education for chemical engineers 8 ( 2 0 1 3 ) e58–e71

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Education for Chemical Engineers

jou rn al hom ep age: www.elsev ier .com/ locate /ece

Spreadsheets for assisting Transport Phenomena Laboratoryexperiences

Aurelio Stammitti ∗

Transport Phenomena Laboratory, Department of Thermodynamics and Transport Phenomena, Universidad Simón Bolívar, Caracas1080A, Venezuela

a b s t r a c t

Academic laboratories have been traditionally used for complementing and reinforcing in a practical way the the-

oretical instruction received in classroom lectures. However, data processing and model evaluation tasks are time

consuming and do not add much value to the student’s learning experience as they reduce available time for result

analysis, critical thinking and report writing skills development. Therefore, this project addressed this issue by

selecting three experiences of the Transport Phenomena Laboratory, namely: metallic bar temperature profiles, tran-

sient heat conduction and fixed and fluidised bed behaviour, and developed a spreadsheet for each one of them.

These spreadsheets, without demanding programming skills, easily process experimental data sets, evaluate com-

plex analytical and numerical models and correlations, not formerly considered and, convey results in tables and

plots. Chemical engineering students that tested the spreadsheets were surveyed and expressed the added value of

the sheets, being user-friendly, helped them to fulfil lab objectives by reducing their workload and, allowed them

to complete deeper analyses that instructors could not request before, as they were able to quickly evaluate, com-

pare and validate different model assumptions and correlations. Students also provided valuable suggestions for

improving the spreadsheet experience. Through these sheets, students’ lab learning experience was updated.

© 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Keywords: Educational spreadsheets; Transport Phenomena Laboratory; Laboratory experience quality; Data

processing task; Hands-on learning; Student analytical thinking

gramme and, comprises a total of ten heat transfer and fluidmechanics experiences (Meléndez and Gutiérrez, 2005). In

1. Introduction

It is well known that laboratory experiences are not onlyused in the academic environment for complementing andreinforcing in a practical way (hands-on approach) the theo-retical concepts introduced to students in lectures, but also,they are used as a means for developing skills, such asacquiring and processing experimental data, comparing suchdata against theoretical models, developing critical and ana-lytical thinking, drawing meaningful conclusions, teamworkand ethics, and the ability to convey experimental findingsand conclusions in the forms of written technical reportsand oral presentations (Stubington, 1995; Arce and Schreiber,2004; Feisel and Rosa, 2005; Domingues et al., 2010; Vazquez-

∗ Correspondence address: Universidad Simón Bolívar, Dpto. Termodinde Transporte, Edif. TYT, Ofic. 101, Apartado Postal 89000, Caracas 1080Venezuela. Tel.: +58 212 906 4113; fax: +58 212 906 3743.

E-mail addresses: aureliostammitti@usb.ve, ssaurelio@hotmail.comReceived 28 August 2012; Received in revised form 13 January 2013; A

1749-7728/$ – see front matter © 2013 The Institution of Chemical Engihttp://dx.doi.org/10.1016/j.ece.2013.02.005

Arenas and Pritzker, 2010; Patterson, 2011; Narang et al., 2012;Vernengo and Dahm, 2012).

It is also a known issue that processing experimental dataand comparing results against theoretical models can be timeconsuming due to iterative and complex calculations, whichreduce the student’s available time for analysis and discus-sion and, in consequence, the resulting report is poor quality(Stubington, 1995; Feisel and Rosa, 2005; Vazquez-Arenas et al.,2009; Vazquez-Arenas and Pritzker, 2010).

The ‘Transport Phenomena Laboratory I (TF-2281)’ courseat the Simón Bolívar University, Caracas, Venezuela (USB), isoffered to the third year of the chemical engineering pro-

ámica y Fenómenos de Transferencia, Laboratorio de FenómenosA, Sartenejas, Baruta, Edo. Miranda,

ccepted 22 February 2013neers. Published by Elsevier B.V. All rights reserved.

education for chemical engineers 8 ( 2 0 1 3 ) e58–e71 e59

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ddition, the heat transfer lab experiences are also offered asart of the heat transfer courses for mechanical engineering.he experiences study some of the following concepts:

Heat transfer: transient heat conduction, steady-state con-duction, radiation between plates, heat exchangers andviscous flow heat transfer.

