California State Polytechnic University, Pomona
Department of Chemical & Materials Engineering
CHE 333L
Transport Laboratory II
LABORATORY GUIDE
This manual was prepared from the materials and
information provided by the Cal Poly Pomona
Chemical Engineering Faculty and Staff
Revised December, 2006 by C.L. Caenepeel
(Modified by Y. Lee for Fall 2009,
Modified by K. Forward for Winter 2014)
1
CHEMICAL ENGINEERING LABORATORY
The Chemical Engineering Laboratory courses are set up as an open-ended learning
experience rather than the traditional data sheet oriented laboratories that are often
performed in other courses.
Pre-Lab Preparation
Read the current assignment and be familiar with the theory relevant to the experiment
and the equipment necessary to take the required data. Read the appropriate sections of
the textbook and references such as Perry's Handbook. After reading the background of
the experiment, prepare in writing, a Pre-Lab Plan. This exercise is intended to provide
the preparation necessary to undertake a successful experimental study.
The written plan should include a sketch of the experimental equipment, showing vessels,
interconnecting piping, valves, and relevant instrumentation. Communicate the purpose
and safe operation of each of these equipment items before starting the experiment. The
correct analysis of data, its accuracy, and correction for nonstandard operating conditions
all require a thorough understanding of the instrumentation. The written plan should
discuss the independent and dependent variables, along with the appropriate technics for
measuring these variables. The plan should address the experimental procedure and the
sequence of operations. The plan should describe the method for collecting data and the
appropriate theory related to the experiment. This pre-lab must be completed before
performing any experiments. Include the pre-lab as an appendix in the laboratory report.
In the Lab
Attendance: All students are to report to the lab at the start of the period. Attendance
in all sessions for the full 2 hours 50 minutes of each period is required. Unauthorized
absences for part or all of any laboratory session will result in a reduced course grade.
Normally, work will be performed in the lab; work in another area requires prior approval
by the instructor.
Safety and Housekeeping: Each student team must complete the safety review form for
each experiment and turn in with the pre-lab report. Good safety practices must be
observed at all times in the laboratory. This practice includes the wearing of proper
clothing, footwear, and eye protection. All equipment must be safely operated and all
chemicals must be safely handled. Broken or damaged equipment should be reported to
the instructor immediately. All equipment should be cleaned and returned to its proper
location after finishing the day's work. A clean laboratory is the responsibility of all
group members. Do not leave the lab until it is clean.
2
Lab Rules:
1. Come to lab dressed properly. Appropriate dress is required for safety reasons. Wear
close toe shoes. Long pants are required. No sleeveless shirts or tank tops are permitted,
long sleeve shirts are preferred. Do not wear a hat. Do not wear long flowing clothes
(that includes a tie). Long, lose hair must be restrained. Wear safety glasses.
2. At all times good safety practices must be observed in the laboratory. An individual,
who violates this rule will not be permitted in the lab.
3. Come prepared and bring the Pre-Lab Plan.
Collection and Analysis of Experimental Data in Laboratory Notebook
Every group must have a lab notebook (with numbered pages). During each lab, any
notes and measurements should be recorded. Each page of the notebook should be
signed by the data taker and witnessed by a group member and the instructor. Original
data sheets should appear in the lab report appendix while the carbon copies should be
attached in the appendix of the lab report. In the lab notebook:









Write in ink and record all observations directly in the notebook.
Do not erase. If necessary line out errors with one line
At the top of each page put the date and the experiment name
When a page filled, sign with date
Never record a calculation, dimension or note on a loose sheet of paper.
Never write on a page after being signed.
Rotate recording among group members. The instructor should sign the notebook
after each lab session.
Sketches of experimental apparatus should be part of notebook. All important
dimensions should be recorded.
Always record the reading that was actually measured.
3
Laboratory Report
Many organizations that employ engineers have standardized their calculation methods
for project progress reports. This is done to facilitate communication within the
organization and to provide better control of work quality. Standardization permits
routine checking of work as well as the opportunity to switch people to the tasks that are
the most urgent.
The written report should have the following structure:
Title Page — The title page should give the title or subject of the experiment, group
number, group member names, course title, course number, course section, date, and
university and department names (See page 3).
Abstract — The abstract should be a summary of the experiment, results and conclusions.
It is usually one paragraph to one page in length. It should briefly summarize the
experimental goal and methodology, results and conclusions. It should not contain
equations, figures, tables, graphs, or references. An abstract should be written so that the
maximum amount of information is contained in the minimum amount of space.
Introduction/Objective — This section states the importance of the experiment and
motivation for performing the laboratory. Also, the goal or objective of the experiment
should be included.
Background — In this section, any theory for the experiment should be included along
with references. Any equations required for the calculations should be included, along
with explanations for each of the parameter.
Procedure — This section should include a brief description of the equipment and
operating parameters, and a sequential reporting of the experimental procedure in the
PAST TENSE and PASSIVE VOICE.
Results and Discussion—This should be the most extensive portion of the report;
concentrate on making this section informative and readable. Remember that results
are measured values in the lab or calculations based on these numbers. Present the
results of the experimental study here. Use graphs and tables with calculated error to
summarize the information if possible. Critically analyze the results, both magnitudes and
trends, and compare them with literature values. Theory should always provide the
underlying basis for this analysis. Provide sufficient detail to support all of the
conclusions in the next report section. Large amounts of raw data should be referenced
from the appendix and not included in this section.
Conclusions—State the conclusions or solution to the problem, based on the analysis of
the results. Remember that conclusions are opinions based on the analysis of the
measured data or values calculated from the data. These opinions are always formed after
comparing the experimental data with literature values and with predicted values based
4
on a theoretical study of the system. State the possible applications of the results and
make recommendations for improving the experiments if necessary.
References—Cite any references used. This is required in all reports.
Appendix—Group all supplemental information in this section. Include the original data
sheets and sketches. Include a detailed sample calculation. List each equation used, with
definitions for variable symbols, and then substitute data values, with units, for each
variable. These calculations should be applied to one data set in a logical progression
through all the equations used in data analysis. Tables from Excel are not considered a
sample calculation.
Write in a readable style and be as concise and clear as possible. Clear and effective
writing will always require a draft copy, which should be reviewed, corrected, and
improved before typing the final version. Good writing is expected, and it will be an
important criterion for establishing the grade of the lab report.
Unless given other instructions, students will submit group laboratory reports. Each
group member is responsible for the entire written report. Inclusion of work from
other, non-referenced sources will result in an "F" grade. Reports must be written in the
format previously described. All reports must be double-spaced, typed.
Laboratory reports are due one week after the scheduled completion of experimental
work, at the beginning of the laboratory period. Late reports will be penalized 20% per
day. A ten minutes late report will be counted as one day late.
How to put together a laboratory report
1. ORGANIZE !!
2. Laboratory data. (Read the section: Collection and Analysis of Experimental Data)
a. What is the error in the measurement of the variables?
b. Identify runs as 1, 2, 3, etc. a different number for each run.
c. Do all of this during the laboratory period.
3. Manipulate laboratory data to perform calculations.
4. Calculate results; for example Diameter, T, k, Cp.
a. What is the error of a replicated experiment?
5. Data and sample calculations are included in the Appendix.
6. Correlate the experimental results with each other and with the literature or theoretical
values.
a. Graphs are best if appropriate.
b. If not a graph, then a table.
5
c. Draw a curve through the data points of the graph. Draw the appropriate graph
(straight line or curve) according to theory of the experiment.
d. Compare experimental results to any literature values or theory. Include the
appropriate theoretical correlation.
7. Read the prescribed laboratory report format and FOLLOW IT.
8. Number pages.
9. Number and title Graphs, Tables, Figures, and Appendix items
10. Aim to be "complete and concise" in the body of the report.
11. Be aware of significant figures.
12. The texts in reports will be read first. Any graph, table, figure or Appendix item
should first be mentioned in the text. Be specific and state; for instance, "see Figure 3 for
∆T vs. time". Figure 3 should then appear on the next possible page.
13. Note that raw data tables or spreadsheets do not make concise, readable result tables
(included in Appendix)
14. Do not forget the title page.
6
California State Polytechnic University, Pomona
Chemical and Materials Engineering
CHE 333L – Transport Laboratory II
Winter Quarter, 2014
EXPERIMENT #1
Cooling Tower Characteristics
INSTRUCTOR:
Keith Forward
SECTION 10
GROUP #1
Einstein, Mary
Smith, Steven
Doe, John
DUE DATE: January 28, 2014
TITLE PAGE
ABSTRACT
INTRODUCTION/OBJECTIVE
BACKGROUND/PROCEDURE
RESULTS & DISCUSSION
CONCLUSIONS & RECOMMMENDATIONS
REFERENCES/APPENDIX
PRE-LAB
TOTAL
7
(5) _______
(10) ______
(10) ______
(20) ______
(25) ______
(10) ______
(10) ______
(10) ______
(100) _____
Experiment 1: Cooling Tower Characteristics
You are to perform an energy balance and determine the number of overall gas transfer
units NOG and the overall gas mass transfer coefficients KGa for a small cooling tower
(designed and constructed by Chris Kaya and Jessica Anderson, Chemical Engineering
students at Cal Poly Pomona,) in the Unit Operation Laboratory. When you develop your
experimental design you must give attention to the fact that for a specified liquid flowrate
there is a minimum gas flowrate. Use the results of this experiment to design an
industrial cooling tower of the same packing. You are also to do cooling tower
performance measurements on the cross flow cooling tower located next to the boiler that
provides the steam for the Unit Operations lab. Execute the experiment that determines
the height of this tower if it used the same packing material as the Kaya/Anderson
cooling tower?
Cooling Tower
Water
Hy2,TL2
z
Packing
materials
Hy, T L
Hy1, T L1
Air
Fig. 1 Schematic representation of the cooling tower in the lab.
The height of contact between water and air can be obtained from the following equation
z=
G
M B K G aP

