Contents1 Introduction 4

2 Methods 11

3 Results and Discussion 15

4 Appendices 214.1 Variable Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.2 Sample Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

1

List of Figures1 Falling Liquid Level in Tray . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Three Drying Regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Falling Drying Rate Regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Marble tray within oven . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Pyronmeter within oven . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Dried Marble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Drying experimental curve for trial 1 . . . . . . . . . . . . . . . . . . . . . . 188 Drying experimental curve for trial 2 . . . . . . . . . . . . . . . . . . . . . . 19

2

List of Tables1 Overall Weight Changes Through Drying . . . . . . . . . . . . . . . . . . . . 152 Average Theoretical Heat and Mass Transfer Coefficients . . . . . . . . . . . 153 Average Experimental Heat and Mass Transfer Coefficients . . . . . . . . . . 164 Drying Experiment Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Data Collected from First Trial (10 on Both Heat and Wind Settings) . . . . 256 Data Collected from Second Trial (10 Heat Setting 7 Wind Setting) . . . . . 267 First Trial Theoretical Parameters . . . . . . . . . . . . . . . . . . . . . . . . 288 Second Trial Theoretical Parameters . . . . . . . . . . . . . . . . . . . . . . 299 First Trial Experimental Parameters . . . . . . . . . . . . . . . . . . . . . . 3110 Second Trial Experimental Parameters . . . . . . . . . . . . . . . . . . . . . 32

3

1 Introduction

Drying is a separation process by phase creation and addition, with use of both an energy

and mass separating agent [1]. The need for drying in many chemical operations is directly

related to the common use of water within these operations; whether as an universal

solvent, convenient coolant, or a reactant. For this reason, water is generally present in

products at the end of numerous chemical processes and in many industries this water must

be removed to form a solid product. Drying is frequently employed in the food industry, as

the complete removal of moisture upon packaging prevents spoilage [2]. Even though drying

occurs spontaneously under normal conditions, the high industrial throughput of material

requires a faster separation process and therefore drying equipment is necessary. While the

exact specifications of equipment may vary, the common goal is to increase the rate of mass

transfer of a liquid species in a solid-liquid mixture to the surrounding vapor. In order for

this mass transfer to occur, the vapor pressure of the liquid must be greater than its partial

pressure in the vapor [1]. If water is being removed from a mixture, the surrounding air

should therefore possess as low humidity as possible. To ensure this water concentration

gradient between the mixture and air, heat is added, which simultaneously lowers the

humidity of the surrounding gas through temperature-dependent saturation limits and

increases the vapor pressure of the liquid in mixture through heat transfer. However, if the

warm air is stagnant above the mixture, then the gas would become saturated and decrease

the rate of drying. Therefore, a fan is often used to provide a constant supply of fresh air

and effectively increase the rate of mass transfer through convection. While these

conditions (high temperature, low humidity, and high air flow rate) are perhaps the most

important factors in increasing mass transfer rate, additional conditions such as internal

diffusion, capillary flow, equilibrium moisture content, and heat sensitivity must also be

considered [1]. Optimizing all of these conditions often cannot be completed attempted

through simulation alone; it requires many empirical tests on pilot-scale plants.

4

Figure 1: These three panels shows how the effect of liquid diffusion through the solid can greatlyeffect the rate of drying. This diffusion is difficult to model, and is often not explicitly included [1].

Because simulating all the facets of drying exactly is difficult, a simplistic model of drying

which is still useful can be used. This model breaks down the entire operation into three

regimes.

1. The mixture warming to the ambient temperature, a film of water remains at the

mixture-air interface.

2. The mixture reaches a steady-state temperature, motivating water to the surface of

the mixture. Vaporization is the limiting step in the separation process.

3. Nearly all of the starting water in the mixture has evaporated. The process becomes

5

dependent on the rate of diffusion of the water through the almost dry solid, causing

the overall rate of drying to decrease.

Figure 2: The three regimes in terms of the moisture content versus time. The first regime occursfrom point A to B, the second regime from B to D, and the third regime from D to infinity [1].

The second regime has a constant time versus moisture content slope, and is most easily

modeled mathematically. Two equations have been developed, one in terms of mass

transfer (equation 1) and the other heat transfer (equation 2).

Rc =h (Tg − Tw)

∆Hvap

(1)

Rc = Mwk (Hs −Ha) (2)

The variables for these equations are defined in the appendix. Measurements taken during

the experimental process provide values for both temperatures and humidities, and the

enthalpy of vaporization may be calculated through a DIPPR relationship [3]. However,

this still leaves three unknowns: flux, mass transfer coefficient, and heat transfer

6

coefficient. The latter value may be estimated through an empirical relationship for a flat

plate and parallel flow.

h = 0.0204G0.8 (3)

Empirical relations also exist for the estimation of the mass transfer coefficient. Based on a

Reynolds number calculation, laminar flow was assumed to exist within the drier. This

determination and the flat plate geometry of the mixture led to equation 4, below.

