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California State Polytechnic University, PomonaDepartment of Chemical & Materials Engineering
CHE 333L
Transport Laboratory IILABORATORY 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)
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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.
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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.
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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
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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.
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a. Graphs are best if appropriate. b. If not a graph, then a table.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.
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California State Polytechnic University, PomonaChemical and Materials Engineering
CHE 333L – Transport Laboratory IIWinter Quarter, 2014
EXPERIMENT #1
Cooling Tower Characteristics
INSTRUCTOR:Keith Forward
SECTION 10
GROUP #1Einstein, MarySmith, Steven
Doe, John
DUE DATE: January 28, 2014
TITLE PAGE (5) _______ABSTRACT (10) ______INTRODUCTION/OBJECTIVE (10) ______BACKGROUND/PROCEDURE (20) ______RESULTS & DISCUSSION (25) ______CONCLUSIONS & RECOMMMENDATIONS (10) ______REFERENCES/APPENDIX (10) ______PRE-LAB (10) ______TOTAL (100) _____
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Experiment 1: Cooling Tower CharacteristicsYou 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
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 =
GM B KG aP ∫H y1
H y2 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.
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28 30 32 34 36 38 40 42 4460
80
100
120
140
160
180
200
Liquid T(C)
Ent
halp
y H
y(kJ
/kg)
Operating lineEquilbrium curve
TL1 TL2
Hy1
Hy2
Figure 2. Temperature enthalpy diagram and operating line for cooling tower.G is the dry air flow in kg/sm2. MB is the molecular weight of air (28.97). KG is the overall mass transfer coefficient based on the gas phase in kmol/sm2atm. 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 y1
H y2 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 ------------------
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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 barvpa=-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
M B
Pvap
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 =
(1093−0.56 T w 1 F)hw−0 .24 (T 1 F−T w1 F )1093+0 . 444T 1 F−T w 1 F
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/sm2 and CpL is the heat capacity of water (4.187 kJ/kgC). 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.
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hw =
M A
M B
Pvap
P−Pvap
3) Hy* is then evaluated from
Hy* = (1.005 + 1.88hw)TL + 2501.4hw
If you need to integrate numerically the expression ∫H y1
H y2 dH y
H y¿−H y use numerical
integration;e.g., trapezoidal rule or the 7 points Simpson’s rule.
NOG = ∫H y1
H y2 dH y
H y¿−H y
NOG =
dH y
3 [f(1) + 4f(2) + 2f(3) + 4f(4) + 2f(5) + 4f(6) + f(7)]
where f(1) =
1H y1
¿ −H y1 , f(7) =
1H y 2
¿ −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.
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
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Experiment 2: Double-pipe Heat ExchangerWe 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
1U i A i =
1Uo Ao =
1hi A i +
1hdi A i +
ro−ri
kA lm +
1hdo Ao +
1ho 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 = UATlm = UoAoTlm = UiAiTlm (1)
where U = overall heat transfer coefficientA = surface area normal to direction of heat transferTlm = average driving force for heat transfer = average temperature
difference between two streams.
(a) Parallel flow (b) Countercurrent flow
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Fig.1 Flow arrangements in heat exchanger
For parallel flow, Tlm is defined by the following equation
Tlm =
(T hi−Tci )−(T ho−Tco )
lnT hi−T ci
Tho−T co (2a)
For countercurrent flow, Tlm is defined by the following equation
Tlm =
(T hi−Tco )−(T ho−T ci)
lnThi−T co
Tho−T ci (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 = mh Cph(Thi - Tho) = mc Cpc(Tco - Tci) (3)
where mh = mass flow rate of the hot stream mc = 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
1U i A i =
1Uo Ao =
1hi A i +
1hdi A i +
ro−ri
kA lm +
1hdo Ao +
1ho Ao (4)
where hi = heat transfer coefficient for the inner tubehdi = fouling coefficient for the inner tubehdo = fouling coefficient for the outside surface of the inner tubeho = heat transfer coefficient for the annular spaceri = inside radius of the inner tubero = outside radius of the inner tubeAi = inside surface area of the inner tubeAo = outside surface area of the inner tube
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Alm = (Ao - Ai)/ln(Ao/Ai)
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)ReD Pr
1+0 . 4 [(D / L )ReD Pr ]2/3 (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−ReD )/365 ]
(NuD ,l )2
+
1
(NuD ,t )2 )-5 (7)
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 diameter1 Kaviany, M. Principle of Heat Transfer, Wiley, 2002, pg. 737
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Dh = 4Ac/P (8)
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 =
π (Do2−Di
2)π (Di+Do ) = Do Di (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 = mc Cpc; Ch = mh 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
=
QQmax (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.