Fluid mechanics: transport properties measurement, flowmeasurement instruments, pressure drop across pipes andfittings and, fixed and fluidised beds.

These experiences have not received any updates or majorevisions in the last 10 years, as neither new models nororrelations have been incorporated in the course. Labora-ory instructors have also realised that reports delivered bytudents have become very similar, almost like a template,epeating the same discussions and conclusions due to lackf drive, the inability of testing and comparing models andorrelations and wasted time in data processing. For these rea-ons and, in order to motivate students and challenge theironclusion drawing abilities, this author decided to propose

project for developing a software tool for each experience,ith aims of assisting time consuming data processing, and

ranting the students the capability of quickly assessing andomparing theoretical and numerical models and correlationsn different scenarios for each laboratory experience.

Through the development of such powerful and yet easy-o-use software tools, it is expected to close the gap betweenhe processing task and understanding the physical conceptsresented in lectures, as students would get plenty of time foromparing experimental results against models, discussingonceptually, quantitatively and qualitatively the occurringhenomenon or process and finally, understanding the effectf variables (Hinestroza and Papadopoulos, 2003; Feisel andosa, 2005; Vazquez-Arenas and Pritzker, 2010; Narang et al.,012).

In order to narrow the scope of the first stage of thisroject, a subset of the available laboratory experiences hado be chosen for developing the respective software tools. Theelection criteria were discussed with laboratory instructorsnd other staff members in the Thermodynamics and Trans-ort Phenomena Department at the USB. After the discussion,his author decided to choose three experiences, taking intoccount the following characteristics:

Mathematical and numerical complexity of theoreticalmodels and correlations.

Experimental data volume. Number of career programmes that employ that experience.

After the analysis, one fluid mechanics and two heat trans-er experiences were selected, as they will be presented inection 2. Next, a software platform needed to be chosen foreveloping the tools and, as shown in Section 3, spreadsheetsrovide balance between simplicity, speed and availability

Kanyarusoke and Uziak, 2011; Stamou and Rutschmann,011) and therefore, this was the preferred platform. Thectual task of developing the spreadsheet tools was carriedut by two groups of fourth year chemical engineering stu-ents (five people in total), under the scope of the courseamed ‘Short Research Project in Chemical Engineering (EP-103)’, tutored by this author. Such course is offered within

he chemical engineering programme as a means of tak-ng students through the whole research process, from the

literature review, experimental or development procedure,collecting and processing data, analysing and drawing con-clusions and finally, preparing a report with a technicalpaper format, followed by an oral presentation before thedepartment staff, using a congress meeting session setting(Coordinación Ingeniería Química, 2008).

The developed spreadsheets were reviewed and debuggedby this author and then, introduced into the ‘TransportPhenomena Laboratory I’ course and tested with a group offifteen students. Lastly, for assessing the effect on learning,students’ response, usefulness and quality of the developedtools, a simple survey was developed and applied to thesestudents after delivering each respective report (Abbas andAl-Bastaki, 2002; Erzen et al., 2003; Domingues et al., 2010), aspresented in Section 5.

This paper summarises the selected laboratory expe-riences and the criteria for their selection. Next, eachspreadsheet is described; typical results are displayed along-side with the observations and comments derived from theirintroduction into the lab course. Remarks and conclusionsexpressed by students in their reports are also included in thiswork. The applied survey is then discussed and, despite it wasonly applied to a small group of students; results are positiveand promising and, together with the conclusions drawn bystudents, the continuation and improvement of this projectare encouraged.

