Keywords: Heat transfer; Energy balance; Agitated vessel; Experiential learning
. Introduction
eat transfer laboratories constitute an important part ofn undergraduate chemical engineering curriculum becausehese allow students to obtain hands-on experiential learn-ng of real processes during the course of their studies. In
ost undergraduate programmes, heat-transfer experimentsre based on small-scale commercially available equipment.hile such experiments demonstrate some of the basic prin-
iples and calculations, they do not always expose students toeal processes and applications that they would be facing inhe industry; hence, students are not able to capture the spiritf industrial experience.
In this paper, we describe a heat-transfer laboratory exper-ment, designed and fabricated in-house, which is part of aourse on heat transfer in the undergraduate Chemical Engi-eering programme at the University of Calgary. Studentsre afforded an opportunity to experience and learn aboutne of the heat transfer processes that is widely employed
n the chemical industry, namely heat transfer in an agi-ated vessel. Mixing and heat transfer in agitated vessels,
n both batch and continuous processes, are very impor-
tant operations for many industrial processes; including:petroleum, mining, pharmaceutical, pulp and papers, foodand wastewater treatment. Therefore, agitated vessels repre-sent an important unit operation in the industry, in which theprocess yield and/or production is influenced by heat trans-fer (Perry and Green, 2008; McCabe et al., 2005). Hence, itis important for undergraduate students to receive experi-ential learning on the operation of agitated vessels and topredict the process performance reliably. This paper presentsa simple teaching experiment that involves both agitationand heat transfer, using simple and inexpensive equipment.The paper also describes experimental determination of theheat transfer rates and the overall heat transfer coefficientbetween steam and water in an agitated vessel. The experi-ment demonstrates heat transfer under transient and steadystate conditions. By performing the experiment, studentsare able to determine the overall heat transfer coefficientexperimentally and compare it with calculated values usingcorrelations in the literature. Further, students are trained onstudying the effect of the following variables on the heat trans-fer rate: the impeller speed and the residence time or waterflow rate.
gary.ca (A.K. Mehrotra).
neers. Published by Elsevier B.V. All rights reserved.
e84 education for chemical engineers 6 ( 2 0 1 1 ) e83–e89
and i
Fig. 1 – Schematic of the agitated vessel
2. Aim of the selected laboratoryexperiment
The main purpose of this heat transfer laboratory is to pro-vide the student with an opportunity to test and evaluate theeffects of a variety of control variables for batch and contin-uous process schemes. Accordingly, the student is able to: (i)analyze transient heating of water in an agitated vessel at dif-ferent impeller speed, (ii) analyze steady state heat transferat different water flow rates and different impeller speed, (iii)perform mass and energy balances and calculate heat trans-fer rates, and (iv) compare the experimental values of overallheat transfer coefficient with those predicted from correla-tions given in the literature.
3. Description of the apparatus and theexperimental procedure
The design of this laboratory experiment comprises eight keycomponents, as follows.
(1) the vessel or tank, which is the main part of this experi-ment. A steam jacket surrounds the cylindrical vessel, inwhich saturated steam is allowed to condense. The vesselis made of SS316 and contains four radial longitudinallymounted baffles for reducing vortex formation, leading toimproved agitation and heat transfer;
(2) a turbine impeller, with 6 straight blades, connected toa variable speed electric motor (whose speed can beadjusted by a speed regulator). The vessel and impellerdesign followed the standard design proportions (Rushtonet al., 1950); all of the dimensions are provided in Fig. 1;
(3) a water supply tank, which provides water to the vessel atthe ambient temperature;
(4) a centrifugal pump for supplying water from the supplytank to the vessel;
(5) steam supply system (connected to low-pressure steamsupply) along with a steam trap;
(6) a rotameter flow meter for adjusting and measuring thewater flow rate;
mpeller (all dimensions in centimetres).
(7) a condensate cooler to lower the temperature of the con-densate exiting from the vessel jacket (to avoid the studentfrom handling hot condensate) before its flow is measured,using a measuring cylinder and stopwatch, prior to beingdischarged to the drain;
(8) five thermocouples and one pressure gauge for monitoringthe water and steam temperatures and the steam pres-sure.