0.664Re1/2Sc1/3 = Sh =kL

D(4)

All of the calculations discussed so far have been mostly theoretical in nature because they

use an empirically-derived relationships that do not take into account the actual rate of

drying in this experiment. To remove these theoretical aspects, the actual rate of drying

can be calculated, as shown in equation 5 below.

Rc =∆mol

∆t× A(5)

This experimental rate of drying may then be substituted into equations 2 and 1. The

experimental heat and mass transfer coefficients may then be determined through algebra.

This evaluation is important because it allows for a comparison between the theoretical

and actual results. If there is a large difference between these results, then secondary

effects, such as capillary action, are likely influencing the rate of drying.

While it is not possible to provide a good comparison of theoretical and empirical in the

other two drying regimes, it is possible to incorporate this data into a total expected time

7

to dry calculation. This calculation begins by analyzing the differential equation which

most generally models the drying process, and thereby governs the shape of figure 6. This

equation is shown below in equation 6.

R = −ms

A

dX

dt(6)

To transform this rate based equation into a value of time, integration must take place, as

shown in equation 7 below.

∫dt = −ms

A

∫dX

R(7)

To continue, an assumption is made that the first regime is very small (less than interval of

measurement, or 4 minutes) and therefore does not need to be considered. To determine

the time for the constant rate period, or the second regime, the rate term may be pulled

out of the integral leading to equation below.

tsecond regime =ms (Xo −Xc)

ARc

(8)

To determine the time of the third regime, an assumption that the rate fell linear to the

moisture content was made, as shown in equation 9. The substitution of the linear

equation into equation 7 then leads to a possible integration and the final result as shown

in equation 10, below.

R =RcX

Xc(9)

8

tthird regime =msXc

ARc

ln

(Xc

Xf

)(10)

The motivation for this assumption was that it was simple and widely used. An illustration

of the linear form is shown in figure 6, along with the two other common assumptions,

parabolic and complex.

Figure 3: The three graphs show the most commonly assumed drying rates for the third regime of afalling drying rate. From top to bottom are linear, parabolic, and complex drying assumptions. For

this analysis the linear rate was chosen as it best modeled the data [1].

9

By adding the assumed zero time of the first regime to the calculated times of the second

and third regimes a total drying time is achieved, as shown below in equation 11.

tT =ms

ARc

((Xo −Xc) + Xcln

(Xc

Xf

))(11)

This equation does not provide a strict comparison between theory and empirical

measurements, but it still provides a method to see if the first assumption of linear drying

versus moisture is true. Furthermore, this analysis combined with the previous calculation

of transfer coefficients enables a robust comparison between the ideal conditions and

controlling factors in theory compared to the actual empirical results.

10

2 Methods

The drying experiment involved preparing a mixture of water and dry marble, and

observing the properties of this mixture as it sits in a hot, convective environment. Before

the drying commences, the rectangular tray (10.75in. x 7.25in.) which holds the marble,

was weighed. This initial measurement allows for the marble to be directly weighed in the

tray. Approximately 300 grams of marble is used in each trial. The tray was subsequently

removed from the balance, and approximately 100 grams of water is mixed until a

homogeneous mixture was formed. This final mixture may then be weighed again so that

the exact weight of the water added can be calculated. The specific measurements for the

empty tray, marble, and water weights may be found in table 1 in the results section.

Figure 4: Tray containing the marble sitting within the oven.

The marble mixture is then placed on a hanging rack within the Armfield Tray Oven,

model UOP8. This oven consists of a metal duct with a heater and fan at one end that

supplies warm air to any object placed in the duct. Both the heater and fan are controlled

by simple knobs that range from the lowest output of 1, to the highest of 10. To insure

that drying finished within the lab period, the heater is always set to 10, while the fan is

set to 10 in the first trial and 7 in the second trial. As the marble sat in the drier,

11

measurements of the total tray and mixture weight, and the mixture temperature are

recorded every three to four minutes. The weight was measured by a scale sitting on top of

the oven that held the hanging oven rack, and the temperature of the cake was measured

by a Fisher Scientific Traceable infrared thermometer. At eight minute intervals, the dry

and wet bulb temperatures may be recorded from a pyronmeter that is placed in a slot of

the duct, either directly upwind or downwind of the marble tray. After the temperature

measurement, the pyronmeter is moved to the alternative position, and eight minutes again

pass to ensure the wet bulb temperature has reached steady-state. The actual values of the

humidity are later calculated from the online app provided by Vaisala [5]. The wind speed

was also measured every eight minutes, with the Airflow LCA 6000 anemometer, held

within an inch of the air duct’s end to insure consist measurements. Finally, the

temperature of the air in the drier was measured by a thermometer taped to the oven rack.

