Contents. 1 Introduction 4. 2 Methods Results and Discussion 15

Contents 1 Introduction 4 2 Methods 11 3 Results and Discussion 15 4 Appendices 21 4.1 Variable Definitions................................ 21 4.2 Sample Calculations............................... 22 4.3 Data........................................ 25 1

List of Figures 1 Falling Liquid Level in Tray........................... 5 2 Three Drying Regimes.............................. 6 3 Falling Drying Rate Regimes........................... 9 4 Marble tray within oven............................. 11 5 Pyronmeter within oven............................. 13 6 Dried Marble................................... 14 7 Drying experimental curve for trial 1...................... 18 8 Drying experimental curve for trial 2...................... 19 2

List of Tables 1 Overall Weight Changes Through Drying.................... 15 2 Average Theoretical Heat and Mass Transfer Coefficients........... 15 3 Average Experimental Heat and Mass Transfer Coefficients.......... 16 4 Drying Experiment Summary.......................... 16 5 Data Collected from First Trial (10 on Both Heat and Wind Settings).... 25 6 Data Collected from Second Trial (10 Heat Setting 7 Wind Setting)..... 26 7 First Trial Theoretical Parameters........................ 28 8 Second Trial Theoretical Parameters...................... 29 9 First Trial Experimental Parameters...................... 31 10 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 greatly effect 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 occurs from 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). R c = h (T g T w ) H vap (1) R c = M w k (H s H a ) (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 = 0.0204G 0.8 (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. 0.664Re 1/2 Sc 1/3 = 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. R c = 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 = m s 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 = m s 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. t second regime = m s (X o X c ) AR c (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 = R cx Xc (9) 8

t third regime = m sx c AR c ln ( Xc X f ) (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 a falling 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. t T = m ( s (X o X c ) + X c ln AR c ( Xc X f )) (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 held within 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 2 empty tray (g) 418 418 marble (g) 299.6 299.6 water (g) 102 102 marble after drying (g) 300.1 301.6 atmosphere pressure (mm Hg) 768 762 ambient 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/m 2 /K) k (m/s) 1 2 II 51.0 0.0129692 III 20.2 0.0042202 II 47.2 0.0086187 III 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/m 2 /K) k (m/s) 1 2 II 23.5 0.0062397 III 23.4 0.0060010 II 20.6 0.0059837 III 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/m 2 /K) k (m/s) t T (min) h (W/m 2 /K) k (m/s) t T (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 Meaning R c mol s 1 m 2 Drying rate, constant R mol s 1 m 2 Drying rate, general h W m 2 K 1 heat transfer coefficient k m s 1 mass transfer coefficient T g K temperature, ambient gas T w K temperature, wet bulb M w mol g 1 molar mass of water H s g m 3 humidity, saturated H a g m 3 humidity, absolute G g s 1 m 2 flux of air though drier Re - Reynolds Number Sc - Schmidt Number Sh - Sherwood Number L m length of tray D m 2 s 1 Mass diffusivity t s time A m 2 area of tray mol mol moles of mixture in tray ms g mass of marble in tray X - moisture content, general X c - moisture content, end second regime X o - moisture content, start second regime X f - moisture content, end third regime H V 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 = H a relative humidity times0.01 (12) 47.7 g m 3 = 26.5 55.5 0.01 (13) Enthalpy of Vaporization Enthalpy V aporization = (5.2053 10 7 ) (1 T ) ( 0.3199 0.212 T + 0.25795 T crit T crit T T crit (14) 2 ) 43, 783( J mol ) = (5.2053 107 ) (1 303 647 )( 0.3199 0.212 303 647 2 303 + 0.25795 ) (15) 647 Theoretical Heat Transfer Coefficient ( P h = 0.0204 287T ) 0.8 1.73 3600 (16) 22

20.17 W ( ) 0.8 101, 592 m 2 K = 0.0204 1.37 3600 (17) 287 298 Theoretical Mass Transfer Coefficient k = 0.664 v air L 1/2 viscosity viscosity D 1/3 D L (18) k m s 0.273 1/2 1/3 0.0007 = 0.6641.37 0.000042 0.0007 0.000042 0.273 (19) Rate of Drying R c = mol t A (20) 0.013 mol sm 2 = 0.167 240 0.05 (21) Moisture Content X = m wet m dry m dry (22) 0.348 = 404.4 300 300 (23) Time of Second Regime t second regime = mol s (X o X c ) AR c (24) 23