Fig. 2 shows a schematic diagram of the laboratory processexperiment. The following is a brief description of the pro-cedure. The supply tank is filled with cold water. It is thenpumped into the vessel using the centrifugal pump, passingthrough a flow meter and flow-regulating valve. The vessel hasan overflow line leading to the drain. Once the vessel is fullwith water, the agitator is turned on and its rotational speedis measured with a hand-held tachometer. Water supply tothe condensate cooler is turned on. Steam is introduced intothe vessel jacket and the condensate formed (due to the heatexchange between steam and water) passes through a steam-trap and the condensate cooler before its rate is measured.
4. Theory
The following sections present a brief description of theunderlying theory to help the student in understanding andanalyzing this experiment.
4.1. The rate of heat transfer
The rate of heat transfer from steam to water in the agitatedvessel is given as Eq. (1). It is dependent on the followingvariables: (i) the overall heat transfer coefficient (U), whichdepends on the water and steam properties, as well as impellerspeed and vessel geometry; (ii) the area of heat transfer (A),which is the area of the vessel wall in contact with the waterand it depends on the water level in the vessel and the vessel
geometry; and (iii) the thermal driving force for heat transfer,which is the temperature difference between the condensing
education for chemical engineers 6 ( 2 0 1 1 ) e83–e89 e85
ation
sv
q
4
IsfnfsThbte
q
wtliw
U
Be
4Isq
U
Fig. 2 – Schematic represent
team in the jacket and the average water temperature in theessel, (Ts − Tf):
= UA(Ts − Tf ) (1)
.2. Energy balance
n the experiment, Tf is a variable that is allowed to reach apecified value while Ts remains constant (in this experiment,or the low-pressure steam supply, Ts = 127 ± 2 ◦C). It is worthoting that Tf is not only affected by the rate of heat trans-
er through the vessel wall, but also by other energy terms,uch as heat losses, fresh water temperature (different than
f), and mechanical energy input. As it is done commonly ineat transfer applications, the mechanical energy impartedy the motor/agitator can be neglected in comparison to thehermal energy terms. Therefore, the (thermal) energy balancequation can be written as follows:
in = qout + qloss + qaccu (2)
here qin is the rate of heat transfer from the steam to waterhrough the vessel wall, qout is the rate of energy with the watereaving the vessel, qloss is the rate of heat loss to the surround-ngs, and qaccu is the rate of energy accumulation in the water
ithin the vessel. Eq. (2) can be written as follows:
A(Ts − Tf ) = mC(Tf − Tin) + qloss + mwCdTf
dt(3)
ased on the experimental conditions, Eq. (3) can be used tostimate U and qloss as described in the following sections.
.2.1. Batch process (transient heat transfer)n this experiment there is no water entering or leaving theystem. Assuming the system to be perfectly insulated (i.e.,
loss = 0), Eq. (3) is simplified as follows:
A(Ts − Tf ) = mwCdTf
dt(4)
of the experimental setup.
integration of both sides yields:
UA
mwCt = ln
[Ts − To
Ts − Tf
](5)
By plotting the experimental results as ln[(Ts − To)/(Ts − Tf)]against t, U is obtained from the slope of the best-fit line. Theheat transfer area, A, is calculated from the vessel geometryand the water level in the vessel. The temperatures Ts, To, andTf are obtained from the thermocouple displays during theexperiment, mw is the water mass in the vessel and is cal-culated from the volume of the water held in the vessel andthe average density, mw = �V, and C is the average specific heatcapacity of water.
Next, the amounts of thermal energy given off by the steamand gained by the water are estimated. In a perfectly insulatedsystem the heat gained by the water should equal the heattransferred from the steam; however, because the system isnot perfectly insulated, the difference between the two termscan be considered as the heat loss. The total heat loss duringthe batch experiment, on a cumulative basis, is estimated asfollows:
qloss = ms� − mwC(Tf − To) (6)
where ms is the total mass of condensate collected and � is thelatent heat of condensation (obtained from the steam table).
