Drying Final Report

700 Dominik DriveCollege Station, TX 77840

November 2, 2011

Dr. Yue Kuo35-A Zachry Engineering CenterTexas A&M UniversityCollege Station, TX 77845-3122

Dear Dr. Kuo:

The enclosed report, entitled “An Analysis of Heat and Mass Transfer in a Drying Process,” was written for the experiment performed by Group 1 on October 19 and October 26 for section 905 of Unit Operations I.

The purpose of the experiment is to study and analyze heat and mass transfer in a drying process, particularly of a sponge. This report introduces the theoretical background on heat and mass transfer coefficients. In addition, this report presents the materials and outlines the procedure of the experiment. The Sample Calculations section describes how calculations were completed. The experimental data is tabulated, and results are analyzed and discussed in the Results and Discussion section. Finally, this report contains recommendations that can help improve experiment efficiency. Additionally, a safety article, entitled “Failure modes of reinforced concrete beams strengthened with carbon fiber sheet in fire” is reviewed.

While everyone helped with the corrections of the report, each team member had the following responsibilities:

Sonya Akhave – She discussed the Materials and Methods for the following report and recorded all the original data during the experiment.

Mahmoud Allahham – He performed all necessary calculations and provided examples for the Sample Calculations section of the report.

Lehron Brune – As the group leader, he wrote the Results and Discussion for the report. He also coordinated meeting times.

Carolyn Bott – She discussed recommendations for the experiment and examined safety concerns according to the attached safety article.

Samuel Congiundi – He wrote the Introduction and Theory section of the report.

An Analysis of Heat and Mass Transfer in a Drying Process

Chen 414-905Group #1

Sonya AkhaveMahmoud Allahham

Lehron BruneCarolyn Bott

Samuel Congiundi

November 2, 2011

Table of ContentsList of Illustrations...................................................................................................................................... iii

Figures........................................................................................................................................................ iii

Tables.......................................................................................................................................................... iii

Summary.......................................................................................................................................................... 1

Introduction..................................................................................................................................................... 2

Objectives................................................................................................................................................... 2

Background................................................................................................................................................ 2

Theory.......................................................................................................................................................... 3

Materials and Methods................................................................................................................................9

Apparatus.................................................................................................................................................... 9

Experimental Procedure......................................................................................................................10

Sample Calculations..................................................................................................................................12

Results and Discussion.............................................................................................................................16

Plot moisture content versus time and determine the constant drying rates.....................16

Plot the drying rate and the sponge temperature as a function of time...............................20

Plot the drying rate as a function of the moisture content.......................................................23

Describe the boundaries for the complete run.............................................................................27

Determine the heat and mass transfer coefficients during the period of constant drying..................................................................................................................................................................... 28

Conclusions............................................................................................................................................. 29

Recommendations......................................................................................................................................30

Nomenclature.............................................................................................................................................. 31

Literature Cited........................................................................................................................................... 32

Safety Article Review...............................................................................................................................33

APPENDIX A: SAFETY ARTICLE.......................................................................................................A1

APPENDIX B: SPREADSHEET CALCULATIONS..........................................................................B1

APPENDIX C: ORIGINAL DATA SHEETS........................................................................................C1

List of Illustrations

Figures

Figure 1: Example of a drying curve..................................................................................5Figure 2: Psychrometric chart.............................................................................................8Figure 3: Drying apparatus..................................................................................................9Figure 4: Moisture content as a function of time for 160° F............................................16Figure 5: Moisture content as a function of time for 170° F............................................17Figure 6: Moisture content as a function of time for 180° F............................................17Figure 7: Moisture content as a function of time for 190° F............................................18Figure 8: Moisture content as a function of time for 200° F............................................18Figure 9: Moisture content as a function of time for 210° F............................................19Figure 10: Drying rate as a function of time for 160° F...................................................21Figure 11: Drying rate as a function of time for 170° F, 180° F, 190° F, 200° F, and 210° F.........................................................................................................................................21Figure 12: Sponge temperature as a function of time for 160° F.....................................22Figure 13: Sponge temperature as a function of time for 170° F, 180° F, 190° F, 200° F, and 210° F..........................................................................................................................23Figure 14: Draying rate as a function of moisture content for 160° F..............................24Figure 15: Draying rate as a function of moisture content for 170° F..............................24Figure 16: Draying rate as a function of moisture content for 180° F..............................25Figure 17: Draying rate as a function of moisture content for 190° F..............................25Figure 18: Draying rate as a function of moisture content for 200° F..............................26Figure 19: Draying rate as a function of moisture content for 210° F..............................26