H y2
H y1
dH y
H *y  H y
In this equation, Hy* is the enthalpy (kJ/kg dry air) of saturated air corresponding to the
liquid temperature TL. Hy is the enthalpy of the air in the tower at the location in the
tower where the liquid temperature is TL. Hy* versus TL is the equilibrium curve in Figure
2. Please note that for a given liquid flowrate to the cooling tower there is a minimum gas
flowrate. This constraint assures that the equilibrium curve is always above the operating
line and therefore the two curves neither touch nor cross one another.
8
200
Operating line
Equilbrium curve
180
160
Enthalpy Hy(kJ/kg)
Hy2
140
120
100
80
Hy1
60
28
TL1 30
32
34
36
Liquid T(C)
38
40
42
TL2
44
Figure 2. Temperature enthalpy diagram and operating line for cooling tower.
G is the dry air flow in kg/sm2. MB is the molecular weight of air (28.97). KG is the
overall mass transfer coefficient based on the gas phase in kmol/sm2atm. a is the
interfacial area per unit volume of packed section in m2/m3. KG and a are normally
combined together as KGa since it is difficult to determine them separately. P is the
operating pressure of the tower in atmospheres. The number of overall gas transfer unit
NOG is defined as
NOG =

H y2
H y1
dH y
H *y  H y
Hy1 is the enthalpy of the inlet air that can be determined from the following procedure:
1) Measure the dry bulb inlet air temperature T1.
2) Measure the wet bulb inlet air temperature Tw1 by using a sling thermometer at
a location far away from the outlet air.
3) Determine the water vapor pressure, Pvap, at the wet bulb temperature Tw1. You
can use the equation from the following Matlab program or determine by it by hand.
Include in this program tabulated water vapor pressure data and the Antoine Eqn. for
estimating the vapor pressure of water at your experimental operating temperatures.
--------- Matlab function to determine water vapor pressure -----------------9
function ff=water_vap(T)
% Water vapor pressure in bar, T in C
%
TK=T+273.15;
Tc=647.3;Pc=221.2; % Tc in K, Pc in bar
vpa=-7.76451;vpb=1.45834;vpc=-2.7758;vpd=-1.23303;
x=1-TK/Tc;
tem=vpa*x+vpb*x.^1.5+vpc*x.^3+vpd*x.^6;
ff=Pc*exp(tem./(1-x));
--------------------------------------------------------------------------------------------4) Determine the saturated humidity hw at the wet bulb temperature Tw1.
hw =
M A Pvap
M B P  Pvap
In this equation MA & MB is the molecular weights of water (18.02) and air(29).
5) Evaluate the humidity h of the inlet air from
h=
(1093  0.56Tw1F )hw  0.24(T1F  Tw1F )
1093  0.444T1F  Tw1F
In this equation T1F and Tw1F are the dry and wet bulb temperatures of the inlet air in
degree F. hw is the humidity from step (4).
6) Determine Hy1 (in kJ/kg dry air) from the following equation with the inlet air
temperature in degree C.
Hy1 = (1.005 + 1.88h)T1 + 2501.4h
The air enthalpy at any location in the tower can be determined from an adiabatic energy
balance
G(Hy  Hy1) = LCpL(TL  TL1)
In this equation L is the water flow rate in kg/sm2 and CpL is the heat capacity of water
(4.187 kJ/kgC). At TL2 we obtain Hy2.
We now need to evaluate Hy* at TL corresponding to Hy by
1) Evaluate the water vapor pressure Pvap at TL.
2) Determine the saturated humidity hw at the liquid temperature TL.
10
M A Pvap
M B P  Pvap
is then evaluated from
hw =
3) Hy*
Hy* = (1.005 + 1.88hw)TL + 2501.4hw
If you need to integrate numerically the expression

H y2
H y1
dH y
use numerical
H *y  H y
integration;e.g., trapezoidal rule or the 7 points Simpson’s rule.
H y2
dH y
H *y  H y
NOG =

