Download - 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
Moisture Content as a Function of Time
Time (min)Moi
stur
e Co
nten
t (lb
m w
ater
/lbm
dry
sam
ple)
Figure 5: Moisture content as a function of time for 170° F
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
Moisture Content as a Function of Time
Time (min)Moi
stur
e Co
nten
t (lb
m w
ater
/lbm
dry
sam
ple)
Figure 6: Moisture content as a function of time for 180° F
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
Moisture Content as a Function of Time
Time (min)Moi
stur
e Co
nten
t (lb
m w
ater
/lbm
dry
sam
ple)
Figure 7: Moisture content as a function of time for 190° F
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
Moisture Content as a Function of Time
Time (min)Moi
stur
e Co
nten
t (lb
m w
ater
/lbm
dry
sam
ple)
Figure 8: Moisture content as a function of time for 200° F
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
Moisture Content as a Function of Time
Time (min)Moi
stur
e Co
nten
t (lb
m w
ater
/lbm
dry
sam
ple)
Figure 9: Moisture content as a function of time for 210° F
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
Drying Rate as a Function of Moisture Content
Moisture Content (lbm water/lbm dry sample)
Dry
ing
Rat
e (l
bm/h
)
Figure 15: Draying rate as a function of moisture content for 170° F
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
Drying Rate as a Function of Moisture Content
Moisture Content (lbm water/lbm dry sample)
Dry
ing
Rat
e (l
bm/h
)
Figure 16: Draying rate as a function of moisture content for 180° F
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
Drying Rate as a Function of Moisture Content
Moisture Content (lbm water/lbm dry sample)
Dry
ing
Rat
e (l
bm/h
)
Figure 17: Draying rate as a function of moisture content for 190° F
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
Drying Rate as a Function of Moisture Content
Moisture Content (lbm water/lbm dry sample)
Dry
ing
Rat
e (l
bm/h
)
Figure 18: Draying rate as a function of moisture content for 200° F
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
Drying Rate as a Function of Moisture Content
Moisture Content (lbm water/lbm dry sample)
Dry
ing
Rat
e (l
bm/h
)
Figure 19: Draying rate as a function of moisture content for 210° F
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.
36
APPENDIX A: SAFETY ARTICLE
APPENDIX B: SPREADSHEET CALCULATIONS
APPENDIX C: ORIGINAL DATA SHEETS
37
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