Tables

Table 1: Drying rate for each temperature........................................................................20Table 2: Periods and critical points for the complete trial at 160° F................................28Table 3: Heat and Mass Transfer Coefficients.................................................................28

1

Summary

The objectives of the second experiment for CHEN 414: Unit Operations were to

analyze drying characteristics of a sponge saturated with water by applying heat and mass

transfer principles. The sponge was exposed to flowing air at six different temperatures,

and the mass of the sponge along with the sponge temperature and air temperature were

recorded every minute. From this data, the drying rate was determined. The heat and

mass transfer coefficients were also calculated. One of the trials was used to examine the

complete drying curve, in which the sponge moisture content was allowed to equilibrate.

From this drying curve, the group was able to determine the boundaries that separated the

major periods. These boundaries included the limits of the periods, the critical moisture

contents, the equilibrium moisture contents, and the constant drying rates. The constant

drying rate was determined for each trial and was used to calculate the heat and mass

transfer coefficients.

After an initial, transient drying period, the sponge temperature was constant over

time. During the trial at 160º F, the sponge temperature increased after the period of

constant drying. The linear decrease in moisture content over time demonstrated that the

magnitude of the drying rate increased with an increase in temperature. In addition, the

calculated heat and mass transfer coefficients remained constant for different

temperatures. In general, the drying curve for the 160º F trial was consistent with the

established shape in literature.

2

Introduction

Objectives

In this experiment, a sponge saturated with water was dried constantly at six

different temperatures. As the sponge dried, heat and mass transfer occurred. By

recording the temperatures of the upstream and downstream air, in addition to the

temperature and mass of the sponge, the heat and mass transfer could be modeled and

analyzed. The first objective was to determine the drying rate of the sponge during the

period of constant drying for each temperature. A plot of that drying rate as a function of

the moisture content was constructed. The second objective was to determine the

boundaries of the drying rate graph for the complete run, which consisted of sections of

different drying rates over the time period of the run. The third and final objective was to

determine the mass and heat transfer coefficients for the period of constant drying rate

specific to each temperature run.

Background

Heat transfer and mass transfer are extremely important in many chemical

engineering applications, including the chemical process industry, oil industry,

pharmaceutical industry, and food processing industry. The drying process, in particular,

is a common process within these industries.

Drying is a process in which a moistened solid undergoes heat and mass transfer

without any other physical or chemical alterations. The moisture leaves the solid as a

gas. This process is achieved by transferring energy to the liquid molecules so that the

they have enough energy to vaporize and leave the solid. A common implementation of

3

the drying process is the exposure of the moistened solid to hot air. In this application,

convective heat transfer occurs at the solid’s surface, causing the liquid at the surface to

vaporize and leave the solid. The rate of this heat transfer, and consequently the mass

transfer of the vapor leaving the solid, is largely dependent on the temperature of the air.

Theory

During the drying process, a wet surface at some temperature is exposed to a

stream of hot air at a different temperature. If the air is not saturated with water,

evaporation at the water surface occurs. This evaporation takes place because the

moisture content in the air is less than that in the wet solid. This difference in moisture

content acts as the driving force for mass transfer. The vaporization of water requires

energy, which is supplied by the transfer of heat contained in the air stream to the water

in the moist solid. At steady state conditions, the heat transferred from the air balances

the heat of vaporization of the water removed from the wet surface at a drying rate of

dw/dt. This steady state heat balance is displayed by Equation (1).

−hc A (T G−T W )= λdwdt

(1)

where

hc = convective heat transfer coefficient (Btu/(h·ft2·ºF))

A = surface area of the sample (ft2)

TG = dry bulb temperature of the air (ºF)

TW = wet bulb temperature of the air (ºF)

λ = latent heat of vaporization (Btu/lbm)

w = total mass of the water (lbm)

t = time (h)

4

Two important parameters are the wet bulb temperature and the dry bulb

temperature. The wet bulb temperature is the lowest temperature that can occur via the

evaporation of water only. It is an indication of the amount of moisture in the air. The

dry bulb temperature, which was measured using a thermocouple in this experiment,

represents the temperature of the upstream air relative to the sponge. The wet bulb

temperature is normally measured by wrapping the bulb of a thermometer in a wet cloth.