NOG =
dH y
[f(1) + 4f(2) + 2f(3) + 4f(4) + 2f(5) + 4f(6) + f(7)]
3
H y1
1
1
, f(7) = *
H  H y1
H y2  H y2
Also note that if the equilibrium and operating line curves are both linear, there is an
analytical solution to the integral used to solve for NOG.
where
f(1) =
*
y1
Minimum Data Analysis
1. Hy & Hy*vs TL plots for each operational liquid flowrate indicating the points
corresponding to the minimum gas flowrate. Determine the minimum air flowrate for
each water flowrate you are using in your experimental design.
2. Determine the amount of heat transfer (KJ/min water cooling) for each experiment that
occurs by methods other than increasing the temperature and humidity of the air.
3. Plot a graph of NOG versus air flow rate at various water flow rates.
4. Plot a graph of KGa versus air flow rate at various water flow rates.
5. Determine the maximum cooling rate for the tower.
6. Base the design of the new cooling tower for the boiler that uses an air flow rate of 1.4
times the minimum value. You may need to discuss with the course instructor the design
reduction in water temperature for this tower.
References
1. Geankoplis, C. J., Transport Processes & Separation Process Principles, Prentice Hall,
2003, pg. 565 & pg. 645
2. Mc Cabe W. L. et al , Unit Operations of Chemical Engineering, McGraw-Hill, 2001,
pg. 608
11
Experiment 2: Double-pipe Heat Exchanger
We have recently purchased a double-pipe heat exchanger and wish to check on its
performance. We plan to use the exchanger to study the variation of the overall heat
transfer coefficient with flow rate. The exchanger has been piped to permit counter and
parallel flow operation. The tube outer diameter is 15 mm with a wall thickness of 0.7
mm. The shell outer diameter is 22 mm with a wall thickness of 0.9 mm. The length for
heat transfer is 1.5 m.
Determine the overall heat transfer coefficient for the exchanger using both experimental
data and generalized correlations. Would you expect the overall heat transfer coefficient
to be different for counter and parallel flow operation?
The overall heat transfer coefficient can be based on the inside or the outside surface area
of the tubes according to the following equation
1
1
1
1
r r
1
1
=
=
+
+ o i +
+
U i Ai
U o Ao
hi Ai
hdi Ai
kAlm
hdo Ao
ho Ao
You can use the correlations given in Incropera for flow inside a pipe (Ref. 1, pg. 508).
Be sure to use the equivalent diameter for the flow in the annular space.
Double-pipe Heat Exchanger
The heat transfer between a hot and a cold streams in a concentric tube heat exchanger is
Q = UATlm = UoAoTlm = UiAiTlm
(1)
where
U = overall heat transfer coefficient
A = surface area normal to direction of heat transfer
Tlm = average driving force for heat transfer = average temperature
difference between two streams.
Thi
Thi
Tho
Tco
Tho
Tco
Tci
Tci
(a) Parallel flow
(b) Countercurrent flow
12
Fig.1 Flow arrangements in heat exchanger
For parallel flow, Tlm is defined by the following equation
Tlm =
(Thi  Tci )  (Tho  Tco )
T  Tci
ln hi
Tho  Tco
(2a)
For countercurrent flow, Tlm is defined by the following equation
Tlm =
(Thi  Tco )  (Tho  Tci )
T  Tco
ln hi
Tho  Tci
(2b)
If there is no heat loss to the surrounding, all the energy leaving from the hot stream will
be transferred to the cold stream, then Q can also be evaluated from
Q = m h Cph(Thi - Tho) = m c Cpc(Tco - Tci)
where
(3)
m h = mass flow rate of the hot stream
m c = mass flow rate of the cold stream
Experimental value of U can be calculated from equation (1) by measuring the inlet,
outlet temperatures, and the flow rates of the hot and cold streams of a heat exchanger
with known surface area for heat transfer. The overall heat transfer coefficient can also be
estimated from the following relation
1
1
1
1
r r
1
1
=
=
+
+ o i +
+
U i Ai
U o Ao
hi Ai
hdi Ai
kAlm
hdo Ao
ho Ao
where
hi = heat transfer coefficient for the inner tube
hdi = fouling coefficient for the inner tube
hdo = fouling coefficient for the outside surface of the inner tube
ho = heat transfer coefficient for the annular space
ri = inside radius of the inner tube
ro = outside radius of the inner tube
Ai = inside surface area of the inner tube
Ao = outside surface area of the inner tube
Alm = (Ao - Ai)/ln(Ao/Ai)
13
(4)
ho
hdo
Annular space
hdi
hi
ri ro
Fig.2 Concentric tube heat exchanger
For laminar flow in a tube, the average heat transfer coefficient might be estimated from
the following correlation
NuD ,l = 3.66 +
0.0668( D / L) Re D Pr
2/3
1  0.4( D / L) Re D Pr 
(5)
For turbulent flow, the heat transfer coefficient might be estimated from the following
correlation
NuD ,t = 0.023ReD4/5Prn
(6)
where n = 0.4 for heating (surface temperature > fluid temperature) and 0.3 for cooling
(surface temperature < fluid temperature).
For transitional flow 2,300 < ReD < 10,000
( NuD )10 = ( NuD ,l )10 + (
exp[( 2,200  Re D ) / 365]
Nu 
2
D ,l
+
1
Nu 
2
)-5
(7)
D ,t
where NuD ,l and NuD ,t are the laminar and turbulent Nusselt numbers given in equations
(5) and (6)1.
For noncircular cross section, the above correlations may be applied by using an effective
or hydraulic diameter
Dh = 4Ac/P
1
(8)
Kaviany, M. Principle of Heat Transfer, Wiley, 2002, pg. 737
14
where Ac and P are the flow cross-sectional area and the wetted perimeter, respectively.
This diameter should be used in calculating ReD and NuD. For flow in an annular space,
the effective diameter is
Dh =
 ( Do2  Di2 )
= Do  Di
 ( Di  Do )
(9)
The maximum amount of heat transfer Qmax between a hot and a cold stream in heat
exchanger is defined as
Qmax = Cmin(Th,i – Tc,i)
(10)
First the cold and hot fluid heat capacity rates Cc and Ch, respectively, are defined as
Cc = m c Cpc; Ch = m h Cph
(11)
The minimum heat capacity rate Cmin is then defined to be Cc or Ch whichever is smaller.
The effectiveness  of a heat exchanger is defined by
=
Q
Qmax
(12)
Experimental Procedure
Turn on the heater for the water. Set the temperature of the water to about 75oC; do not
exceed 80oC. While the water is heating calibrate the cold-water flow meter. The flow
meter is read from the top of the float.
Set the valves for counter flow using the diagram on the exchanger or T.K. Nguyen
website (http://www.csupomona.edu/~tknguyen/che435/heat.htm). Set the hot water flow
rate at half the maximum allowable value and vary the cold water flow rate. At each
setting, record the inlet, outlet, and middle temperatures of the hot and cold streams when
the system reaches steady state. At least five cold water readings should be measured.
Repeat the procedure at half the maximum allowable value for the cold water flow rate
while varying the hot water flow rate. Repeat the entire procedure for parallel flow.
Minimum Data Analysis
1. At a fixed hot water flow rate, plot a graph of experimental U versus ReD using Eq. (1)
for both parallel and counter flow.
15
2. At a fixed cold water flow rate, plot a graph of experimental U versus ReD using Eq.
(1) for both parallel and counter flow.
3. Look up the values of hdi ,hdo and k from reference. Calculate hi and ho from
correlations as represented by Eq. (5), (6) and (7). Repeat (1) and (2) for calculated U
using Eq. (4).
5. Plot the effectiveness of the heat exchanger for both parallel and counter flow as a
function of ReD as in (1) and (2). Note: You should use Q calculated by the following
equation
Q = 0.5[ m h Cph(Thi - Tho) + m c Cpc(Tco - Tci)]
6. Discuss the limitations of Eqs. (5) and (6).
References
1. Incropera, F. P. and DeWitt D. P, Fundementals of Heat and Mass Transfer, Wiley,
2002.
2. Hanesian, D. and Perna A. J., “A Laboratory Manual for Fundamentals of Engineering
Design”, NJIT.
3. Walas S. M., “Chemical Process Equipment, Selection and Design”, Butterworths,
1988.
16
Experiment 3: Gas Absorption Column, Operational
Characteristics
You are to study the characteristics of a gas absorption column and its operational
effectiveness. You will determine: (1) the pressure drop across a wet column as a
function of air flow rate and water flow rate (2) the rate of absorption of carbon dioxide
(CO2) in air by sodium hydroxide (NaOH) solution at various CO2 concentration and
NaOH concentration.
You will examine the equipment and plan your experiment carefully. Find out how to
use the gas analysis equipment attached to the column to measure CO2 concentration in
the gas phase. Devise a titration method for measuring the amount of CO 2 absorbed by
the NaOH solution. These measurements are necessary to perform a CO2 material
balance on the column.
In your analysis, you will calculate the overall mass transfer coefficient, KOGa. at
different
gas and liquid flow rates. With the calculated KOGa, you will be able to design an
industrial column. You will determine flooding conditions for the column.
Suggested flow rates for pressure drop experiments
Air – 50 to 200 liters/min
Water 0-4 liters/min
Suggested average flow rates for CO2 absorption experiments
CO2 - 3 liters/min
Air - 30 liters/min
? M NaOH solution* - 3 liters/min
For the mass transfer analysis portion of your experiment please do the following:
 Select a NaOH concentration that is low enough to minimize the consumption of
chemicals and yet is high enough to absorb an appreciable amount of CO2 during
about 1 hour operation of the tower.
 Carefully read the gas absorption operations manual. This manual not only outlines
how to operate the equipment but also how to analyze the experimental data in order
to determine the change in CO2 concentration of the gas phase and the NaOH and
Na2CO3 concentrations of the liquid phase.
Minimum Data Analysis for Gas Absorption
 Develop a material balance analysis based on appropriate gas and liquid phase
analysis. Explain the discrepancies among these three material balances.
 For each set gas flowrates determine the minimum liquid flowrate in order to assure
that the equilibrium and operating lines do not touch or intersect each other.
 Develop plots that show the effect of liquid and gas flowrates on the values of NOG
and KGa
17
You should explain why packings are effective in mass transfer. You should also discuss
the advantages and disadvantages of packed columns versus plate columns.
You will find a good discussion on packed column characteristics in the text by Henley
and Seader(11) and a comparison of packed and plate columns by Henry Kister(10)
In a packed column used for gas-liquid contact, the liquid flows downward over the
surface of the packing and the gas flows upward in the void space of the packing
material. A low pressure drop and, hence, low energy consumption is very important in
the performance of packed towers. The packing material provides a very large surface
area for mass transfer, but it also results in a pressure drop because of friction generated
between the fluids and the packings.
The performance of packed towers depends upon the hydraulic operating characteristics
of wet and dry packing. In dry packing, there is only the flow of a single fluid phase
through a column of stationary solid particles. Such flow occurs in fixed-bed catalytic
reactor and sorption operations (including adsorption, ion exchange, ion exclusion, etc.)
In wet packing, two-phase flow is encountered. The phases will be a gas and a liquid in
distillation, absorption, or stripping. When the liquid flows over the packing, it occupies
some of the void volume in the packing normally filled by the gas; therefore, the
performance of wet packing is different from that of dry packing.
For dry packing, the pressure drop may be correlated by Ergun equation
 P 