2. Selected Transport PhenomenaLaboratory experiences

As mentioned in Section 1, for the initial stage of this project,only three laboratory experiences were chosen. The selectioncriteria, discussed with staff members and instructors, con-sidered the experimental data volume to be processed, themathematical and numerical complexity of classic analytictheoretical models and correlations used for describing eachphenomenon, and last but not least, the impact related to thenumber of students to be benefited with this initiative.

As the set of heat transfer exercises available serve bothchemical and mechanical engineering programmes, it wasdecided to take two heat transfer exercises and one fluidmechanics exercise. Now, considering the topics covered inheat transfer theoretical courses, steady state and transientheat conduction subjects are widely discussed, however, usu-ally simplified analytic solutions are presented and short timeis given to the numerical approach. Therefore, the lab experi-ences dedicated to studying these phenomena are selected, asthey pose relative complexity in their theoretical and numer-ical models. It should be clarified that traditionally, in the lab,students were required to code these solutions, and frequentlyfailed to accomplish the task for several reasons, such as poortime management and insufficient computer programmingskills, even though the ‘Applied Numerical Methods in Engi-neering’ course is a prerequisite for enrolling in the laboratory.

On the other hand, within the fluid mechanics course, thetopic of flow through fixed and fluidised beds is not coveredand yet, there is a lab experience that studies it. As this expe-rience has never been updated, typically, students fail to fullyunderstand the underlying concepts due to lack of theoreticalbackground and insufficient information available in the labbooklet (Meléndez and Gutiérrez, 2005), just one simple modeland no correlations at all. This is the third experience chosen

for this project. The selected experiences are summarised asfollows.

e60 education for chemical engineers 8 ( 2 0 1 3 ) e58–e71

Fig. 1 – Temperature profiles expe

∞ 0 CYL

2.1. Temperature profiles

This experience studies the heat conduction through solidmetallic bars (aluminium and stainless steel) of different crosssection diameters. The experimental apparatus is shown inFig. 1. The main objectives of this experience are (Meléndezand Gutiérrez, 2005):

• Visualising bars’ temperature profile evolution when heatedat one end exposed to air.

• Comparing air convection coefficient values estimatedthrough correlations and analytic models.

• Estimating steel’s thermal conductivity.

Students record temperature readings for each bar untilreaching a steady state condition. An example of the typicaldata set obtained is shown in Fig. 2.

In order to fulfil the lab objectives, students must quanti-tative contrast data against models. Eq. (1) shows the classicDifferential Equation (DE) that models the temperature profilefor a constant cross-section area fin. For this DE there are setsof combinations of Boundary Conditions (BC), as presented inEq. (2) (Incropera et al., 2007):

d2T

dx2− hP

kAc(T − T∞) = 0 (1)

x = 0 : T = TBase (heated end)

x = L :

⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩

T = T∞ (infinite fin)

dT

dx= 0 (insulated end)

dT

dx= (T∞ − T) ·

(h

k

)(convective end)

(2)

Analytic solutions for Eq. (1) are presented by Incroperaet al. (2007) for each BC in Eq. (2), and these may also be solved

Fig. 2 – Temperatures profiles experi

rience laboratory equipment.

numerically through the finite difference method (Billo, 2007).Students were usually told to evaluate only the analytic solu-tions. The numerical counterpart was frequently left aside, asstudents needed to code the solutions each time and, repeat-edly faced coding problems, which delayed data processingand, making them sometimes even fail to deliver the reporton time.

2.2. Transient heat conduction

In this lab experience is studied the heating process of solidobjects of different non-metallic homogeneous materials. Themain goals are (Meléndez and Gutiérrez, 2005):

• Estimating and comparing water’s heat convection coeffi-cient values around different object shapes.

• Estimating the thermal conductivity of an ‘Unknown Mate-rial’ sample.

The experimental laboratory equipment consists of a reg-ulated temperature water bath where the sample objectsare submerged as shown in Fig. 3. Students measure thetemperature at the centre of the sample object and recordtime/temperature until reaching a close-to-equilibrium con-dition. Typical experimental results are presented in Fig. 4.