Similarly, the wet bulb temperature was measured by exposing a thermocouple to the

surface of the sponge in this experiment. A requirement for the evaporation of water in

the sponge is that the latent heat of vaporization must be transferred to the water. The

latent heat of vaporization is the amount of energy required to convert a unit of mass of

substance from the liquid phase to the gaseous phase at a given temperature and pressure.

The driving force for the mass transfer of water into the air is the difference

between the vapor pressure of the water at the phase interface and the partial pressure of

water in the air. At the phase interface, the pressure will be equal to the vapor pressure of

the water at the wet bulb temperature. The equation for the molar rate of water

vaporization is displayed by Equation (2).

(2)where

NA = molar rate of water vaporization (lbmol/h)

kg = mass transfer film coefficient (lbmol/(h·ft2·psi))

PW = vapor pressure of water at the interface (psia)

PG = partial pressure of water in the bulk gas phase (psia)

The partial pressure of water in the air is determined by the relative or absolute

humidity, while the vapor pressure of the water at the interface will depend on the wet

5

bulb temperature. After the molar rate of water vaporization is determined, the mass

drying rate can be determined by Equation (3).

(3)

The number 18 in Equation (3) is the molar mass of water. Knowing the drying rate aids

in characterizing other aspects of the drying process.

The moisture content, X, is defined as the mass of water divided by the mass of

the dry sample. The moisture content can also be defined as the mass fraction of water in

the sample. The calculations in this experiment are based on the former definition. The

correlations between the drying rate and the moisture content depend on the operating

conditions of the drying process, which include air velocity, air temperature, and air

humidity. The drying rate can be plotted as a function of the moisture content to obtain a

drying curve. The shape of the drying curve reflects the characteristics of the solid itself;

consequently, the shape will differ for each solid. A typical drying curve is displayed in

Figure 1.

Figure 1: Example of a drying curve

6

The drying curve can aid in understanding the overall drying process of a

material. The drying curve is separated into four periods:

Period I0 is the initial transient drying period. The sample either heats or cools to

the wet bulb temperature of the air. In this experiment, the sample is heating to

the wet bulb temperature.

Period I is the constant drying rate period. The water in the sample fills the pores

to the surface where the water vaporizes and diffuses into the air.

Period II is the first falling rate period. Slower transport to the surface occurs as

the capillaries being to dry.

Period III is the second falling rate period. Vaporization is not at the surface but

inside the sample. Vapor must diffuse through the solid to the surface and then

into the air.

Figure 1 also displays different points on the curve that represent a significant

change. These points also indicate the beginning or end of a period. They are labeled

X0, X1, X2, X3, X4, and X5:

X0 represents the beginning of the drying process when the material is at the

maximum moisture content. In this experiment, the sponge is saturated with

water.

X1 represents the moisture content when the sample has reached the wet bulb

temperature. At this point, the drying rate will be constant.

X2 represents the first critical point, which is the moment that the drying rate

begins to decrease.

X3 represents the second critical point, which separates Periods II and III.

7

X4 represents the point at which the drying rate begins to slow even more.

X5 represents the equilibrium moisture content, which is the amount of water that

cannot be removed at the specified operation conditions.

The conditions during which the initial and constant drying rates occur affects the

later periods on the drying curve where the drying rate decreases. For example, if the

material is exposed to air at a higher temperature that causes the material to initially dry

more rapidly, the material will continue to dry quickly in the low moisture range. In

addition, the temperature of the material remains stable during the constant rate period

due to evaporative cooling. There is sufficient mass of water within the solid such that

all the heat transferred to the sample is used to vaporize the water instead of being used to

increase the temperature of the solid.1

As mentioned earlier, relative humidity is used to calculate the partial pressure of

water in air. The relative humidity can be estimated on a psychrometric chart, illustrated

in Figure 2.