 h 
 Dp gc 


  f v s 2 
 3 
1

 = 150
+ 1.75
N Re
1   
(1)
where
P
h
Dp
f
vs
conditions

= pressure drop through the packed bed
= bed height
= particle diameter
= fluid density
= superficial velocity at a density averaged between inlet and outlet
= bed porosity
NRe = average Reynolds number based upon superficial velocity
D p vs  f

When the packing has a shape different from spherical, an effective particle diameter is
defined
Dp =
6V p
6(1   )
=
As
Ap
(2)
18
where
As
= interfacial area of packing per unit of packing volume, ft2/ft3 or m2/m3
The effective particle diameter Dp in Eq. (1) can be replaced by sDp where Dp now
represents the particle size of a sphere having the same volume as the particle and s the
shape factor. The bed porosity, , which is the fraction of total volume that is void is
defined as


volume voids
volume of entire bed
volume of entire bed  volume of

volume of entire bed

R 2h 
=
particles
weight of all particles
particle density
R 2h
(3)
where R = inside radius of column, As and  are characteristics of the packing.
Experimental values of  can easily be determined from Eq. (3) but As for non-spherical
particles is usually more difficult to obtain. Values of As and  are available for the
common commercial packing in the various references (Ref. 2, 4). As for spheres can be
computed from the volume and surface area of a sphere.
For wet packing, the pressure drop correlation is given by Leva (Ref. 7)
 P 
L /  L