7, 385s = 16.67 (0.348 0.06) 0.05 0.013 (25) Time of Third Regime t third regime = mol sx c ln AR c ( Xc X f ) (26) 13, 375s = ( ) 16.67 0.06 0.06 0.05 0.013 ln 0.03 (27) Total Time to Dry t T = (t second regime + t third regime ) 1 60 (28) 346min = (t second regime + t third regime ) 1 60 (29) 24

4.3 Data Table 5: Data Collected from First Trial (10 on Both Heat and Wind Settings) t (min) mass total (g) T ( F) air speed (m/s) T d ( F) T w ( F) psychrometer location 0 821 73.3 1.27 3 818 74.4 1.46 92.50 80.25 outlet 6 817 76.4 1.50 9 814 78.1 1.46 94.50 80.50 inlet 12 811 76.4 1.69 15 810 78.9 1.35 93.75 78.00 outlet 18 807 80.1 1.78 21 806 77.9 1.11 99.50 78.00 inlet 24 803 78.2 1.32 27 801 76.6 1.26 94.25 80.25 outlet 30 798 76.4 1.77 33 796 75.4 1.69 99.00 77.75 inlet 36 793 78.0 1.75 39 791 77.8 1.76 83.75 79.75 outlet 42 789 75.8 1.73 45 787 78.7 1.75 98.50 78.75 inlet 48 784 75.4 1.77 51 781 77.6 1.65 93.25 79.75 outlet 54 779 77.9 1.67 57 777 78.4 1.71 98.75 78.00 inlet 60 775 77.8 1.65 63 773 76.9 1.64 94.00 81.00 outlet 66 771 75.9 1.65 69 769 77.2 1.73 99.25 78.50 inlet 72 767 79.6 1.77 75 764 80.6 1.75 94.00 80.00 outlet 78 762 78.0 1.66 81 760 76.6 1.72 99.75 79.75 inlet 84 758 77.8 1.73 87 755 76.6 1.71 94.25 80.00 outlet 90 754 76.4 1.73 93 752 76.3 1.71 100.00 78.00 inlet 96 749 78.2 1.66 99 747 76.3 1.76 94.50 80.50 outlet 102 746 78.2 1.75 105 744 76.6 1.65 99.50 77.50 inlet 108 742 77.6 1.55 111 739 79.9 1.74 95.00 80.75 outlet 25

t (min) mass total (g) T ( F) air speed (m/s) T d ( F) T w ( F) psychrometer location 114 738 78.2 1.76 117 737 75.1 1.67 99.75 77.00 inlet 120 735 75.9 1.77 123 734 77.0 1.77 95.25 79.75 outlet 126 732 78.7 1.71 129 731 82.1 1.80 100.00 77.00 inlet 132 730 82.6 1.80 135 728 84.6 1.83 95.50 80.00 outlet 138 727 86.6 1.78 141 727 90.3 1.79 98.75 76.00 inlet 144 725 90.6 1.74 147 724 92.2 1.73 96.00 79.75 outlet 150 723 92.2 1.72 153 723 93.1 1.75 100.00 76.25 inlet 156 723 95.4 159 722 95.9 1.85 96.50 78.00 outlet 162 722 96.2 1.65 165 722 97.3 1.71 100.00 76.50 inlet 168 721 97.4 1.65 171 721 97.4 1.69 96.50 79.00 outlet 174 721 97.3 1.74 Table 6: Data Collected from Second Trial (10 Heat Setting 7 Wind Setting) t (min) mass total (g) T ( F) air speed (m/s) T d ( F) T w ( F) psychrometer location 0 824 79.6 1.39 4 822 82.9 92.00 88.50 outlet 8 821 84.3 1.37 12 811 87.0 105.00 89.00 inlet 16 810 86.8 1.42 20 810 87.8 98.25 85.00 outlet 24 807 87.1 1.37 28 805 86.0 105.00 87.00 inlet 32 802 88.4 1.37 36 799 87.9 98.50 86.50 outlet 40 795 86.9 1.38 44 793 84.9 105.00 84.50 inlet 48 789 86.6 1.37 52 787 87.4 105.00 89.00 outlet 26