Since this temperature did not fluctuate at any time, the measurement was only taken at

the beginning of the drying process.

12

Figure 5: Pyronmeter placed within the oven. Both the wet and dry bulb thermometers are heldwithin the metal case.

After the marble was able to maintain its weight for 12 minutes (and therefore likely did

not contain any water) the tray was removed from the oven and placed on the original

balance. If the weight of the marble was within 1 gram of the marble before any water was

added to it then the drying process was considered complete. If the weight was greater

than 1 gram, then the tray was placed back in the oven. At the conclusion of the

experiment, the oven was turned off, and the marble was disposed of in a bucket. This

procedure was originally set forth in the Cooper Union Lab Manual [?].

13

Figure 6: Tray and parts of the marble cake after drying has completed.

14

3 Results and Discussion

To investigate the heat and mass transfer characteristics of the drying experiment,

the theoretical transfer coefficients were compared to empirical values calculated from the

collected data, a summary of which can be found in table 1. The conditions for each trial

were kept relatively similar except for the air speed; the air speed of trial 1 is greater than

that of trial 2.

Table 1: Overall Weight Changes Through Drying

Trial 1 Trial 2empty tray (g) 418 418marble (g) 299.6 299.6water (g) 102 102

marble after drying (g) 300.1 301.6atmosphere pressure (mm Hg) 768 762ambient temperature (◦F) 38 41

The theoretical mass transfer coefficient was first determined using the relationships

illustrated in equation 1 and equation 2. The parameters required to solve for the coefficient,

namely the absolute and saturation humidities, the enthalpy of vaporization, and the heat

transfer coefficient, were calculated for each measurement using their dependence on the

temperature of the solid-liquid mixture as well as the dry and wet bulb temperatures. To

calculate the heat transfer coefficients and the mass transfer coefficients, equation 3 and

equation 4, respectively, were employed; these values are displayed in the appendix. Table

2 displays the average empirical heat and mass transfer coefficients for drying regimes two

and three for both trials.

Table 2: Average Theoretical Heat and Mass Transfer Coefficients

Trial Drying Regime h (W/m2/K) k (m/s)

1II 51.0 0.0129692III 20.2 0.0042202

2II 47.2 0.0086187III 22.3 0.0041661

15

As seen from their values, the transfer coefficients are greater for regime two, as expected,

since the drying rate is quicker for the second drying regime. Because trial 1 has a greater

air speed, the drying rate of trial 1, as well as its transfer coefficients, should be greater than

those of trial 2 which the data supports for regime two. Regime three for both trials should

be similar as they only depend on the rate of diffusion of water through the marble mixture.

Subsequently, another method was utilized to determine the mass and heat transfer

coefficients using experimental data. The change in moisture content of the solid-liquid

mixture per unit time calculated for each measurement was used to determine the drying

rate and empirical transfer coefficients by applying equation 5, the results of which are shown

in the appendix; the average transfer coefficients for each drying regime and for both trials

are shown in table 3.

Table 3: Average Experimental Heat and Mass Transfer Coefficients

Trial Drying Regime h (W/m2/K) k (m/s)

1II 23.5 0.0062397III 23.4 0.0060010

2II 20.6 0.0059837III 20.7 0.0058684

With both a theoretical value and an experimental one for the mass and heat

transfer coefficients, a percent error can be calculated for both coefficients for each trial. A

theoretical total time for drying can be calculated using equation 11 for each measurement

and averaged to estimate an actual time for drying. Table 4 displays a summary of the values

determined by the calculations.

Table 4: Drying Experiment Summary

theoretical empirical Abs. % Diff.

trial h (W/m2/K) k (m/s) tT (min) h (W/m2/K) k (m/s) tT (min) h k

1 23.4 0.0061587 164 40.6 0.0100008 166 42 38

2 20.6 0.0059524 184 37.8 0.0069366 180 45 14

16

As seen from the table, the transfer coefficients calculated from the collected data are greater

than those generated from equations. This is probably due to the fact that the water loss

determined from the humidities of the inlet and outlet doesn’t properly account for all the

water lost from the mixture. Water vapor may escape from the various holes such as those

used to set the psychrometer in the drying unit, and therefore utilizing a mass balance can

draw an incomplete picture of the situation. Measuring the mass of the mixture itself to

generate moisture content at each interval should be a far more accurate representation of the

water lost of the mixture. With a greater amount of water loss accounted for, the calculated

drying rate and transfer coefficients should be greater in the empirical scenario.