8

Figure 2: Psychrometric chart

A psychrometric chart is a graph that displays the thermodynamic properties of an

air and water mixture at constant pressure. The chart can be used to determine the

relative humidity for each trial if the dry bulb temperature, wet bulb temperature, mass

fraction of water in air, and enthalpy are known.

9

Materials and Methods

Apparatus

The apparatus used in the drying experiment is shown below in Figure 3.

Figure 3: Drying apparatus

The drying apparatus consists of a recirculating dryer that has an air passageway

and a blower, L. The air velocity is controlled by a variable-speed motor, M, or a

butterfly valve, K. In this experiment, maximum air velocity was maintained. The

temperature controller, B, along with the pneumatic valve, C, is used to maintain the

temperature of the air (dry bulb temperature) that is flowing into the chamber containing

the sponge by regulating the amount of steam that goes to the heating coils. The hot air

flows through the chamber and then circulates back to the blower.

10

While performing this experiment, it was important to be aware of the safety

hazards. Since this experiment involves hot steam lines, hot ductwork, and hot air, burn

hazard is a significant concern. The steam line, control valve on the line, steam

condensate line, steam trap, and the header on the steam coils are not insulated.

Therefore, it is important to never touch these surfaces. Since air at temperatures of 160-

210° F is fed into the air duct, the duct can also be dangerous to touch. An insulated

glove should be used when handling the sponge in the air duct and when closing the

steam valve.

Experimental Procedure

The first step in conducting the drying experiment was to turn on the blower,

steam and instrument air to allow the air to heat up to the desired temperature. The

instrument air pressure was constant at 20 psig, and the temperature controller was used

to set the desired temperature for each trial. The Mettler-Toledo Balance was then turned

on and the tare button was pressed to zero the balance. The dry sponge was initially

placed on the holding rack to determine the dry weight. The sponge was then soaked in

water until the sponge started to drip. The soaked sponge was then placed on the rack and

the thermocouple was inserted into the center of the sponge. Because the sponge

continuously moves due to the flow of air, the average sponge weight was determined

over a three second period. This average value provides a much more accurate reading

compared to instantaneous readings.

Once the sponge was situated on the holding rack with the thermocouple inserted,

Group I recorded the following data every minute:

11

Average sample weight

Sponge temperature inside the air duct

Downstream temperature (TW)

Upstream temperature (TG)

The temperatures were given in degrees Fahrenheit, and the unit for sample weight was

in grams. One member recorded the results on paper, and another member plotted the

data in Microsoft Excel. The drying rate and the sponge temperature were both plotted as

functions of time. These plots were used to ensure that the constant drying rate lasted at

least 15 min.

This process was repeated at five more temperatures (six total) in order to analyze

the effect of temperature on the heat and mass transfer coefficients. The temperatures

used for this experiment were 160° F, 170° F, 180° F, 190° F, 200° F, and 210° F. One

trial, performed at the lowest temperature of 160° F, was used to examine the complete

drying curve. This trial was continued until the drying rate decreased below 0.2 g/min.

The trials at the other temperatures were conducted until the constant drying rate period

reached at least 15 min. At the end of each laboratory period, the steam and blower were

turned off to shut down the experiment.

12

Sample Calculations

Several unit conversions were performed in this experiment. The most frequent

conversion involved obtaining flow rates in English units from the measured values in

metric units. The conversion was calculated as follows:

q ( lbm

h )=q ( gmin )×

60 min1h

×0.0022 lbm

1 g(4)

The first step of the calculations for each temperature in this experiment was to

determine the constant drying rate. This was achieved by first calculating the moisture

content according to equation (5) and plotting it as a function of time.

MoistureContent , X=W s−W d

W d(5)

where

ws = Weight of wet sponge

wd = Weight of dry sponge

For example, at t = 5 min for 200° F, the moisture content was

X=176.11 g−12.64 g12.64 g

=12.93275316lbm water

lbm dry sample

Since this calculation involved a ratio of two equal units, no conversion factors were

necessary.

13

The overall value of the constant drying rate for each temperature, dw/dt, was

obtained by multiplying the slope of the plot of moisture content as a function of time by

the dry weight of the sponge. The following calculation was performed for t = 5 min for

200° F. The absolute values of the drying rates were taken.

dwdt

=|(−0.033158lbm water

lbm dry sample )|∗(027808 lbm dry sample )=0.419lbm

h

The next step for this experiment was to calculate the heat transfer coefficients for

the period of constant drying rate at each temperature. The steady state balance relevant

to this step is displayed in equation (1).