t (min) mass total (g) T ( F) air speed (m/s) T d ( F) T w ( F) psychrometer location 56 785 84.3 1.40 60 783 86.2 110.00 81.75 inlet 64 779 87.4 1.40 68 777 89.3 100.00 85.00 outlet 72 775 84.6 1.45 76 772 85.9 110.00 81.25 inlet 80 768 84.3 1.42 84 765 84.3 100.00 85.00 outlet 88 763 82.8 1.41 92 761 84.4 110.00 81.75 inlet 96 758 84.8 1.44 100 755 84.5 97.50 85.50 outlet 104 754 85.3 1.43 108 752 84.8 110.00 82.25 inlet 112 749 88.0 1.46 116 747 82.4 100.00 85.00 outlet 120 745 85.2 1.44 124 744 84.9 110.00 86.50 inlet 128 742 86.0 1.42 132 739 84.1 100.00 89.25 outlet 136 739 86.8 1.41 140 737 88.3 110.00 81.00 inlet 144 736 84.4 1.42 148 734 87.8 100.00 84.50 outlet 152 734 89.8 1.42 156 732 84.6 110.00 80.60 inlet 160 731 93.3 1.39 164 731 90.9 100.00 83.50 outlet 168 730 93.3 1.44 172 729 95.8 110.00 80.00 inlet 176 728 98.9 1.41 180 727 95.1 100.00 82.50 outlet 184 727 96.7 1.37 188 727 99.0 110.00 80.00 inlet 27

Table 7: First Trial Theoretical Parameters t (min) T (K) H a (g/m 3 ) H s (g/m 3 ) H vap (J/mol) h (W/m 2 /K) k (m/s) 0 296 3 297 21.73 36.91 44,028 24.7 0.0067719 6 298 21.56 37.97 43,988 74.0 0.0188097 9 299 21.39 39.11 43,947 70.8 0.0179916 12 298 20.18 38.71 43,988 22.6 0.0057596 15 299 18.97 38.26 43,947 67.8 0.0144070 18 300 18.12 41.26 43,906 22.6 0.0039870 21 299 17.27 45.14 43,947 70.8 0.0150176 24 299 19.23 41.43 43,947 49.4 0.0126021 27 298 21.19 38.82 43,988 67.9 0.0151518 30 298 19.18 41.17 43,988 41.8 0.0081275 33 297 17.16 44.50 44,028 67.8 0.0257190 36 299 20.53 33.49 43,947 49.4 0.0489441 39 298 23.89 28.43 43,988 47.3 0.0178551 42 297 21.11 33.56 44,028 45.2 0.0087036 45 299 18.33 43.86 43,947 70.9 0.0160950 48 297 19.65 40.36 44,028 74.1 0.0198908 51 298 20.96 37.72 43,988 47.2 0.0104897 54 299 19.23 40.41 43,947 45.2 0.0083232 57 299 17.49 44.19 43,947 47.2 0.0105474 60 298 19.79 40.86 43,988 49.4 0.0134940 63 298 22.09 38.56 43,988 47.3 0.0105069 66 297 19.97 41.12 44,028 45.3 0.0082444 69 298 17.85 44.80 43,988 47.2 0.0102103 72 299 19.43 41.19 43,947 73.9 0.0189974 75 300 21.00 38.55 43,906 49.3 0.0103156 78 299 20.01 41.55 43,947 49.4 0.0084026 81 298 19.01 45.46 43,988 49.4 0.0102149 84 298 19.97 41.72 43,988 74.1 0.0186222 87 298 20.92 38.82 43,988 23.6 0.0049057 90 298 19.02 41.67 43,988 45.3 0.0077550 93 298 17.12 45.78 43,988 70.8 0.0147736 96 299 19.26 41.82 43,947 49.4 0.0125398 99 298 21.39 39.11 43,988 22.6 0.0049451 102 299 19.08 41.54 43,947 41.8 0.0078340 105 298 16.76 45.13 43,988 45.3 0.0097623 108 298 19.14 41.90 43,988 73.9 0.0183389 111 300 21.51 39.69 43,906 22.6 0.0048043 114 299 18.85 41.98 43,947 20.9 0.0037955 117 297 16.19 45.46 44,028 45.3 0.0092748 120 297 18.28 42.23 44,028 24.7 0.0056642 123 298 20.36 39.98 43,988 45.2 0.0092153 126 299 18.24 42.35 43,947 20.8 0.0037442 28