 =  10
 h 

  G
2
v

v



(4)
where P is the pressure drop (psf), h is the packing height (ft), L is the liquid mass flow
rate per unit area (lb/hr-ft2), Gv is the gas mass flow rate per unit area (lb/hr-ft2), L is the
liquid density (lb/ft3), V is the gas density (lb/ft3), and  and  are packing parameters
(Ref. 5, 7).
For each column studied, determine the pressure drop at various air flow rates (correct
rotameters for pressure and temperature). Keep the liquid flow rate constant at different
gas rates.
Table 1. Packing Information
R: Raschig Rings, B: Berl Saddle
--------------------------------------------------------------------------------------------------------Norminal
Approximate Approximate Approximate
Effective
Size,
Number per Weight per
Surface area Percent Free Diameter
Inch
Cu. Ft.
Cu. Ft., lb
Sq. Ft./Cu. Ft. Gas Space Dp, Inch
19
--------------------------------------------------------------------------------------------------------R: 1/4
88000
46
240
73
0.22
R: 5/16
40000
56
145
64
0.31
R: 3/8
24000
51
134
68
0.35
B: 1/4
113000
56
274
60
0.23
B: 1/2
16200
54
142
63
0.42
B: 3/4
5000
48
82
66
0.58
--------------------------------------------------------------------------------------------------------Minimum Data Analysis
1. Plot a graph of P/h versus Gv for the column and compare with published data
(Ref. 5, 7).
2. For the runs with wet packing correlate your data by Eq. (4). Determine your measured
values of  and .
Design Problem
Assuming that an air /CO2 (9%) stream (10,000 liters/min @ stp) is to be treated
commercially to remove 95% of the CO2. Design one or more gas absorption towers to
accomplish this. Your design must include, the type of packing, the diameter of the
tower and the height of the packing. Also include other essential elements in your
design.
References
1. Middleman, Stanley, An Introduction to Fluid Dynamics, Wiley, 1998, pg. 411
2. Mc Cabe W. L. et al , Unit Operations of Chemical Engineering, McGraw-Hill, 1993,
pg. 689
3. Hanesian, D. and Perna A. J., “A Laboratory Manual for Fundamentals of Engineering
Design”, NJIT.
4. Perry, J. H., Chemical Engineers’ Handbook, McGraw-Hill, 1984, pg. 18-23
5. Wankat, P. C., Equilibrium Staged Separations, Elsevier, 1988, pg.420
6. Leva M., Chem. Eng. Prog. Symp. Ser. 50(10): 51 (1954).
7. Max S. Peters and Klaus D. Timmerhaus, Plant Design and Economics For Chemical
Engineers, McGraw-Hill, 1991, pg. 694.
8. Foust, "Principles of Unit Operations"
9. Leva, "Tower Packings and Packed Tower Design", United States Stoneware
Co.
10. Henry Kister “ Distillation Operation”; “Distillation Design”
11. Seader, J. D. and Henley E. J., Separation Process Principles, Wiley, 1998, pg. 325
20
Experiment 4: Water Heater Efficiency
You are to explain the operation of a hot water heater. A working model and various
control components are available in the laboratory. Develop a schematic representation of
the control system and measure the appropriate variables. The heater is designed to use
natural gas as fuel. In this area the Southern California Gas Company (Sempra Utilities)
indicates that the higher heating value of their fuel on 3/12 & 3/13/07 were 1022 & 1021
Btu/ft3 at 60oF and 1 atm. The following compositions were also provided:
Component
3/12mole %
3/13mol%
N2
0.82
0.77
Carbon dioxide, CO2
0.97
1.02
Methane, CH4
95.66
95.74
Ethane, C2H6
2.01
1.94
Propane, C3H8
0.36
0.35
Isobutane,i-C4H10
0.06
0.06
n-Butane,n-C4H10
0.07
0.07
Isopentane,i-C5H12
0.02
0.02
n-Pentane,n-C5H12
0.01
0.01
C6 +
0.03
0.03
Use the composition data provided to computer the lower heating value of the natural
gas.
Please check the heating value and the efficiency of the heater over a range of water flow
rates and gas rates. Use an enthalpy balance to approximate the heat loss to the
surroundings exclusive of the heat exiting up the stack. This will give us an idea of the
minimum space and air requirements needed in an enclosure for the heater. What gas
pressure do we need normally? If equipment is available, do an analysis of the stack gas
from the heater and determine the excess air being introduced with the burner
arrangement supplied. (Please note that the Bacharach gas analyzer uses a sensor to
measure % O2, CO(ppm) and NOx(ppm) in the stack gas. This analyzer also measures
the temperature of the stack gas and uses assumed composition of the natural gas &
enthalpy change rate of the heated water to approximate the CO2 content of the flue gas,
the % excess air & the efficiency of the natural gas burner.
You are also to perform any other standard tests used to evaluate water heaters. Compare
your ratings with those claimed for your water heater. Use this experience to perform
an energy balance on the boiler that provides steam for our Unit Operations lab.
21
Heater Efficiency
Flue gas
Inlet water
Outlet water
Inlet air and gas
Fig. 1 Hot water heater
The schematic of the water heater used in the Unit Operation Laboratory is shown in
Figure 1. The heat supplied to the water can be obtained from an energy balance over the
gas streams
Qsupplied =
n AR Hˆ r0
A
+
 n Hˆ
i
i