−hc A (T G−T W )= λdwdt

(1)

Rearranging this equation and solving for the heat transfer coefficient, hc

hc=−λ

dwdt

A(TG−TW )

The surface area of the sponge was calculated as follows:

A=2 ( Length∗Width )+2 ( Length∗Height )+2 (Width∗Height )

By substituting the measured dimensions of the sponge and converting to ft2, the group

determined the surface area of the sponge to be

A=[2(5 38∗3)+2(5 3

8∗0.75)+2∗(3∗0.75 )]i n2 ×

1 f t2

144 in2=0.3112 f t 2

14

The instantaneous drying rate, dw/dt, was calculated at each time interval by using an

instantaneous slope formula as shown in Equation (6).

dwdt

=w2−w1

t 2−t1(6)

For example, the value of dw/dt at t = 5 min for 200° F was calculated as follows:

dwdt

=163.47−166.24 g5−4 min

×60 min

1 h×

0.0022lbm

1 g=0.36564

lbm

h

With a value of λ = 970.4 Btu/lbm obtained from literature, the heat transfer coefficient

was calculated at t = 5 min for 200° F as follows:2

hC=970.4 (Btu

lbm )∗0.36564(lbm

hr)

0.3112 ( f t 2)∗(205−98 )(℉ )=12.21( Btu

h∗ft2∗° F )The final step was to determine the mass transfer coefficient for each run. The mass

balance on the sponge is displayed in Equation (3).

dwdt

=−18 k g∗A∗(PW−PG) (3)

Rearranging this equation and solving for the mass transfer coefficient yields

k g=

dwdt

−18∗A∗( PW−PG )(7)

The vapor pressure of water was calculated using Antoine’s equation with values of A, B,

and C obtained from literature.2

15

PW=exp(A− B59

(T W−32 )+C )=exp(16.3872− 3885.759

( TW−32 )+230.17 )For an average Tw of 108°, the vapor pressure of water was calculated as follows:

PW=exp(16.3872− 3885.759

(108−32 )+230.17 )=1.245 psia

To calculate the partial pressure of water in the air, the dry and wet bulb temperatures

were first used to estimate the relative humidity on a psychrometric chart. The partial

pressure was then calculated according to Equation (8).

PG=RH100

∙ PW (8)

where

RH = relative humidity

For 200° F, RH was estimated to be 5.75%; thus, the partial pressure was

PG=5.75100

∙1.245=0.0716 psia

Substituting these values into Equation (7), the mass transfer coefficient for 200° F was

calculated as follows:

k g=−0.419

−18∗0.3112∗(1.245−0.0716 )=0.0638

lbmol

h∗f 2∗psia

16

Similar calculations were performed for the remaining five temperatures. Overall heat

transfer coefficients were obtained for each run by averaging the values over the entire

time interval for each respective temperature.

17

Results and Discussion

Plot moisture content versus time and determine the constant drying rates.

The first objective was to plot the moisture content as a function of time during

the period of constant drying. Moisture content was calculated according to Equation (5),

as described in the Sample Calculations. The graphs for each temperature are displayed

in Figures 4 through 9.

10 15 20 25 30 35 40 45 50 55 600

2

4

6

8

10

12

14

16

f(x) = − 0.176973499344341 x + 15.8060303877753R² = 0.99996347579082

Moisture Content as a Function of Time

Time (min)Moi

stur

e Co

nten

t (lb

m w

ater

/lbm

dry

sam

ple)

Figure 4: Moisture content as a function of time for 160° F

18

2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

18

f(x) = − 0.196437546537605 x + 16.0273885424423R² = 0.999673412439022


Time (min)Moi

stur

e Co

nten

t (lb

m w

ater

/lbm

dry

sam

ple)


2 4 6 8 10 12 14 16 18 200

2

4

6

810

12

14

1618

f(x) = − 0.208721146686525 x + 17.6566630212212R² = 0.999755176413559


Time (min)Moi

stur

e Co

nten

t (lb

m w

ater

/lbm

dry

sam

ple)