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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[mh Cph(Thi - Tho) + mc 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.
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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 CO2 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/minWater 0-4 liters/minSuggested average flow rates for CO2 absorption experimentsCO2 - 3 liters/minAir - 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
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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
( ΔPh )
[ Dp gc
ρ f vs 2 ]( ε3
1−ε ) = 150
1−εN Re + 1.75 (1)
whereP = pressure drop through the packed bedh = bed heightDp = particle diameterf = fluid densityvs = superficial velocity at a density averaged between inlet and outlet
conditions = bed porosity
NRe = average Reynolds number based upon superficial velocity
Dp vs ρf
μ
When the packing has a shape different from spherical, an effective particle diameter is defined
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Dp =
6 V p
A p =
6(1−ε)A s (2)
whereAs = 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 voidsvolume of entire bed
volume of entire bed−volume of particlesvolume of entire bed
=
πR2h−weight of all particlesparticle density
πR2 h (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)
( ΔPh )
= (10βL/ ρL) (Gv2
ρv)
(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 InformationR: Raschig Rings, B: Berl Saddle
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---------------------------------------------------------------------------------------------------------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---------------------------------------------------------------------------------------------------------R: 1/4 88000 46 240 73 0.22R: 5/16 40000 56 145 64 0.31R: 3/8 24000 51 134 68 0.35
B: 1/4 113000 56 274 60 0.23B: 1/2 16200 54 142 63 0.42B: 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 ProblemAssuming 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. 6893. 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. 18-235. Wankat, P. C., Equilibrium Staged Separations, Elsevier, 1988, pg.4206. 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
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Experiment 4: Water Heater Efficiency
21
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 0.77Carbon dioxide, CO2 0.97 1.02Methane, CH4 95.66 95.74 Ethane, C2H6 2.01 1.94Propane, C3H8 0.36 0.35Isobutane,i-C4H10 0.06 0.06n-Butane,n-C4H10 0.07 0.07Isopentane,i-C5H12 0.02 0.02n-Pentane,n-C5H12 0.01 0.01C6+ 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.
Heater Efficiency
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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 =
nAR Δ H r0
ν A + ∑
outletni H i
∑inlet
ni H i(1)
whereA = any reactant or productnAR = moles of A produced or consumed in the processnA = stoichiometeric coefficient of A
Reference conditions (Ref. 1): reactant and product species at To in the state of
aggregation for which Δ H 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,outHw , out nw,in
Hw , in (2)
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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.
Figure 2 Water heater experiment.Gas Analyzer Preparation:
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Cold Water
Valve
Gas Meter
Hot Air
Pressure Gauge
Thermom
Flow
Flue
Natural Gas
Hot Water
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.
References1. Felder R. M. and Rousseau R. W., Elementary Principles of Chemical
Processes, Wiley, 2000, pg. 450
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Experiment 5: Gas Separation Membrane
26
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.
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
t (xP yp) (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
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thickness is called the permeability PO2 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.
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.
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 = d ( xn)
dA = PO2
t (xP yp) = Q’O2(xP yp)
Therefore 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
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balance for nitrogen around the differential volume element in the membrane yields
d[(1x)n] = Q’N2 [(1x)P (1y)p)]dA (5)
Dividing equation (4) by equation (5), we obtain
d ( xn)d [ (1−x )n ] =
Q 'O 2
Q'N 2
xP− yp(1−x )P−(1− y ) p (6)
The ratio d ( xn)
d [(1−x )n ] is just the molar flow rate of oxygen over that of nitrogen in the permeate stream, therefore it is equal to the ratio of
the mole fraction of oxygen over that of nitrogen y
1− y as shown
schematically in Figure 4. Let * = Q 'O2
Q'N 2 , equation (6) becomes
y1− y = *
xP− yp(1−x )P−(1− y ) p (7)
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.
