STATE UNIVERSITY 32

33 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 Averages SLOPE Tray Ave /8/2014 LOUISIANA STATE UNIVERSITY 33

34 Appendix I Raw Data for Low_Low Continued W Heat of Vaporization (J/g) 2441 T wet (F/C) T dry (F/C) Vapor pressure water at 24C (mmhg) T infinity (average of constant drying) Antoine's Vapor pressure water at 24C (Pascals) T surface (average of constant drying) Ca inf (kg mois/m^3) Cas (kg mois/m^3)) P/RT Specific Heat, cp (J/kg K) Density of air Linear dynamic viscosity (Pa s) Interpolation change in mass (g/min) k conductivity (W/m K) constant drying region starts at 20 minutes Slope of line kinematic viscosity air (m^2/s) Prandtl number Reynolds number Diffusivity (m2/s) Scmidt number Appendix Contents 10/8/2014 LOUISIANA STATE UNIVERSITY 34

35 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 Theoretica Experimen Chilton-Colburn Analogy j H j D Theoretica Experimen /8/2014 LOUISIANA STATE UNIVERSITY 35

36 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 Averages SLOPE Tray Ave /8/2014 LOUISIANA STATE UNIVERSITY 36

37 Appendix I Raw Data for High_Low Continued W Heat of Vaporization (J/g) 2445 T wet (F/C) T dry (F/C) Vapor pressure water at 24C (mmhg) T infinity (average of constant drying) Antoine's Vapor pressure water at 24C (Pascals) T surface (average of constant drying) Ca inf (kg mois/m^3) Cas (kg mois/m^3)) P/RT Specific Heat, cp (J/kg K) Density of air Linear dynamic viscosity (Pa s) Interpolation change in mass (g/min) k conductivity (W/m K) constant drying region starts at 20 minutes Slope of line kinematic viscosity air (m^2/s) Prandtl number Reynolds number Diffusivity (m2/s) Scmidt number Appendix Contents 10/8/2014 LOUISIANA STATE UNIVERSITY 37

38 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 Theoretical Experimental Chilton-Colburn Analogy j D Theoretical Experimental j H 10/8/2014 LOUISIANA STATE UNIVERSITY 38

39 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

40 Heat DOE Appendix III Design of Experiment Appendix Contents Velocity Heat Run Y1 Y2 Divisor Result Effects AVE V H VH Mass DOE Velocity Heat Run Y1 Y2 Divisor Result Effects AVE V H VH 10/8/2014 LOUISIANA STATE UNIVERSITY 40

41 Appendix IV Values of Constants Appendix Contents R= in 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= B= C= Area of tray= m 2 Length= m 2 Width= m 2 10/8/2014 LOUISIANA STATE UNIVERSITY 41

42 Appendix V Values of Heat/Mass Transfer Coefficients Appendix Contents High_High Heat and Mass Transfer Coefficients h k Theoretical Experimental Low_Low Heat and Mass Transfer Coefficients h k Theoretical Experimental Low_High Heat and Mass Transfer Coefficients h k Theoretical Experimental High_Low Heat and Mass Transfer Coefficients h k Theoretical Experimental /8/2014 LOUISIANA STATE UNIVERSITY 42

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