19

2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

18

f(x) = − 0.229837583767686 x + 16.6900944713328R² = 0.999507704198284


Time (min)Moi

stur

e Co

nten

t (lb

m w

ater

/lbm

dry

sam

ple)


2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

f(x) = − 0.251164603499629 x + 14.169121137379R² = 0.999795108726282


Time (min)Moi

stur

e Co

nten

t (lb

m w

ater

/lbm

dry

sam

ple)


20

2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

f(x) = − 0.263188756515264 x + 15.030293652271R² = 0.999716138066314


Time (min)Moi

stur

e Co

nten

t (lb

m w

ater

/lbm

dry

sam

ple)


According to the moisture content graphs, the absolute value of the slope

increases as the temperature increases. This slope represents the rate of change of

moisture content with time. A higher magnitude of the slope constitutes a higher drying

rate. In other words, the drying rate increases as the temperature increases, which is a

result of more energy being transferred to the sponge. To confirm this observation, the

slopes of each graph were converted to drying rates, as described in the Sample

Calculations. These results are displayed in Table 1.

21

Table 1: Drying rate for each temperature

Temperature (°F) Drying Rate (lbm/h)

160 0.295

170 0.328

180 0.348

190 0.383

200 0.419

210 0.439

Plot the drying rate and the sponge temperature as a function of time

The next objective was to plot the drying rate and sponge temperature as

functions of time. The drying rates in the following results differ from those in the

previous section in that these results use instantaneous drying rates calculated at each

data point. The period of constant drying occurs when the slope of the curve is zero. The

plot of the drying rate as a function of time for 160 ºF is displayed in Figure 10.

22

0 20 40 60 80 100 1200

0.1

0.2

0.3

0.4

0.5

Drying rate as a Function of Time

Time (min)

Dry

ing

Rat

e (l

bm

/h)

Figure 10: Drying rate as a function of time for 160° F

For this complete trial at 160° F, the drying rate was constant but then decreased

over time after one hour had elapsed. The plot of the drying rate as a function of time for

the other temperatures is shown in Figure 11.

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Drying Rate as a Function of Time

170 F180 F190 F200 F210 F

Time (min)

Dry

ing

Rat

e (l

bm

wat

er/h

r)

Figure 11: Drying rate as a function of time for 170° F, 180° F, 190° F, 200° F, and 210° F

23

Figure 11 demonstrates that there was an observed constant drying rate at each

temperature, as indicated by the zero slopes. If data for trials in Figure 11 were collected

over a time interval similar in length to that at 160° F, the drying rates would also

eventually decrease.

The sponge temperature as a function of time was also plotted. The results for

160° F are displayed in Figure 12.

0 20 40 60 80 100 1200

20

40

60

80

100

120

140

Sponge Temperature as a Function of Time

Time (min)

Spon

ge T

emp

erat

ure

(F)⁰

Figure 12: Sponge temperature as a function of time for 160° F

Initially, the sponge temperature increased slightly as the absorbed energy was

used to raise the temperature of the water. After twenty minutes elapsed, the sponge

temperature remained constant, which was a result of all the energy being transferred to

the sponge being used to vaporize the water. The sponge temperature increased after

approximately 80 minutes had elapsed, at which point there was not enough moisture in

24

the sponge to absorb all the transferred energy. The sponge temperature as a function of

time for the other temperatures is displayed in Figure 13.

0 5 10 15 20 2570

75

80

85

90

95

100

105

110

115

Sponge Temperature as a Function of Time

170180190200210

Time (min)

Tem

per

atu

re (

F)⁰

Figure 13: Sponge temperature as a function of time for 170° F, 180° F, 190° F, 200° F, and 210° F

As observed in Figure 13, the sponge temperature increased during the period of

transient drying and then remained constant during the period of constant drying. The

transient drying period was longer for higher temperatures.

Plot the drying rate as a function of the moisture content

The next objective was to plot the drying rate as a function of moisture content for

each temperature. These plots are displayed in Figures 14 through 19.