y i
1− y i = *
xR P− y i p(1−x R)P−(1− y i) p (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
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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
ΔR−ΔF d (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
yPnP dΔ
ΔR−ΔF = Q’O2dA
Separate the variables and integrate
yPnP∫ΔF
ΔR dΔΔ = Q’O2 (R F)∫0
Am dA
yPnP
ln ( ΔR
ΔF)
= Q’O2 (R F)Am
yPnP = Q’O2lm Am (10)
where the log mean average lm is defined as
lm =
ΔR−ΔF
lnΔR
ΔF = (xP yp)lm =
( xP− yp )R−( xP− yp )F
ln( xP− yp )R( 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
(1yP)nP = Q’N2 [(1x)P (1y)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,
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xF = xR( 1 ) + yP (13)
Similarly, equations (7), (10), and (12) in dimensionless forms are
y i
1− y i = *
xR r− y i
(1−x R)r−(1− y i ) (14)
yPnP
nR
nF
1Q'N 2 =
nR
nF
1Q'N 2 Q’O2lm Am
yP
nR
Q'N 2 Am pnP
nF = (1−nP
nF) Q 'O2
Q'N 2 (xr y)lm
yPKR = (1 )*(xr y)lm (15) where (xr y)lm is defined by Eq. (11)
(1yP) KR = (1 )[(1x)r (1y))]lm (16) where [(1x)r (1y))]lm is defined by Eq. (11) with x’s and y’s replaced by (1-x)’s and (1-y)’s
where r = P/p and KR = nR
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)
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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 %.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.
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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)
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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.
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 = ∫0
A s h (T ( x )−T∞ )dA s
where dAs = Pdx and P = perimeter of the fin.
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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
f
q f
qc =
−kA ∂T∂ x
|x=0
hA(T s−T∞) =
∫0
A s h(T ( x )−T∞ )dAs
hA(T s−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.
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 = xD
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
limitΔx→0 [ q x−q x+Δx
Δx ] –
limitΔx→0 [ Δqc
Δx ] = 0
–
dqx
dx –
dqc
dx = 0
dqc = hdAs(T(x) T)
The energy equation becomes
35
–
dqx
dx – h
dA s
dx (T(x) T) = 0
Substituting Fourier's law qx = – kA
dTdx where A is the cross-sectional area normal to the
x-direction, the energy equation becomes
ddx [kA dT
dx ] – h
dA s
dx (T(x) T) = 0
since As = Px,
dA s
dx = P
For constant k and A, the energy equation becomes a second order ordinary differential equation (ODE) with constant coefficients.
d2 Tdx2
–
hPkA (T(x) T) = 0 (2)
The above equation is a non-homogeneous ODE which can be made homogeneous by introducing a new variable = T(x) T
d2 θdx2
–
hPkA = 0 (3)
Let m2 =
hPkA , the solution to the homogenous ODE can be written as
= B1sinh(mx) + B2cosh(mx) (4)
The constants B1 and B2 can be evaluated using the following boundary conditions
at x = 0, T = Tb = b (5a)
at x = L, −k dT
dx = h(T T)
dθdx = (5b)
to obtain the temperature distribution along the pin fin
θθb =
cosh m(L−x )+ hmk
sinh m(L−x )
cosh mL+ hmk
sinh mL(6)
36
and the fin heat transfer rate
qf =
Msinh mL+ h
mkcosh mL
coshmL+ hmk
sinh mL(7)
where
= T T, b = Tb T, m = ,
M = b(hPkA)0.5, P = perimeter = D, A = πD2
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,
NuD ={0 .60+
0 .387 RaD1/6
[1+( 0.559 /Pr )9/16 ]8 /27 }2
(9)
This equation is valid for Rayleigh number RaD < 1012 where RaD = GrLPr =
. 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
=
1ρ ( ∂ ρ
∂T )p =
1ρ
pRT 2
=
1T (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.
37
f =
q f
hAcθb (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 =
q f
hA f θb (12)
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.
38
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.
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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 bottom2 Left bottom3 Left center4 Left top16 Center top17 Right top18 Right center19 Right bottom20 Steam21 Tank outlet22 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.
40
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.
= (1a)Where
K = exp (UoA/WcCpc) (1b)
Ti = initial temperature of water in the tankTf = temperature of water in the tank at time Tci = inlet temperature of cooling waterWc = mass flow rate of cooling waterCpc = specific heat of cooling waterCc = specific heat of tank waterm = mass of water in the tank = time required to cool water in the tank from Ti to Tf
A = outside area of coil tubeUo = 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 oft and plot Uo versus T. Does Uo vary with T
41
2. The overall heat transfer coefficient can also be determined from
(2) where
k = thermal conductivity of coil tube
ri = inside radius of coil tube
ro = outside radius of coil tube
(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
= density of cooling fluid
= viscosity of cooling fluid
(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 diameterCalculate the overall heat transfer coefficient using Eq. (2).
42
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, (hoDc/kt), and the Reynolds number for agitation, (Da
2N/µ). The experimental values for ho 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.
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