4.2.2. Continuous process (steady state heat transfer)In this experiment, the water is pumped into the vessel at aconstant rate throughout the experiment and measurementsare recorded at steady state. The energy balance calculationinvolves equating the rate of heat transferred from the con-densing steam to the rate of heat gained by the water stream,as follows:
qs = qin = ms� (7)
e86 education for chemical engineers 6 ( 2 0 1 1 ) e83–e89
Fig. 3 – Schematic of the temperature profile between thecondensing steam (in the jacket) and water being heated (in
the agitated vessel).
where qs = qin is the rate of heat transferred from the steamand ms is the condensate mass flow rate. Similarly, the rate ofheat transferred to the water stream is calculated as follows:
qout = mwC(Tout − Tin) (8)
where qout is the rate of heat transfer to water, mw is the watermass flow rate, Tout is the temperature of outlet water stream,and Tin is the temperature of inlet water stream. Again, in aperfectly insulated system, qin = qout. However, heat is lost tothe environment in the steady state process, and the differ-ence, (qin − qout), represents the rate of heat loss.
4.3. Heat transfer through the vessel wall
The overall heat transfer coefficient, U, represents three ther-mal resistances in series, as shown schematically in Fig. 3.
U (taken to be based on the inside vessel heat transfer area)can be estimated theoretically as follows:
where Utheo is the theoretical overall heat transfer coefficient,hi is the heat transfer coefficient for water (inside the vessel),ho is the heat transfer coefficient for condensing steam (out-side the vessel or in the jacket), Ai is the inside vessel wallsurface area, Ao is the outside vessel wall surface area, ri isthe inside vessel radius, ro is the outside vessel radius, L isthe depth of water in the vessel, and k is the average thermalconductivity of the vessel wall.
The values for water depth, radii, and inner and outervessel surface areas are obtained directly from the vesseldimensions. k is obtained from literature for SS316 at itsaverage temperature (Holman, 2002). The inside heat trans-fer coefficient for an agitated vessel with 6-flat-bladed turbineimpeller is estimated from the following correlation (McCabeet al., 2005):
( )( )2/3( ) ( )
hi = 0.44
kw
Dt
nD2a�
�
C�
kw
1/3 �
�w
0.24(10)
where kw is the thermal conductivity of water in the vessel, Dt
is the inside vessel diameter, Da is the impeller diameter, n isthe impeller speed, � is the density of water, C is the specificheat capacity of water, � is the viscosity of water, �w is theviscosity of water at the wall temperature. All liquid propertiesare evaluated at the average water temperature.
The following correlation for the condensation of a sat-urated vapor on a vertical plate can be used to estimatethe outside heat transfer coefficient (inside the steam jacket)(Holman, 2002):
ho = 1.13
[�(� − �v)ghfgk3
c
L�(Ts − Tw)
]1/4
(11)
where � is the density of condensate, �v is the density of steam,g is the gravitational acceleration, hfg is the latent heat ofcondensation of steam, kc is the thermal conductivity of con-densate, L is the height of the condensation surface (assumedequal to the depth of water in the vessel), � is the viscosity ofcondensate, Ts is the saturated steam temperature, and Tw isthe wall temperature. All condensate properties are evaluatedat the film temperature, Tf = (Ts + Tw)/2.
4.4. Estimating the vessel wall temperature
The vessel wall temperature, Tw, is needed for calculating bothhi and ho from Eqs. (10) and (11), respectively. However, a trial-and-error procedure is needed to estimate Tw. Following theschematic diagram presented in Fig. 3, q could be calculatedthrough the three thermal resistances as follows:
Convection in the steam side : q = hoAo(Ts − Tws)
Conduction through the wall : q = 2�kL
ln(ro/ri)(Tws − Twc)
Convection in the water side : q = hiAi(Twc − Tc)
To avoid a double trial-and-error procedure for estimatingboth Tws and Twc, for simplicity it can be assumed that Tws ≈Twc = Tw.
5. Observations and discussions
5.1. Batch experiment
In this part, the student could study the transient heat trans-fer at three impeller speeds. Fig. 4a shows an increase in watertemperature with time at impeller speeds of 100, 250, and500 rpm. The results clearly show that an increase in the agita-tion rate increases the rate of heat transfer. Note that the timefor the water to reach a temperature of 90 ◦C decreases withan increase in the impeller speed. That is, an increase in theextent of forced convection decreases the thermal resistance,leading to an increase in the rate of heat transfer. The resultsplotted in Fig. 4b confirm a linear relationship predicted by Eq.(5) at all three impeller speeds. It is possible to estimate anaverage value of the overall heat transfer coefficient, U, fromthe slope of each best-fit line. Since U is directly proportionalto slope of the best-fit line, the results in Fig. 4b indicate anincrease in U with an increase in the impeller speed.