25

0 2 4 6 8 10 12 140

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Drying Rate as a Function of Moisture Content

Period ILinear (Period I)Period ILinear (Period I)Period IILinear (Period II)Period IIILinear (Period III)Period IV

Moisture Content (lbm water/lbm dry sample)

Dry

ing

Rat

e (l

bm/h

)

0

Figure 14: Draying rate as a function of moisture content for 160° F

12 13 14 15 160

0.1

0.2

0.3

0.4

0.5

f(x) = 0.000566089009984671 x + 0.325283689963566



Dry

ing

Rat

e (l

bm/h

)


26

13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 180

0.1

0.2

0.3

0.4

0.5

f(x) = − 0.00971178746339532 x + 0.499779936160003



Dry

ing

Rat

e (l

bm/h

)


12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 170

0.1

0.2

0.3

0.4

0.5

0.6

f(x) = − 0.00844124655141633 x + 0.498765095469353



Dry

ing

Rat

e (l

bm/h

)


27

10 10.5 11 11.5 12 12.5 13 13.5 14 14.50

0.10.20.30.40.50.60.70.8

f(x) = 0.00995894146979939 x + 0.311036608405851



Dry

ing

Rat

e (l

bm/h

)


10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 150

0.1

0.2

0.3

0.4

0.5

0.6

f(x) = − 0.00984542113019335 x + 0.555392420177079



Dry

ing

Rat

e (l

bm/h

)


28

As expected, the zero slopes on each graph indicate a constant drying rate. Figure

14 displays the complete run for 160° F. This graph illustrates how the drying rate

changes as the moisture content in the sponge decreases. The following section will

explain this phenomenon in more detail.

Describe the boundaries for the complete run

Figure 14 was used to determine the boundaries of the drying curve, including the

period limits, the critical moisture contents, the equilibrium moisture content, and the

constant drying rate. The constant drying rate for 160º F was 0.295 lbm/h. Under the

current operating conditions, there is a specific amount of water that cannot be dried,

which is known as the equilibrium moisture content. The point (X5, 0) on the drying

curve represents the equilibrium moisture content, which was 0.355 lbm water/ lbm dry

sample.

The periods were determined by observing major differences in slope. Figure 14

illustrates that in Period I0, the sponge was heated to the wet bulb temperature of the air.

Period I, the constant drying rate period, exhibited a constant temperature. The first

falling rate period, Period II, should have a steeper slope than Period III, the second

falling rate period; however, this was not observed in the results. This discrepancy may

be due to one or two outlying values that affected the best-fit line. Finally, Period IV

represents the final transition in which the equilibrium moisture content is observed. The

drying curve boundaries are displayed in Table 2.

29

Table 2: Periods and critical points for the complete trial at 160° F

PeriodBoundary (lbm water/lbm

dry sample)

Critical Moisture Content

(lbm water/ lbm dry sample)

Period I0 15.502 - 12.602 X0 15.502

Period I 12.459 – 4.661 X1 12.202

Period II 4.661 - 2.661 X2 4.661

Period III 2.661 - 0.578 X3 2.661

Period IV X4 0.578

Determine the heat and mass transfer coefficients during the period of constant drying

The last objective was to determine the heat and mass transfer coefficients during

the period of constant drying for each temperature. These transfer coefficients were

calculated as described in the Sample Calculations. The results are displayed in Table 3.

Table 3: Heat and Mass Transfer Coefficients

Temperature (°F)

Heat Transfer Coefficient

(Btu/(h·ft2·°F))

Mass Transfer Coefficient

(lbmol/(h·ft2·psia))

160 15.09 0.058

170 13.71 0.068

180 13.01 0.062

190 12.94 0.066

200 13.08 0.064

210 12.30 0.065

The heat and mass transfer coefficients should be independent of temperature.

The standard deviation for the heat transfer coefficients was 0.96, and the standard

deviation for the mass transfer coefficients was 0.0035. These standard deviations

30

demonstrate that the transfer coefficients remained relatively constant as the temperature

changed.

Conclusions

The results obtained in the drying experiment were consistent with the original

hypotheses. The group observed that the mass and heat transfer rates were proportional

to the respective concentration and temperature gradients. However, heat and mass

transfer coefficients remained relatively constant as the temperature changed.

The drying rate was based on the recorded weight of the sponge over time, so

these results were not affected by possible inaccuracies in temperature readings. As a

result, the drying rate increased linearly with temperature. The complete drying curve

was plotted for 160° F, from which the periods, the equilibrium moisture content, and the

critical moisture contents were determined. Overall, the results agreed with the theory

and equations discussed earlier in this report.