t (min) T (K) H a (g/m 3 ) H s (g/m 3 ) H vap (J/mol) h (W/m 2 /K) k (m/s) 129 301 16.12 45.80 43,865 22.6 0.0045941 132 301 18.34 42.52 43,865 49.2 0.0112731 135 302 20.55 40.26 43,825 21.6 0.0046610 138 303 18.02 41.86 43,784 0 0 141 305 15.49 44.18 43,702 43.1 0.0091005 144 306 17.81 42.23 43,660 24.5 0.0053651 147 306 20.13 40.84 43,660 22.5 0.0044276 150 306 17.76 42.85 43,660 0 0 153 307 15.38 45.80 43,619 0 0 156 308 16.77 43.32 43,578 22.4 0.0047750 159 309 18.15 41.42 43,537 0 0 162 309 16.89 43.33 43,537 0 0 165 309 15.62 45.78 43,537 21.5 0.0042942 168 309 17.41 43.28 43,537 0 0 171 309 19.19 41.44 43,537 0 0 174 309 9.60 41.44 43,537 0 0 Table 8: Second Trial Theoretical Parameters t (min) T (K) H a (g/m 3 ) H s (g/m 3 ) H vap (J/mol) h (W/m 2 /K) k (m/s) 0 300 43,815 21.35302834 4 301 31.633 31.633 43,749 21.24906688 0.0000365 8 302 30.058 30.058 43,721 21.20530512 0.0000411 12 304 28.483 28.483 43,666 21.12147735 0.0000427 16 304 26.293 26.293 43,670 21.12766125 0.0000449 20 304 24.102 24.102 43,650 21.09678244 0.0000447 24 304 24.915 24.915 43,664 21.11838693 0.0000442 28 303 25.728 25.728 43,686 21.15243762 0.0000450 32 304 26.417 26.417 43,638 21.07830385 0.0000369 36 304 27.105 27.105 43,648 21.09370015 0.0000354 40 304 24.931 24.931 43,668 21.12456879 0.0000445 44 303 22.756 22.756 43,709 21.18661208 0.0000579 48 303 25.490 25.490 43,674 21.13384922 0.0000425 52 304 28.224 28.224 43,658 21.10912177 0.0000332 56 302 26.530 26.530 43,721 21.20530512 0.0000443 60 303 24.835 24.835 43,682 21.1462374 0.0000453 64 304 24.840 24.840 43,658 21.10912177 0.0000428 68 305 24.845 24.845 43,619 21.05065412 0.0000385 72 302 21.264 21.264 43,715 21.19595397 0.0000704 76 303 17.683 17.683 43,688 21.15553926 0.0000892 80 302 21.264 21.264 43,721 21.20530512 0.0000714 84 302 24.845 24.845 43,721 21.20530512 0.0000507 88 301 21.533 21.533 43,751 21.2522005 0.0000744 29

t (min) T (K) H a (g/m 3 ) H s (g/m 3 ) H vap (J/mol) h (W/m 2 /K) k (m/s) 92 302 18.220 18.220 43,719 21.20218704 0.0000907 96 302 22.212 22.212 43,711 21.18972501 0.0000651 100 302 26.204 26.204 43,717 21.19906999 0.0000454 104 303 22.621 22.621 43,700 21.17417064 0.0000607 108 302 19.037 19.037 43,711 21.18972501 0.0000817 112 304 21.941 21.941 43,646 21.09061886 0.0000546 116 301 24.845 24.845 43,759 21.26474538 0.0000553 120 303 24.235 24.235 43,703 21.17727946 0.0000429 124 303 23.624 23.624 43,709 21.18661208 0.0000389 128 303 26.861 26.861 43,686 21.15243762 0.0000352 132 302 30.097 30.097 43,725 21.21154438 0.0000350 136 304 23.757 23.757 43,670 21.12766125 0.0000517 140 304 17.416 17.416 43,640 21.08138108 0.0000803 144 302 20.837 20.837 43,719 21.20218704 0.0000739 148 304 24.258 24.258 43,650 21.09678244 0.0000442 152 305 20.573 20.573 43,609 21.0353284 0.0000564 156 302 16.888 16.888 43,715 21.19595397 0.0001040 160 307 19.996 19.996 43,537 20.92874704 0.0000459 164 306 23.104 23.104 43,587 21.00169999 0.0000400 168 307 19.735 19.735 43,537 20.92874704 0.0000474 172 309 16.365 16.365 43,486 20.85335797 0.0000508 176 310 19.170 19.170 43,422 20.76071945 0.0000268 180 308 21.974 21.974 43,500 20.87440526 0.0000313 184 309 19.170 19.170 43,467 20.82636721 0.0000358 188 310 16.365 16.365 43,420 20.75774652 0.0000340 30