Following the theory presented in Section 4, the studentcan perform mass and energy balances at different impeller
speeds for estimating the thermal energy transferred by steamand gained by water, the overall heat transfer coefficient, and
education for chemical engineers 6 ( 2 0 1 1 ) e83–e89 e87
he amount of heat lost to the surrounding. Table 1 shows theesults for impeller speeds of 100, 250, and 500 rpm. The stu-ent would observe that the impeller speed, which affects theime it takes for the water to reach a final temperature of 90 ◦C,as an effect on heat loss as well. The relative amounts of heat
oss were 30%, 29%, and 25% at 100, 250, and 500 rpm, respec-ively. Those also affect the mass of condensate collected and,herefore, the energy supplied by the condensing steam, qs.
.2. Continuous flow experiment
n this set of experiments, the student could investigate theffect of water flow rate and the impeller speed on the over-ll heat transfer coefficient. One set of experimental resultsbtained, at a constant impeller speed of 500 rpm, for thehange in water temperature with time is plotted in Fig. 5. Theteady state water temperature is accomplished more rapidly
t a higher water flow rate. The results also show that, athe same impeller speed of 500 rpm, the steady state water
0
0.2
0.4
0.6
0.8
1
1.2
4003002001000
Ln(Ts-T
o/Ts-T)
Time (s)
500 rpm
250 rpm100 rpm
0
20
40
60
80
100
4003002001000
Tem
pera
ture
(ºC
)
Time (s)
500 rpm
250 rpm
100 rpm
(a)
(b)
ig. 4 – Effect of the impeller speed on the overall heatransfer coefficient.
Fig. 5 – Effect of water flow rate on the steady statetemperature, the impeller speed is 500 rpm.
temperature decreases as the flow rate increases. In Fig. 6,the results from two experiments at the same water flow rateof 7.8 L/min show that the steady state water temperature isslightly higher at an impeller speed of 500 than 250 rpm. Fromthese results, the student should be able to deduce that therate of heat transfer increases with an increase in the impellerspeed.
Table 2 presents a summary of the experimental resultsobtained from the continuous flow experiments along withthe theoretical results obtained from heat transfer calcu-lations described in the previous section. The overall heattransfer coefficient is observed to increase with the impellerspeed. The water flow rate does not affect the overall heattransfer coefficient as much. At both impeller speeds, Utheo ispredicted to be less than Uexp at a lower water flow rate but
the trend is reversed at the higher water flow rates.
0
10
20
30
40
50
60
70
8006004002000
Tem
pera
ture
(ºC
)
Time (s)
500 rpm
250 rpm
Fig. 6 – Effect of impeller speed on the steady statetemperature, the fresh water flow rate is 7.8 L/min.
e88 education for chemical engineers 6 ( 2 0 1 1 ) e83–e89
Table 2 – Results from the continuous flow experiments.
6. Performance, reporting and evaluationsof the experiment
All of the students taking the heat-transfer course areassigned to a number of laboratory groups or teams, witheach group consisting of 4 students. There are four (4) heat-transfer experiments in the course, which allows each studentto assume the leadership role for one of the experiments whilethe other members acting as assistants or helpers. This lead-ership role is thus assumed by each team member for oneof the four experiments in a planned way. All members ineach group are required to arrange a “dry run” session with alaboratory instructor or a graduate teaching assistant, a fewdays prior to actually performing the experiment, in orderto become acquainted with the equipment, the objective ofthe experiment, procedure, and the underlying theory. During
this session, students are also instructed about the laboratorysafety aspects. During the performance of the experiment,
Table 3 – Components of laboratory report and itsgrading scheme.
Component Details Mark Grade
General
Letter of transmittal 1
10Title page 1Table of contents, figuresand tables
3
References 2Report quality 3
Introduction
Summary 3
22
Introduction 5Theory 5Description of apparatus 3Experimental procedure 4Nomenclature 2
Results
Raw data 5
27Treatment of data (tablesand figures)
12
Sample calculations 10
Discussion
Discussion of obtainedresults
15
30Compared with correlatedvalues
5
Compared with 2 othergroups
5
Error analysis and possiblesources of error
5
Conclusions
Conclusions 711Recommendations 3
Appendix: “Original” datasheets and samplecalculations
1
Total 100
23.4 37.7 35.4 6.1
all group members are asked questions related to the experi-ments and “participation marks” are awarded based on theirknowledge and active contributions to the laboratory session.Along with the laboratory work and collection of data, thegroup leader for the specific experiment is responsible forpreparing and submitting a final detailed or “formal” reportthat should follow the format presented in Table 3. The reportgrade is based on the mark distribution presented in Table 3as well.