Another important distinction to note is the similar and different coefficients for

each trial. The heat transfer coefficients for both trials are relatively similar as expected

since the heater setting was set to the maximum of 10 for both trials. The mass transfer

coefficients for the first trial noticeably exceeds those of the second trial, again as expected;

the fan setting and therefore air speed are all greater in the first trial than the second one.

Faster air speeds means an increased rate of convective mass transfer and mass transfer

coefficient. This would also effect the total time of drying for both theoretical and actual

values; the second trial has greater drying times as expected. While the percent errors

between theoretical and empirical values are relatively large, they are still within the margin

of error to be good predictors for future experiments. The calculated mass and heat transfer

coefficients may provide good estimates for rates of drying processes. The estimated drying

times, however, are nearly equal and should be very valuable information for similar drying

processes.

Figure 7 and figure 8 show the plots of the time drying versus the moisture content

of the mixture for both trials. While it is expected to observe three distinct regimes of drying

on the plots, only two are seen for both figures. When the mixture first begins the drying

process, the drying rate should steadily increase as the liquid reaches a constant temperature

inside the oven, regime two should occur afterwards when the temperature of the mixture

17

and also the drying rate are approximately constant and should result in a linear section of

the drying curve. For the plots generated from experimental data, the curves seem to trend

linearly from the beginning; the first regime of drying likely happens too quickly for the

plots to display. As seen from the raw data in the appendix, the temperature of the mixture

reaches a constant value after only one or two measurements.

Figure 7: Drying experimental curve for trial 1

18

Figure 8: Drying experimental curve for trial 2

When all the water at the surface of the mixture exposed to the air evaporates,

the third drying regime starts. The rate of drying in this regime is no longer dependent on

the rate of vaporization of the water; the diffusion of water through the marble is the rate

limiting step, which severely decreases the rate of drying. This can be seen in both figure 7

and figure 8 as the drying curves approach zero moisture content asymptotically.

19

References

[1] Seader, J. D.; Henley, E. J.; Roper, D. K. Seader. Separation process principles. Hoboken,

NJ: Wiley, 2011.

[2] Boyer, R.; Huff, K. Using Dehydration to Preserve Fruits, Vegetables, and Meats. Virginia

Cooperative Extension, 2008.

[3] Green, Don W., and Robert H. Perry. Perry’s Chemical Engineering Handbook. 8th ed.

New York, NY: McGraw Hill, 2007.

[4] “Drying.” ChE 372 Senior Chemical Engineering Laboratory. The Cooper Union; New

York, NY.

[5] "Vaisala Humidity Calculator 5.0." Vaisala Humidity Calculator 5.0. Accessed February

22, 2017. http://go.vaisala.com/humiditycalculator/5.0/.

20

4 Appendices

4.1 Variable Definitions

Symbol Units MeaningRc mol s−1 m−2 Drying rate, constantR mol s−1 m−2 Drying rate, generalh W m−2 K−1 heat transfer coefficientk m s−1 mass transfer coefficientTg K temperature, ambient gasTw K temperature, wet bulbMw mol g−1 molar mass of waterHs g m−3 humidity, saturatedHa g m−3 humidity, absoluteG g s−1 m−2 flux of air though drierRe - Reynolds NumberSc - Schmidt NumberSh - Sherwood NumberL m length of trayD m2 s−1 Mass diffusivityt s timeA m2 area of traymol mol moles of mixture in trayms g mass of marble in trayX - moisture content, generalXc - moisture content, end second regimeXo - moisture content, start second regimeXf - moisture content, end third regime

∆HV ap J mol−1 enthalpy of water vaporization

21

4.2 Sample Calculations

To reach values for the transfer coefficients and time to completion, calculations

were completed that roughly model the equations set out in Separation Process Principles [1].

To begin these calculations absolute humidity, relative humidity and vapor pressures were

calculated from the gathered wet and dry bulb temperatures, and the online tool provided

by Viasala [5]. From this point on, equations gathered from Perry’s Chemical Engineering

Handbook [3] and Separation Process Principles [1] were used to complete the analysis. A

description of these calculations are shown below.