31

Recommendations

Overall, this experiment was fairly simple to perform once the group became familiar

with the equipment and knew how to set the dryer temperature. However, after finishing

the experiment, Group I found several possible improvements that could be implemented.

Use digital scales and temperature readings connected directly to the computer to

record results. This would make the process of data collection much more

convenient and would also allow for more accurate results collected at exact 1

minute intervals.

Make a note on the blue valve behind the dryer that it is hot when the experiment

is completed.

Write a detailed explanation on how to set the temperature of the dryer.

32

Nomenclature

A = the surface area of the sample (ft2)

H = the height of the sponge (in)

hc = the convective heat transfer coefficient (Btu/(h·ft2·ºF))

kg = the mass transfer film coefficient (lbmol/(h·ft2·psi))

NA = the molar rate of water vaporization (lbmol/h)

PG = the partial pressure of water in the bulk gas phase (psia)

PW = the vapor pressure of water at the interface (psia)

RH = relative humidity

TG = the dry bulb temperature of the air (ºF)

TW = the wet bulb temperature of the air (ºF)

W = the width of the sponge (in)

w = the total mass of the water (lbm)

wd = the mass of the dry sponge (lbm)

ws = the mass of the wet sponge (lbm)

X = the mass fraction of water in the sample (lbm water/ lbm dry sample)

λ = the latent heat of vaporization (Btu/lbm)

33

Literature Cited

1. Traub D. The Drying Curve, Part 2. Process Heating. Available at

http://www.process-heating.com/CDA/Articles/Drying_Files/3b1a99d56e268010

VgnVCM100000f932a8c0. Accessed October 30, 2011.

2. Smith JM, Van Ness HC, Abbott, MM. Introduction to Chemical Engineering

Thermodynamics. 7th ed. New York, NY: McGraw-Hill; 2005.

34

Safety Article Review

Liu F, Wu B, Wei D. Failure modes of reinforced concrete beams strengthened with carbon fiber sheet in fire. Fire Safety Journal [serial online]. October 2009;44(7):941-950. Available from: Academic Search Complete, Ipswich, MA. Accessed October 31, 2010.

The safety article came from the Fire Safety Journal, the official Journal for the

International Association for Fire Safety Science (IAFSS). The article deals with the

strengthening of reinforced concrete (RC) beams using carbon fiber and how mechanical

and heat properties are affected by intense heat (in the case of a fire). The study was

carried out at the South China University of Technology. They took a 4,000-mm beam of

steal reinforced concrete and further strengthened it with carbon fiber sheets on the

outside of the beam. It is shown that elevated temperature may cause a change in the

failure mode of RC beams strengthened with carbon fiber sheet (CFS), as flexural failure

at room temperature can be transformed into shear failure in fire.

Reinforced concrete strengthened with carbon fiber sheets is becoming a common

method used in bridges and buildings needing additional strength as they begin to age due

to fatigue and as demands become higher. The problem that has been discovered is that in

the event of a fire, the carbon fiber bond to the concrete fails and all additional strength

the carbon fiber originally gave to the concrete is negated, thus allowing the concrete to

fail in a more catastrophic way (shearing, rather than flexing). At room temperature, and

at temperatures up to 350°C, steel will retain near 100% of its strength and only

experiences a decrease in strength when temperatures reach 700° C. Carbon fiber, on the

other hand, starts to lose strength via the bond between the carbon and the concrete

failing at temperatures as low as 70°C.

35

In addition to analyzing the underlying science behind this phenomenon, the

authors of this article made several suggestions. They suggested that insulation could

help the building, but only to a certain extent, as a flexing failure is much safer in a fire

than a complete shearing failure. They also suggested that a building will exhibit different

behavior than the one illustrated in their experiment. In a building, there are many more

supporting beams that could transfer heat and mechanical strength; whereas the

experiment took only one beam with the entire load going to it. Finally, they emphasized

the need for further research in more realistic conditions, taking into account more beams

so as to better model a real building.

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APPENDIX A: SAFETY ARTICLE

APPENDIX B: SPREADSHEET CALCULATIONS

APPENDIX C: ORIGINAL DATA SHEETS

Drying Final Report

Documents

Transcript of Drying Final Report