 n Hˆ
i
i
(1)
inlet
outlet
where
A
= any reactant or product
nAR = moles of A produced or consumed in the process
A = stoichiometeric coefficient of A
Reference conditions (Ref. 1): reactant and product species at To in the state of
aggregation for which Hˆ r0 is known, and nonreactive species at any convenient
temperature. The first term on the right hand side of Eq.(1) can also be obtained from the
heating value of the gas. The heat received by the water is given by
Qreceived = nw,out Hˆ w,out  nw,in Hˆ w,in
22
(2)
Experimental data can be collected by the following suggested procedure:
Starting up the Water Heater:
Light the pilot if necessary. The water heater in the Unit Operation Lab is similar to
the set-up shown in Figure 2.
Hot Air
Outlet
Valve
Flue
Stack
Thermom
.eter
Cold
Water
Flow
Meter
Hot
Water
Pressure
Gauge
Gas Meter
Natural Gas
Inlet
Figure 2 Water heater experiment.
23
Gas Analyzer Preparation:
1. If it needs to be charged, plug in the unit and turn it on.
2. Before operating, read the summary to become familiar with the operation of the
gas analyzer.
3. Set the mode at "span" and take a reading at normal atmospheric condition. This
calibrates the instrument. The unit should come to reset once it is finished. The unit
is now ready to take readings.
Data Collection:
1. Read and record atmospheric temperature and pressure.
2. Adjust the water and gas rates to the desired values. Use the calibration graph to
determine the water flow rate. Determine the volumetric gas rate. Record these flow
rates.
3. Read and record the gas pressure & temperature.
4. Allow the system to reach steady temperature readings. Usually this will take
15-20 minutes.
5. Record the temperature readings of the inlet and outlet streams of water and gas.
A digital thermocouple should be used to take the temperature of the gas exiting the
stack. The water temperatures should be taken both by the water heater thermometers
and by thermometers submerged in the flowing streams (at the inlet and outlet). Note
any difference between these two temperatures.
6. Take readings from the gas analyzer by inserting the analyzer rod in the space
between the heater and stack duct. To begin the reading process, press "start".
7. Keep the rod over the opening until a constant temperature reading is displayed.
This should take about 2-3 minutes. Record the outlet gas temperature (duct
temperature), percent oxygen, percent carbon dioxide, percent efficiency, and percent
excess air. Also note the CO and NOx levels.
8. Repeat steps 1-7 of data collection for other water and gas flow rates. To save
time, take data at constant gas rate and varying water rate, then change the gas rate.
Attempt to perform a few replicate experiments to establish the reproducibility of this
experimental apparatus.
Minimum Data Analysis
1. Use the heat balance to evaluate |Qreceived/Qsupplied| for various air flow rates and
water flow rates. Compare these values with the values reported by the gas
analyzer.
2. Verify the higher gas heating values provided by Sempra Utilities from the heat
of combustion. Also compute the lower heating value of the natural gas.
3. Computer the % excess air, % CO2 in stack gas, and compare with the values
reported by the gas analyzer.
4. Report the approximate results of the energy balance on the boiler that provides
steam to the Unit Operations lab.
References
24
1. Felder R. M. and Rousseau R. W., Elementary Principles of Chemical Processes,
Wiley, 2000, pg. 450
25
Experiment 5: Gas Separation Membrane
Figure 1. Hollow-fiber module used for air separation.
Gas separation with polymer membrane is becoming an important component of separation
technology1. Examples of commonly used membrane separations are enrichment of nitrogen
from air, hydrogen separation in ammonia plants and refineries, removal of carbon dioxide from
natural gas, and removal of volatile organic compounds from mixtures with light gases. Gas
separation membranes are often packaged in hollow fiber modules depicted in Figure 1. As air
flows under pressure into the module through the bores of the hollow fiber, some of the air gases
permeate through the wall of the fibers into the shell of the hollow fiber. The gas in the shell side
of the fibers leaves the module as the permeate stream. Since oxygen, water, and carbon dioxide
are more permeable than nitrogen and argon, the gas in the fiber bore is enriched as it moves
from the feed to the residue end of the module.
P
>
p
P
>
P
O
2
N
2
y
,p
N
O
2
1
y
N
N
2
t
x
,P
1
x
Figure 2. Schematic of a membrane with thickness t used to separate O2 from N2.
The flux NO2 of oxygen across the membrane shown in Figure 2 is given as
NO2 =
PO2
(xP  yp)
t
(1)
where PO2 is the permeance of the membrane to oxygen, x is the mole fraction of oxygen on the
upstream, or high pressure P, side of the membrane, and y is the mole fraction of oxygen on the
downstream, or low pressure p, side of the membrane. The ratio of permeance to membrane
thickness is called the permeability PO 2 of the membrane to oxygen. The permeability can be
viewed as a mass transfer coefficient that connects the flux with the driving force for transport,
which is the partial pressure difference between the upstream and downstream sides of the
membrane.
26
We now need to consider the fact that as the feed gas travels through the hollow fibers, its
composition changes as selective permeation depletes the more permeable components from the
feed gas mixture. Figure 3 illustrates the ideal countercurrent flow pattern for the binary mixture
of oxygen and nitrogen moving through the fiber module.
Permeate
p
d(yn)
yP, nP=nF
dA
P
xn
Feed
xF, nF
yi
xn+d(xn)
Retentate
xR, nR
Figure 3. Ideal countercurrent flow pattern through the separator.
The total mole and O2 species balances around the separator are2
nF = nR + nP
(2)
xFnF = xRnR + yPnP
(3)
where nF, nR, and nP are the molar flow rates of the feed, retentate, and permeate streams,
respectively, and xF, xR, and xP are the feed, retentate, and permeate O2 mole fraction,
respectively. The molar flux of oxygen through a differential area dA in the membrane is
given by equation (1) or by
NO2 =
Therefore
d ( xn) PO2
=
(xP  yp) = Q’O2(xP  yp)
dA
t
d(xn) = Q’O2(xP  yp)dA =  d(yn)
(4)
The above equation is just the O2 species balance around the differential volume element
in the membrane. The reduction in the O2 molar flow rate d(xn) of the retentate stream
provides the same O2 molar flow rate d(yn) through the membrane. P and p are the
average retentate and permeate side pressures, respectively. Similar species balance for
nitrogen around the differential volume element in the membrane yields
d[(1x)n] =  Q’N2 [(1x)P  (1y)p)]dA
(5)
Dividing equation (4) by equation (5), we obtain
Q'
d ( xn)
xP  yp
=  O2
Q ' N 2 (1  x ) P  (1  y ) p
d [(1  x )n ]
27
(6)
d ( xn)
is just the molar flow rate of oxygen over that of nitrogen in the
d [(1  x )n ]
permeate stream, therefore it is equal to the ratio of the mole fraction of oxygen over that
Q 'O 2
y
of nitrogen
as shown schematically in Figure 4. Let * =
, equation (6)
Q' N 2
1 y
becomes
The ratio
y
xP  yp
= *
1 y
(1  x ) P  (1  y ) p
(7)
d(yn)
p
Permeate
yP, nP=nF
yi
xn
Feed
xF, nF
xn+d(xn)
P
Retentate
xR, nR
Figure 4. Molar flow rate ratio is equal to mole fraction ratio.
The separation factor * is assumed to be constant. The permeate composition at the
capped end of the hollow fibers is obtained from equation (7) by replacing y with yi and x
with xR.
x R P  yi p
yi
= *
(1  x R ) P  (1  yi ) p
1  yi
(7)
When the change in feed mole fraction of oxygen is less than 50%, the driving force for
diffusion across the membrane,  = xP  yp, is assumed to be a linear function of the
change in the molar flow on the feed side of the membrane
d(xn) =
( xn) R  ( xn) F
d
R  F
(8)
From the species balance around the separator xFnF = xRnR + yPnP
(xn)R  (xn)F =  (yn)P
(9)
Combine equations. (8) and (9) with equation (4) d(xn) = Q’O2(xP  yp)dA, we obtain
28
d
=  Q’O2dA
R  F
 yPnP
Separate the variables and integrate
yPnP 
R
F
Am
d
= Q’O2 (R  F)  dA
0


yPnP ln  R
 F

 = Q’O2 (R  F)Am

yPnP = Q’O2lm Am
(10)
where the log mean average lm is defined as
lm =
R  F
( xP  yp ) R  ( xP  yp ) F
= (xP  yp)lm =

( xP  yp ) R
ln R
ln
F
( xP  yp ) F
(11)
Equation (10) expresses the molar flow rate yPnP of oxygen as a function of the
permeance Q’O2 or mass transfer coefficient, area of membrane Am for mass transfer, and
an average driving force lm across the membrane. Similarly, the molar flow rate of
nitrogen in the permeate stream can be found
(1yP)nP = Q’N2 [(1x)P  (1y)p)]lmAm
(12)
The oxygen species balance, xFnF = xR( nF  nP) + yPnP, can be written in dimensionless
form using the definition of the cut  = nP/nF,
xF = xR( 1  ) + yP
(13)
Similarly, equations (7), (10), and (12) in dimensionless forms are
x R r  yi
yi
= *
(1  x R )r  (1  yi )
1  yi
yPnP
yP
nR 1
n
1
= R
Q’O2lm Am
nF Q' N 2
nF Q' N 2
 n
nP
nR
= 1  P
Q ' N 2 Am p n F
 nF
 Q 'O 2