Saturation Humidity

Saturation Humidity =Ha

relative humidity times0.01(12)

47.7g

m3=

26.5

55.5 × 0.01(13)

Enthalpy of Vaporization

Enthalpy V aporization = (5.2053 ∗ 107) ∗ (1 − T

Tcrit

)(0.3199 − 0.212 ∗ T

Tcrit

+ 0.25795 ∗ T

Tcrit

2

)

(14)

43, 783(J

mol) = (5.2053 ∗ 107) ∗ (1 − 303

647)(0.3199 − 0.212 ∗ 303

647+ 0.25795 ∗ 303

647

2

) (15)

Theoretical Heat Transfer Coefficient

h = 0.0204

(P

287T∗ 1.73 ∗ 3600

)0.8

(16)

22

20.17W

m2K= 0.0204

(101, 592

287 ∗ 298∗ 1.37 ∗ 3600

)0.8

(17)

Theoretical Mass Transfer Coefficient

k = 0.664vair × L

viscosity

1/2viscosity

D

1/3

× D

L(18)

km

s= 0.664

1.37 × 0.273

0.0007

1/2 0.0007

0.000042

1/3

× 0.000042

0.273(19)

Rate of Drying

Rc =∆mol

∆t× A(20)

0.013mol

sm2=

0.167

240 × 0.05(21)

Moisture Content

X =mwet −mdry

mdry

(22)

0.348 =404.4 − 300

300(23)

Time of Second Regime

tsecond regime =mols (Xo −Xc)

ARc

(24)

23

7, 385s =16.67 (0.348 − 0.06)

0.05 × 0.013(25)

Time of Third Regime

tthird regime =molsXc

ARc

ln

(Xc

Xf

)(26)

13, 375s =16.67 × 0.06

0.05 × 0.013ln

(0.06

0.03

)(27)

Total Time to Dry

tT = (tsecond regime + tthird regime) ×1

60(28)

346min = (tsecond regime + tthird regime) ×1

60(29)

24

4.3 Data

Table 5: Data Collected from First Trial (10 on Both Heat and Wind Settings)

t (min) masstotal (g) T (◦F) air speed (m/s) Td (◦F) Tw (◦F) psychrometer location0 821 73.3 1.273 818 74.4 1.46 92.50 80.25 outlet6 817 76.4 1.509 814 78.1 1.46 94.50 80.50 inlet12 811 76.4 1.6915 810 78.9 1.35 93.75 78.00 outlet18 807 80.1 1.7821 806 77.9 1.11 99.50 78.00 inlet24 803 78.2 1.3227 801 76.6 1.26 94.25 80.25 outlet30 798 76.4 1.7733 796 75.4 1.69 99.00 77.75 inlet36 793 78.0 1.7539 791 77.8 1.76 83.75 79.75 outlet42 789 75.8 1.7345 787 78.7 1.75 98.50 78.75 inlet48 784 75.4 1.7751 781 77.6 1.65 93.25 79.75 outlet54 779 77.9 1.6757 777 78.4 1.71 98.75 78.00 inlet60 775 77.8 1.6563 773 76.9 1.64 94.00 81.00 outlet66 771 75.9 1.6569 769 77.2 1.73 99.25 78.50 inlet72 767 79.6 1.7775 764 80.6 1.75 94.00 80.00 outlet78 762 78.0 1.6681 760 76.6 1.72 99.75 79.75 inlet84 758 77.8 1.7387 755 76.6 1.71 94.25 80.00 outlet90 754 76.4 1.7393 752 76.3 1.71 100.00 78.00 inlet96 749 78.2 1.6699 747 76.3 1.76 94.50 80.50 outlet102 746 78.2 1.75105 744 76.6 1.65 99.50 77.50 inlet108 742 77.6 1.55111 739 79.9 1.74 95.00 80.75 outlet

25

t (min) masstotal (g) T (◦F) air speed (m/s) Td (◦F) Tw (◦F) psychrometer location114 738 78.2 1.76117 737 75.1 1.67 99.75 77.00 inlet120 735 75.9 1.77123 734 77.0 1.77 95.25 79.75 outlet126 732 78.7 1.71129 731 82.1 1.80 100.00 77.00 inlet132 730 82.6 1.80135 728 84.6 1.83 95.50 80.00 outlet138 727 86.6 1.78141 727 90.3 1.79 98.75 76.00 inlet144 725 90.6 1.74147 724 92.2 1.73 96.00 79.75 outlet150 723 92.2 1.72153 723 93.1 1.75 100.00 76.25 inlet156 723 95.4159 722 95.9 1.85 96.50 78.00 outlet162 722 96.2 1.65165 722 97.3 1.71 100.00 76.50 inlet168 721 97.4 1.65171 721 97.4 1.69 96.50 79.00 outlet174 721 97.3 1.74