7. A selected example of application
To ensure that conducting the laboratory experimentenhances students’ understanding and enriches theirproblem-solving skills, the final examination in this heat-transfer course always includes questions pertaining to thelaboratory experiments. Given below, as an example, is onesuch final examination question related to this particularexperiment.
Question: A jacketed-agitated vessel is used for heating water(C = 4.18 kJ/(kg K)) from 10 ◦C to 80 ◦C. The heat transfercoefficient for water (in kW/(m2 K)) is given by: [hi = 1.5 n2/3],where n is the impeller speed in rev/s. Saturated steam at110 ◦C condenses in the jacket, for which the average heattransfer coefficient (in kW/(m2 K)) is given by:[ho = 13(Tg − Tw)−0.25]. Both the diameter and height of thevessel are 0.50 m. Calculate the mass rate of water that canbe heated using this agitated vessel at an impeller speed of240 rev/min. Also calculate the hourly steam consumption.[Data: The latent heat of vaporization for water at 110 ◦C is2.23 MJ/kg.]
Solution:
Assumptions:
1. This is a steady state process.
2. The system is perfectly insulated, so no heat loss to theenvironment.
3. Heat transfer resistance for the vessel wall is neglected.
Given:
Tin = 10 ◦C; Tout = Tc = 80 ◦C;hi = 1500(240/60)2/3 = 3780 W/(m2 K)
Steam at 110 ◦C condenses in the jacket, thusho = 13,000(110 − Tw)−0.25
� = 2.23 × 106 J/kg
Analysis:
Eqs. (1), (7) and (8) yield:
mcCc(Tout − Tin) = UA(Ts − Tout) = ms�
Thus, mc × 4180 × (80 − 10) = U × (� × 0.5 × 0.5)(110 − 80)
education for chemical engineers 6 ( 2 0 1 1 ) e83–e89 e89
8
Tlbcbca
mc = 8.053 × 10−5U
U can be estimated by applying Eq. (9), as follows:
U = 1(1/hi)+(1/ho) =
[1
3780 + 113,000(110−Tw)−0.25
]−1
The wall temperature, Tw, can be estimated from atrial-and-error procedure using the procedure describedin Section 4.4, as follows:
Following a few iterations, Tw = 99.7 ◦C. Therefore, U, mc
and ms can be calculated accordingly. The final answersare as follows:
U (overall heat transfer coefficient) = 2490 W/(m2 K)
mc (water flow rate) = 720 kg/h
ms (steam condensation rate) = 94.5 kg/h
. Conclusions
he use of an in-house designed, developed and fabricatedaboratory apparatus involving a jacketed agitated vessel haseen found to be an excellent tool for teaching some importantoncepts of heat transfer. The experiential learning acquiredy the student through this experiment complements their
lassroom education. In particular, two important conceptsre demonstrated in this experiment, namely: heat transfer
under transient and steady state conditions. Experimentalvariables that may have effects on the heat transfer rate aretested through a series of planned experiments; these includeimpeller speed and water flow rate. As indicated by their for-mal and informal feedback, the student enjoyed the laboratoryexperience, especially by using a robust experimental appara-tus. The flexibility and benefits of this laboratory experimentmake it a great tool to capture students’ imagination andenthusiasm.
Acknowledgments
Financial and technical support for this experimental appa-ratus was provided by the Department of Chemical andPetroleum Engineering in the Schulich School of Engineeringat the University of Calgary.
References
Holman, J.P., 2002. Heat Transfer. McGraw-Hill Book Company,New York, NY.
McCabe, W., Smith, J., Harriott, P., 2005. Unit Operations ofChemical Engineering. McGraw-Hill Book Company, NewYork, NY.
Perry, R.H., Green, D.W., 2008. Perry’s Chemical Engineers’Handbook. McGraw-Hill Book Company, New York, NY.
Rushton, J.H., Costich, E.W., Everatt, H.J., 1950. Power
characteristics of mixing impellers. Chem. Eng. Prog. 46,395–476.
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