(xr  y)lm
 Q' N 2
29
(14)
yPKR = (1  )*(xr  y)lm
where (xr  y)lm is defined by Eq. (11)
(15)
(1yP) KR = (1  )[(1x)r  (1y))]lm
(16)
where [(1x)r  (1y))]lm is defined by Eq. (11) with x’s and y’s
replaced by (1-x)’s and (1-y)’s
nR
where r = P/p and KR =
Q ' N 2 Am p
The algebraic model equations (13-16) represent a system with four equations in eight
variables: xF, xR, yP, r, yi, , *, and KR. The system can be solved with measured values
of xF, xR, yP, and r, leaving yi, , *, and KR as unknowns in the solution.
The algebraic equations (13) through (16) can be solved by the following iterative
method using EXCEL. Imagine that if you could combine equations (13-16) by
eliminating , *, and KR, then you would have one equation and one unknown yi.
Because of the non-linear nature of these equations, you cannot combine them
algebraically and you have to solve for yi by trial-and error. The following is a procedure
that you can use.
Step (1) Calculate  using Equation (13) from measured values of xF, xR and yP
Step(2) Guess a value for yi. Choose a value for yi such that xR P > yi p or yi< xR P/ p
to ensure that the log mean driving force defined by equation(11) is valid.
Step (3) Calculate  using Equation (14)
Step (4) Calculate KR using Equation (15)
Step (5) Calculate the Left Hand Side (LHS) and Right Hand Side (RHS) of Equation
(16).
Step (6) Use SOLVER in EXCEL to find the value of yi such that the absolute value
of (RHS-LHS) equals zero.
The algebraic equations (13) and (16) can also be solved by Newton’s method presented
in Appendix A
Experimental Procedure
Compressed air at about 110 psig is supplied to the membrane module through an air
regulator. The supplied air pressure can be controlled by turning the knob on top of the
regulator. The oxygen concentration is measured by a portable oxygen analyzer model
GPR-30. You can calibrate the oxygen analyzer by turn it on while in the ambient air and
set the oxygen concentration to 21.0 %.
30
Adjust the inlet pressure of the membrane module to 30 psig. Read the flow rate on the
permeate side of the membrane and set the same flow rate for the retentate. Record the
oxygen concentrations on both sides of the membrane when the system reaches steady
state. The permeate pressure p is assumed to be the ambient pressure and the retentate
pressure P is the average of the feed and retentate pressures as measured by the pressure
gages.
Measure the oxygen concentrations and the retentate pressures again at the retentate flow
rates of twice and four times the permeate flow rate. Repeat the procedure at 40, 50, 60,
70, and 80 psig.
Analysis
1. Plot the experimental separation factor * as a function of r (= P/p) and discuss the
results.
2. Compare calculated cut  with experimental  (= nP/nF) and plot the experimental and
calculated cut  (= nP/nF) as a function of r and discuss the results.
3. If you are using the Newton’s method, present one iteration at 30 psig and  = 0.5
using the guessed values yi = 0.2,  = 0.5, * = 6, and KR = 2. Clearly indicate how
you evaluate the Jacobian matrix.
4. Explain the difference in the diffusion rates of gases through the membrane.
References
1. Coker, D. T., Prabhakar, R., Freeman, ”Tools for Teaching Gas Separation Using
Polymers,” Chemical Engineering Education, 36, Winter 2002, 60
2. Davis, R. A., Sandall, O. C., “A Simple Analysis for Gas Separation Membrane
Experiments,” Chemical Engineering Education, 36, Winter 2002, 74
3. Welty, J. R., Wicks, C. E., Wilson, N. E., and Rorrer, G. L., Fundamentals of
Momentum, Heat and Mass Transfer, John Wiley and Son, (2001)
31
Experiment 6: Extended Surface Heat Transfer:
Heat Transfer along a Cylindrical Fin
In this heat transport lab you will study and perform calculations for extended surface
heat transfer. As part of the experiment you will be using automated data collection
instruments and thermocouples.
We will be interested in the performance of an aluminum pin fin available in our
laboratory. You should determine the temperature distribution for both free and forced
convection flows and compare the experimental measurements with the predicted values.
Introduction
Consider the area A on the surface shown in Figure 1 where heat is being transfer from
the surface at a fixed temperature Ts to the surrounding fluid at a temperature T with a
heat transfer coefficient h. The heat transfer rate may be increased by increasing the
convection coefficient h, reducing the fluid temperature T, or adding materials to the
area A.
Plate
As
As
A
A
L
Surface
Figure 1. Use of extended surface or fin to enhance heat transfer.
Look on the plane side-view of the surface and the surface with fin. The heat transfer rate
without the fin from area A to the surrounding fluid is
qc = hA(Ts  T)
With the fin attached to the area A, the heat transfer to the surrounding fluid must first be
transferred by conduction from area A to the fin
qf =  kA
T
x
=
x 0

As
0
h(T ( x)  T )dAs
where dAs = Pdx and P = perimeter of the fin.
32
For the extended surface to enhance the heat transfer rate, the ratio of heat transfer with
and without the fin must be greater than one
T
q
x x 0
f  f =
=
qc
hA(Ts  T )
 kA

As
0
h(T ( x)  T )dAs
hA(Ts  T )
(1)
f is called the fin effectiveness. For the fin to be cost effective, the fin effectiveness
should be greater than 2. The temperature profile along the fin must be determined before
the fin effectiveness can be calculated. Consider the cylindrical extended surface with
diameter D shown in Figure 2. To simplify the analysis, we will assume one-dimensional
heat transfer in the x direction, steady state, no heat generation, no radiation, constant
heat transfer coefficient, and constant physical properties.
T
T(x)
Tb
A
L
x
dx
Figure 2. A cylindrical fin with convective end.
An energy balance will be applied to a differential control volume, xA, shown in Figure
2. Since temperature is dependent on x, a differential distance along x must be chosen.
The surface area of the control volume is
As = xP = xD
From the energy balance applied to the control volume xA
qx – (qx+x + qc) = 0
Divide the equation by x and take the limit as x 0
limit  q x  q x  x 
limit  qc 
–
=0


Δx  0 
Δx  0  x 
x

–
dq x
dq c
–
=0
dx
dx
dqc = hdAs(T(x)  T)
33
The energy equation becomes
dq x
dA
– h s (T(x)  T) = 0
dx
dx
dT
Substituting Fourier's law qx = – kA
where A is the cross-sectional area normal to the
dx
x-direction, the energy equation becomes
–
d
dx
since As = Px,
dAs
 dT 
kA dx  – h dx (T(x)  T) = 0
dAs
=P
dx
For constant k and A, the energy equation becomes a second order ordinary differential
equation (ODE) with constant coefficients.
hP
d 2T
–
(T(x)  T) = 0
2
kA
dx
(2)
The above equation is a non-homogeneous ODE which can be made homogeneous by
introducing a new variable  = T(x)  T
hP
d 2
–
 =0
2
kA
dx
Let m2 =
(3)
hP
, the solution to the homogenous ODE can be written as
kA
 = B1sinh(mx) + B2cosh(mx)
(4)
The constants B1 and B2 can be evaluated using the following boundary conditions
at x = 0, T = Tb   = b
d h
dT
at x = L,  k
= h(T  T)  
= 
dx
dx k
(5a)
(5b)
to obtain the temperature distribution along the pin fin

=
b
h
sinh m( L  x )
mk
h
cosh mL 
sinh mL
mk
cosh m( L  x ) 
34
(6)
and the fin heat transfer rate
h
cosh mL
mk
qf = M
h
cosh mL 
sinh mL
mk
sinh mL 
(7)
where
0.5
 = T  T ,
b = Tb  T,
M = b(hPkA)0.5,
P = perimeter = D,
 4h 
m= 
 ,
 kD 
D 2
A=
4
The heat transfer coefficient for a long, horizontal cylinder can be estimated from
appropriate empirical correlations for free and forced convection flow1. For forced
convection, the heat transfer coefficient may be estimated from
NuD = 0.3 + [0.62 ReD1/2Pr1/3[1 + (0.4/Pr)2/3]-1/4][1 + (ReD/282,000)5/8]4/5 (8)
This equation is valid for cross flow and ReDPr > 0.2. The physical properties should be
evaluated at the film temperature Tf = 0.5(Ts + T). For free convection,
1/ 6


0.387 Ra D
NuD = 0.60 
9 / 16 8 / 27 
[1  (0.559 / Pr) ] 

2
(9)
This equation is valid for Rayleigh number RaD < 1012 where RaD = GrLPr =
g  (Ts  T ) D 3
. The physical properties should be evaluated at the film temperature Tf =

0.5(Ts + T).  is the expansion coefficient that depends on the fluid. For an ideal gas,  =
p/RT, the expansion coefficient can be determined
=
1
1   
1 p
=