Table 6: Data Collected from Second Trial (10 Heat Setting 7 Wind Setting)

t (min) masstotal (g) T (◦F) air speed (m/s) Td (◦F) Tw (◦F) psychrometer location0 824 79.6 1.394 822 82.9 92.00 88.50 outlet8 821 84.3 1.3712 811 87.0 105.00 89.00 inlet16 810 86.8 1.4220 810 87.8 98.25 85.00 outlet24 807 87.1 1.3728 805 86.0 105.00 87.00 inlet32 802 88.4 1.3736 799 87.9 98.50 86.50 outlet40 795 86.9 1.3844 793 84.9 105.00 84.50 inlet48 789 86.6 1.3752 787 87.4 105.00 89.00 outlet

26

t (min) masstotal (g) T (◦F) air speed (m/s) Td (◦F) Tw (◦F) psychrometer location56 785 84.3 1.4060 783 86.2 110.00 81.75 inlet64 779 87.4 1.4068 777 89.3 100.00 85.00 outlet72 775 84.6 1.4576 772 85.9 110.00 81.25 inlet80 768 84.3 1.4284 765 84.3 100.00 85.00 outlet88 763 82.8 1.4192 761 84.4 110.00 81.75 inlet96 758 84.8 1.44100 755 84.5 97.50 85.50 outlet104 754 85.3 1.43108 752 84.8 110.00 82.25 inlet112 749 88.0 1.46116 747 82.4 100.00 85.00 outlet120 745 85.2 1.44124 744 84.9 110.00 86.50 inlet128 742 86.0 1.42132 739 84.1 100.00 89.25 outlet136 739 86.8 1.41140 737 88.3 110.00 81.00 inlet144 736 84.4 1.42148 734 87.8 100.00 84.50 outlet152 734 89.8 1.42156 732 84.6 110.00 80.60 inlet160 731 93.3 1.39164 731 90.9 100.00 83.50 outlet168 730 93.3 1.44172 729 95.8 110.00 80.00 inlet176 728 98.9 1.41180 727 95.1 100.00 82.50 outlet184 727 96.7 1.37188 727 99.0 110.00 80.00 inlet

27

Table 7: First Trial Theoretical Parameters

t (min) T (K) Ha (g/m3) Hs (g/m3) ∆Hvap (J/mol) h (W/m2/K) k (m/s)0 2963 297 21.73 36.91 44,028 24.7 0.00677196 298 21.56 37.97 43,988 74.0 0.01880979 299 21.39 39.11 43,947 70.8 0.017991612 298 20.18 38.71 43,988 22.6 0.005759615 299 18.97 38.26 43,947 67.8 0.014407018 300 18.12 41.26 43,906 22.6 0.003987021 299 17.27 45.14 43,947 70.8 0.015017624 299 19.23 41.43 43,947 49.4 0.012602127 298 21.19 38.82 43,988 67.9 0.015151830 298 19.18 41.17 43,988 41.8 0.008127533 297 17.16 44.50 44,028 67.8 0.025719036 299 20.53 33.49 43,947 49.4 0.048944139 298 23.89 28.43 43,988 47.3 0.017855142 297 21.11 33.56 44,028 45.2 0.008703645 299 18.33 43.86 43,947 70.9 0.016095048 297 19.65 40.36 44,028 74.1 0.019890851 298 20.96 37.72 43,988 47.2 0.010489754 299 19.23 40.41 43,947 45.2 0.008323257 299 17.49 44.19 43,947 47.2 0.010547460 298 19.79 40.86 43,988 49.4 0.013494063 298 22.09 38.56 43,988 47.3 0.010506966 297 19.97 41.12 44,028 45.3 0.008244469 298 17.85 44.80 43,988 47.2 0.010210372 299 19.43 41.19 43,947 73.9 0.018997475 300 21.00 38.55 43,906 49.3 0.010315678 299 20.01 41.55 43,947 49.4 0.008402681 298 19.01 45.46 43,988 49.4 0.010214984 298 19.97 41.72 43,988 74.1 0.018622287 298 20.92 38.82 43,988 23.6 0.004905790 298 19.02 41.67 43,988 45.3 0.007755093 298 17.12 45.78 43,988 70.8 0.014773696 299 19.26 41.82 43,947 49.4 0.012539899 298 21.39 39.11 43,988 22.6 0.0049451102 299 19.08 41.54 43,947 41.8 0.0078340105 298 16.76 45.13 43,988 45.3 0.0097623108 298 19.14 41.90 43,988 73.9 0.0183389111 300 21.51 39.69 43,906 22.6 0.0048043114 299 18.85 41.98 43,947 20.9 0.0037955117 297 16.19 45.46 44,028 45.3 0.0092748120 297 18.28 42.23 44,028 24.7 0.0056642123 298 20.36 39.98 43,988 45.2 0.0092153126 299 18.24 42.35 43,947 20.8 0.0037442