Table 9: First Trial Experimental Parameters t (min) X h (W/m 2 /K) k (m/s) t T (min) 0 0.348 3 0.338 21.4 0.0059895 220 6 0.334 21.9 0.0060630 205 9 0.324 21.4 0.0059738 193 12 0.314 24.0 0.0063650 181 15 0.311 20.1 0.0056305 172 18 0.301 25.1 0.0064161 145 21 0.298 17.2 0.0050263 126 24 0.288 19.7 0.0055802 152 27 0.281 19.0 0.0055409 193 30 0.271 24.9 0.0064587 153 33 0.264 24.0 0.0061953 127 36 0.254 24.7 0.0064953 214 39 0.247 24.8 0.0066808 675 42 0.241 24.5 0.0064884 227 45 0.234 24.7 0.0063741 137 48 0.224 24.9 0.0064848 162 51 0.214 23.6 0.0063291 200 54 0.207 23.8 0.0062763 158 57 0.201 24.3 0.0062517 130 60 0.194 23.6 0.0062688 160 63 0.187 23.5 0.0063654 207 66 0.181 23.6 0.0062783 160 69 0.174 24.5 0.0063096 130 72 0.167 24.9 0.0064727 156 75 0.157 24.7 0.0065202 193 78 0.151 23.7 0.0062991 159 81 0.144 24.4 0.0063577 135 84 0.137 24.5 0.0064284 158 87 0.127 24.3 0.0064411 189 90 0.124 24.5 0.0063767 149 93 0.117 24.3 0.0062295 123 96 0.107 23.7 0.0062591 150 99 0.100 24.8 0.0065588 193 102 0.097 24.7 0.0064165 150 105 0.090 23.6 0.0060976 123 108 0.084 22.4 0.0060419 149 111 0.074 24.6 0.0065276 190 114 0.070 24.8 0.0064221 146 117 0.067 23.8 0.0060991 118 120 0.060 24.9 0.0064072 141 123 0.057 24.9 0.0065236 174 126 0.050 24.3 0.0062956 140 31

t (min) X h (W/m 2 /K) k (m/s) t T (min) 129 0.047 25.3 0.0063275 118 132 0.043 25.3 0.0064648 141 135 0.037 25.6 0.0066435 175 138 0.033 25.1 0.0064102 142 141 0.033 25.2 0.0062681 120 144 0.027 24.6 0.0063254 140 147 0.023 24.5 0.0064372 169 150 0.020 24.4 0.0062857 137 153 0.020 24.7 0.0061903 115 156 0.020 0 0 130 159 0.017 25.8 0.0065429 149 162 0.017 23.6 0.0061051 131 165 0.017 24.3 0.0061350 117 168 0.013 23.6 0.0061361 134 171 0.013 24.0 0.0063119 157 174 0.013 24.6 0.0064046 133 Table 10: Second Trial Experimental Parameters t (min) X h (W/m 2 /K) k (m/s) t T (min) 0 0.358 4 0.351 20.3 0.0062111 891 8 0.348 20.2 0.0061223 320 12 0.314 20.5 0.0061073 196 16 0.311 20.8 0.0060861 214 20 0.311 20.5 0.0059524 237 24 0.301 20.2 0.0059391 201 28 0.294 20.2 0.0059780 174 32 0.284 20.2 0.0059970 209 36 0.274 20.2 0.0060267 261 40 0.261 20.3 0.0059607 193 44 0.254 20.2 0.0058678 152 48 0.241 20.2 0.0059587 172 52 0.234 20.3 0.0060854 196 56 0.227 20.5 0.0060624 141 60 0.221 20.5 0.0060038 111 64 0.207 20.5 0.0060038 145 68 0.201 20.8 0.0060571 209 72 0.194 21.1 0.0059584 143 76 0.184 20.9 0.0057545 109 80 0.171 20.8 0.0058964 143 84 0.161 20.7 0.0060358 208 88 0.154 20.6 0.0058756 144 32

t (min) X h (W/m 2 /K) k (m/s) t T (min) 92 0.147 20.8 0.0057344 111 96 0.137 21.0 0.0059606 155 100 0.127 20.9 0.0061182 260 104 0.124 20.9 0.0059621 157 108 0.117 21.0 0.0058268 113 112 0.107 21.2 0.0060018 147 116 0.100 21.1 0.0061100 208 120 0.094 21.0 0.0060685 162 124 0.090 20.9 0.0060266 133 128 0.084 20.8 0.0061246 183 132 0.074 20.7 0.0062221 291 136 0.074 20.6 0.0059633 158 140 0.067 20.7 0.0056601 108 144 0.064 20.8 0.0058498 140 148 0.057 20.8 0.0060055 202 152 0.057 20.8 0.0058498 140 156 0.050 20.6 0.0056400 106 160 0.047 20.4 0.0057639 137 164 0.047 20.7 0.0059525 191 168 0.043 21.0 0.0058419 136 172 0.040 20.8 0.0056229 105 176 0.037 20.6 0.0057558 133 180 0.033 20.4 0.0058562 180 184 0.033 20.2 0.0056736 133 188 0.033 20.2 0.0055134 106 33