 =
2
T
  T  p  RT
(10)
Fin performance is assessed by two factors: Fin Effectiveness, f, and the Fin Efficiency,
f. Fin effectiveness is defined as the ratio of the fin heat transfer rate to the heat transfer
rate that would exist without the fin as given by equation (1) earlier.
35
f =
qf
hAc b
(11)
Fin efficiency is defined as the ratio of the actual amount of heat transferred to the
amount of heat that would be transferred if the entire fin was at the base temperature.
f =
qf
(12)
hAf  b
For this experiment you will determine the temperature distribution, the amount of
energy transferred to the air, the fin effectiveness, and the fin efficiency for both forced
and free convection.
Procedure:
For Free Convection :
1. Turn on the Variac. Check to make sure that the heater connected to the fin is
connected with the variac.
2. Record the fin temperatures using the DAC express software. Instructions for using
the software are given in appendix C. Stop recording the temperatures when the
system reaches steady state.
3. Read and record the ambient air temperature and pressure. Record the humidity using
the wet bulb thermometer.
For Forced Convection :
4. Turn the air blower on. Adjust the variac so that the based temperature of the fin has
approximately the same value as in free convection.
5. Measure the air velocity by placing the wind velocity meter near the fin. It is
suggested that at least 5 readings over different x position along the fin be taken to
obtain an average value.
6. Wait until the system reach steady state and record the temperatures along the fin.
Repeat steps 1-6 for at least two more settings. Turn everything off and clean up.
Note: What is the criterion for a steady state temperature?
Report :
Should included:
1] Derive equations 6 & 7.
2] Determine the temperature distribution for both free and forced convection.
36
3] Compare the predicted values with the experimental values. Note: the predicted and
experimental values have the same base temperature.
4] Determine the fin effectiveness and fin efficiency for both free and forced
convection.
References:
1) Incropera and De Witt, Fundamentals of Heat and Mass Transfer, Wiley 2002.
2) Chapman, A. J., Heat Transfer, McMillan Publishing Co., 1985.
3) Any CRC Handbook of Physics and Chemistry.
37
Experiment 7: Unsteady-State Heat Transfer in an
Agitated Square Tank
Introduction:
In this experiment you will calculate, from experimental data, the overall heat transfer
coefficient for heat transfer between the water in a cooling coil and the hot water in an
agitated square tank.
Apparatus:
The variable-speed, propeller-agitated, insulated, square tank has three different size
impellers. The O.D.'s of the three impellers are 12”, 9”, and 6” respectively. The tank
contains a cooling coil which has 5 turns of 5/8” O.D. copper tubing (0.035 inch wall
thickness). The temperatures at various locations of the system are measured by
thermocouples as shown in Table 1.
Table 1 Thermocouple channels.
Channel
Location
1
Center bottom
2
Left bottom
3
Left center
4
Left top
16
Center top
17
Right top
18
Right center
19
Right bottom
20
Steam
21
Tank outlet
22
Free thermocouple
Procedure:
1. Pour tap water into the tank until it covers the coil. Turn on the agitator to see if the
water still covers the coils. If not, add additional water.
2. Measure the amount of water in the tank and heat it to above 150oF by passing
steam through the coil.
3. The experimental run is then conducted by running cooling water through the coil to
cool the water in the tank from about 150oF to about 125oF. These temperatures
do not have to be exactly 150oF and 125oF, but the experimental temperatures
must be measured accurately.
38
4. Record the water temperature in the tank, and the inlet and outlet cooling water
temperature using the DAC express software. Instructions for using the software
is given in appendix C. Measure the flow of the cooling water during step 3
above at least three times. Measure the impeller speed by a strobe light.
5. Repeat steps 2-4 for each impeller at three different impeller speeds and two
different water flow rates. If you cannot complete all of these runs, be sure to at
least cover the widest range of conditions possible.
6. Measure the helix diameter of the cooling coil.
Note: Here are several questions to consider as you are performing this experiment.
a. How much of the copper heat transfer surface is covered with scale?
b. What is the thickness of the scale?
c. What do you estimate the composition of the scale to be?
d. How will you account for the scale in your calculations?
e. What should be the value for the tank diameter?
Report:
1. The following formula can be used to determine the overall heat transfer coefficient
from the experimental data.
ln
WC
Ti  tci
= c pc
mC p
T f  tci
1

1   
K

(1a)
Where
K = exp (UoA/WcCpc)
(1b)
Ti = initial temperature of water in the tank
Tf = temperature of water in the tank at time 
Tci = inlet temperature of cooling water
Wc = mass flow rate of cooling water
Cpc = specific heat of cooling water
Cc = specific heat of tank water
m = mass of water in the tank
 = time required to cool water in the tank from Ti to Tf
A = outside area of coil tube
Uo = overall heat transfer coefficient base on A
a. Derive Eq. (1a). Plot the Left Hand Side of Eq. (1a) versus . Calculate Uo from the
slope of the resulting straight line.
b. Recalculate the overall heat transfer coefficient Uo with smaller interval oft and plot
Uo versus T. Does Uo vary with T
2. The overall heat transfer coefficient can also be determined from
39
1
1 r ln  ro / ri   ri / ro 
  i

U o hi
k
hi
(2)
where
k = thermal conductivity of coil tube
ri = inside radius of coil tube
ro = outside radius of coil tube
k  dV   C   
d 
hi  0.023 c  i c c   pc c   1  3.5 i 
d i  c   k c  
dc 
0.8
0.4
(3)
kc = thermal conductivity of cooling liquid
di = inside diameter of cooling coil
dc = diameter of the coil helix
Vc = mean linear velocity of cooling fluid
 c = density of cooling fluid
 c = viscosity of cooling fluid
k  D 2N  
ho  0.17 t  a

Dc   
0.67
 Cp 


 kt 
0.67
0.1
 Da   Dc 

  
 Dt   Dt 
0.5
(4)
kt = thermal conductivity of fluid inside tank
Dc = outside diameter of cooling coil
Da = diameter of impeller
N = rotation speed of impeller, rev./unit time
 = density of tank fluid
 = viscosity of tank fluid
Dt = tank diameter
Calculate the overall heat transfer coefficient using Eq. (2).
3. Compare your experimental results (Uo from 1.a) with values obtained from Eq. (2).
4. Using your experimental values for the individual heat transfer coefficient outside
the coil, prepare a single graph of Nu vs. Re, using the Nusselt number, (h oDc/kt),
and the Reynolds number for agitation, (Da2N/µ). The experimental values for ho
40
can be obtained by first calculating hi using Equation (3). Calculate ho using
Equation (2) where Uo are experimental values determined from Step (2)
5. by using Eqs. (1), (2), and (3).
5. Perform an energy balance for one of your experimental runs. Do not neglect any
terms that you can measure or approximate. Clearly state any assumptions made.
What is the % error in your energy balance?
6. Discuss the experimental errors associated with this study.
References:
1. W. L. McCabe & J. C. Smith & P. Harriott, Unit Operations of Chemical Engineering,
5th ed., pp. 451-453, McGraw-Hill, 1976.
2. Incropera and De Witt, Fundamentals of Heat and Mass Transfer, Wiley 1996.
3. A. H. P. Skelland, W.K. Blake, J.K. Dabrowski, J.A. Ulrich and T.F. Mach, Heat
transfer to coils in a propeller-Agitated Vessel, AICHE, Vol. 11, 1965, p. 951.
Note: You may ask your instructor to borrow copy of the last reference.
41
42