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t (min) T (K) Ha (g/m3) Hs (g/m3) ∆Hvap (J/mol) h (W/m2/K) k (m/s)129 301 16.12 45.80 43,865 22.6 0.0045941132 301 18.34 42.52 43,865 49.2 0.0112731135 302 20.55 40.26 43,825 21.6 0.0046610138 303 18.02 41.86 43,784 0 0141 305 15.49 44.18 43,702 43.1 0.0091005144 306 17.81 42.23 43,660 24.5 0.0053651147 306 20.13 40.84 43,660 22.5 0.0044276150 306 17.76 42.85 43,660 0 0153 307 15.38 45.80 43,619 0 0156 308 16.77 43.32 43,578 22.4 0.0047750159 309 18.15 41.42 43,537 0 0162 309 16.89 43.33 43,537 0 0165 309 15.62 45.78 43,537 21.5 0.0042942168 309 17.41 43.28 43,537 0 0171 309 19.19 41.44 43,537 0 0174 309 9.60 41.44 43,537 0 0

Table 8: Second Trial Theoretical Parameters

t (min) T (K) Ha (g/m3) Hs (g/m3) ∆Hvap (J/mol) h (W/m2/K) k (m/s)0 300 43,815 21.353028344 301 31.633 31.633 43,749 21.24906688 0.00003658 302 30.058 30.058 43,721 21.20530512 0.000041112 304 28.483 28.483 43,666 21.12147735 0.000042716 304 26.293 26.293 43,670 21.12766125 0.000044920 304 24.102 24.102 43,650 21.09678244 0.000044724 304 24.915 24.915 43,664 21.11838693 0.000044228 303 25.728 25.728 43,686 21.15243762 0.000045032 304 26.417 26.417 43,638 21.07830385 0.000036936 304 27.105 27.105 43,648 21.09370015 0.000035440 304 24.931 24.931 43,668 21.12456879 0.000044544 303 22.756 22.756 43,709 21.18661208 0.000057948 303 25.490 25.490 43,674 21.13384922 0.000042552 304 28.224 28.224 43,658 21.10912177 0.000033256 302 26.530 26.530 43,721 21.20530512 0.000044360 303 24.835 24.835 43,682 21.1462374 0.000045364 304 24.840 24.840 43,658 21.10912177 0.000042868 305 24.845 24.845 43,619 21.05065412 0.000038572 302 21.264 21.264 43,715 21.19595397 0.000070476 303 17.683 17.683 43,688 21.15553926 0.000089280 302 21.264 21.264 43,721 21.20530512 0.000071484 302 24.845 24.845 43,721 21.20530512 0.000050788 301 21.533 21.533 43,751 21.2522005 0.0000744

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t (min) T (K) Ha (g/m3) Hs (g/m3) ∆Hvap (J/mol) h (W/m2/K) k (m/s)92 302 18.220 18.220 43,719 21.20218704 0.000090796 302 22.212 22.212 43,711 21.18972501 0.0000651100 302 26.204 26.204 43,717 21.19906999 0.0000454104 303 22.621 22.621 43,700 21.17417064 0.0000607108 302 19.037 19.037 43,711 21.18972501 0.0000817112 304 21.941 21.941 43,646 21.09061886 0.0000546116 301 24.845 24.845 43,759 21.26474538 0.0000553120 303 24.235 24.235 43,703 21.17727946 0.0000429124 303 23.624 23.624 43,709 21.18661208 0.0000389128 303 26.861 26.861 43,686 21.15243762 0.0000352132 302 30.097 30.097 43,725 21.21154438 0.0000350136 304 23.757 23.757 43,670 21.12766125 0.0000517140 304 17.416 17.416 43,640 21.08138108 0.0000803144 302 20.837 20.837 43,719 21.20218704 0.0000739148 304 24.258 24.258 43,650 21.09678244 0.0000442152 305 20.573 20.573 43,609 21.0353284 0.0000564156 302 16.888 16.888 43,715 21.19595397 0.0001040160 307 19.996 19.996 43,537 20.92874704 0.0000459164 306 23.104 23.104 43,587 21.00169999 0.0000400168 307 19.735 19.735 43,537 20.92874704 0.0000474172 309 16.365 16.365 43,486 20.85335797 0.0000508176 310 19.170 19.170 43,422 20.76071945 0.0000268180 308 21.974 21.974 43,500 20.87440526 0.0000313184 309 19.170 19.170 43,467 20.82636721 0.0000358188 310 16.365 16.365 43,420 20.75774652 0.0000340

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Table 9: First Trial Experimental Parameters

t (min) X h (W/m2/K) k (m/s) tT (min)0 0.3483 0.338 21.4 0.0059895 2206 0.334 21.9 0.0060630 2059 0.324 21.4 0.0059738 19312 0.314 24.0 0.0063650 18115 0.311 20.1 0.0056305 17218 0.301 25.1 0.0064161 14521 0.298 17.2 0.0050263 12624 0.288 19.7 0.0055802 15227 0.281 19.0 0.0055409 19330 0.271 24.9 0.0064587 15333 0.264 24.0 0.0061953 12736 0.254 24.7 0.0064953 21439 0.247 24.8 0.0066808 67542 0.241 24.5 0.0064884 22745 0.234 24.7 0.0063741 13748 0.224 24.9 0.0064848 16251 0.214 23.6 0.0063291 20054 0.207 23.8 0.0062763 15857 0.201 24.3 0.0062517 13060 0.194 23.6 0.0062688 16063 0.187 23.5 0.0063654 20766 0.181 23.6 0.0062783 16069 0.174 24.5 0.0063096 13072 0.167 24.9 0.0064727 15675 0.157 24.7 0.0065202 19378 0.151 23.7 0.0062991 15981 0.144 24.4 0.0063577 13584 0.137 24.5 0.0064284 15887 0.127 24.3 0.0064411 18990 0.124 24.5 0.0063767 14993 0.117 24.3 0.0062295 12396 0.107 23.7 0.0062591 15099 0.100 24.8 0.0065588 193102 0.097 24.7 0.0064165 150105 0.090 23.6 0.0060976 123108 0.084 22.4 0.0060419 149111 0.074 24.6 0.0065276 190114 0.070 24.8 0.0064221 146117 0.067 23.8 0.0060991 118120 0.060 24.9 0.0064072 141123 0.057 24.9 0.0065236 174126 0.050 24.3 0.0062956 140

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t (min) X h (W/m2/K) k (m/s) tT (min)129 0.047 25.3 0.0063275 118132 0.043 25.3 0.0064648 141135 0.037 25.6 0.0066435 175138 0.033 25.1 0.0064102 142141 0.033 25.2 0.0062681 120144 0.027 24.6 0.0063254 140147 0.023 24.5 0.0064372 169150 0.020 24.4 0.0062857 137153 0.020 24.7 0.0061903 115156 0.020 0 0 130159 0.017 25.8 0.0065429 149162 0.017 23.6 0.0061051 131165 0.017 24.3 0.0061350 117168 0.013 23.6 0.0061361 134171 0.013 24.0 0.0063119 157174 0.013 24.6 0.0064046 133

Table 10: Second Trial Experimental Parameters

t (min) X h (W/m2/K) k (m/s) tT (min)0 0.3584 0.351 20.3 0.0062111 8918 0.348 20.2 0.0061223 32012 0.314 20.5 0.0061073 19616 0.311 20.8 0.0060861 21420 0.311 20.5 0.0059524 23724 0.301 20.2 0.0059391 20128 0.294 20.2 0.0059780 17432 0.284 20.2 0.0059970 20936 0.274 20.2 0.0060267 26140 0.261 20.3 0.0059607 19344 0.254 20.2 0.0058678 15248 0.241 20.2 0.0059587 17252 0.234 20.3 0.0060854 19656 0.227 20.5 0.0060624 14160 0.221 20.5 0.0060038 11164 0.207 20.5 0.0060038 14568 0.201 20.8 0.0060571 20972 0.194 21.1 0.0059584 14376 0.184 20.9 0.0057545 10980 0.171 20.8 0.0058964 14384 0.161 20.7 0.0060358 20888 0.154 20.6 0.0058756 144

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t (min) X h (W/m2/K) k (m/s) tT (min)92 0.147 20.8 0.0057344 11196 0.137 21.0 0.0059606 155100 0.127 20.9 0.0061182 260104 0.124 20.9 0.0059621 157108 0.117 21.0 0.0058268 113112 0.107 21.2 0.0060018 147116 0.100 21.1 0.0061100 208120 0.094 21.0 0.0060685 162124 0.090 20.9 0.0060266 133128 0.084 20.8 0.0061246 183132 0.074 20.7 0.0062221 291136 0.074 20.6 0.0059633 158140 0.067 20.7 0.0056601 108144 0.064 20.8 0.0058498 140148 0.057 20.8 0.0060055 202152 0.057 20.8 0.0058498 140156 0.050 20.6 0.0056400 106160 0.047 20.4 0.0057639 137164 0.047 20.7 0.0059525 191168 0.043 21.0 0.0058419 136172 0.040 20.8 0.0056229 105176 0.037 20.6 0.0057558 133180 0.033 20.4 0.0058562 180184 0.033 20.2 0.0056736 133188 0.033 20.2 0.0055134 106

33