The classic analytic solutions of transient temperature pro-files are shown in Eqs. (3)–(6) (Incropera et al., 2007).

(T − T0

T∞ − T0

)CUBE

= f 3Plate(Bip, Fop, x∗

p) where x∗p = x

Lp

Fop = · t

L2p

(3)

(T − T0

T − T

)= fPlate(Bip, Fop, x∗

p) · fCylinder(Bic, Foc, r∗c )

where r∗c = r

RcFoc = · t

R2c

(4)

ence typical experimental data.

education for chemical engineers 8 ( 2 0 1 3 ) e58–e71 e61

Fig. 3 – Transient heat conduction experience laboratoryequipment.

Fig. 4 – Transient heat conduction experience typicalexperimental data.

Fig. 5 – Fixed and fluidised beds exp

fPlate(Bip, Fop, x∗p) =

∞∑n=1

Cn,p · exp(−�2n,p · Fop) · cos(�n,p · x∗

p) (5)

fCylinder(Bic, Foc, r∗c ) =

∞∑n=1

Cn,c · exp(−�2n,c · Foc) · J0(�n,p · r∗

c ) (6)

The �n parameters are the positive n roots of the respec-tive transcendental equations for plate and cylinder, whichdepend on the Biot numbers for each geometry (Bip = h·Lp/k;Bic = h·Rc/k) (Incropera et al., 2007).

It must be remarked that the implicit solution of Eqs. (3) and(4) for the convection coefficient can turn to be complex andcumbersome as these are series of infinite terms. Customarily,students were asked to use the one-term simplification of Eqs.(5) and (6), which is only valid for Fo > 0.2 (Incropera et al., 2007).However, this has led to inaccurate and some times, numeri-cally inconsistent results that students were unable to neitherexplain nor speculate upon the error source. Therefore, moreseries terms must be incorporated in order to improve thequality of estimated convection coefficients. So, here becomesnecessary the use of computational tools for performing suchcomplex calculations in reasonable time.

2.3. Fixed and fluidised beds

This lab session encourages students to observe and comparethe behaviours of fixed and fluidised beds for the solid–gas andsolid–liquid systems. The goal for this experience is to eval-uate the main parameters that describe this phenomenon,such as pressure drop, Froude and Reynolds numbers, bedvoid fraction and minimum fluidisation velocity (Meléndezand Gutiérrez, 2005). The experimental equipment consists oftwo rectangular Plexiglas columns filled with bed pellets, asshown in Fig. 5.

For each fluid–solid system, starting from the fixed bed con-

dition (ε0 ≈ 0.38), students gradually increase the fluid flow rateand record bed pressure drop and bed height until reaching

erience laboratory equipment.

e62 education for chemical engineers 8 ( 2 0 1 3 ) e58–e71

Fig. 6 – Fixed and fluidised beds experience typical

experimental data.

the fluidisation condition. Typical experimental data for bothsystems are presented in Fig. 6.

Students are here required to plot Froude number Eq. (7),bed porosity Eq. (8), pressure drop and the Wilhelm–Kwaukparameter Eq. (9) vs. Reynolds number Eq. (10) (McCabe et al.,2005) in order to identify the transition regions. Finally, theyare asked to compare the experimental pressure drop valuesagainst the Ergun (1952) equation for fixed beds, Eqs. (11) and(12) for fluidised beds. No other models or correlations arerequested.

Frdp = u20

gdp(7)

ε = 1 −(

L0

L

)(1 − ε0) (8)

K�P =d3

p�f

2�2f

(�P

L0

)(9)

Redp = �f u0dp

�f(10)

( ) [2 2 ] [

2]

�P

L Ergun= 150

�f u0(1 − ε)

gdpε3Redp+ 1.75

�f u0(1 − ε)

gdpε3(11)

(�P

L

)FB

= g(1 − ε)(�p − �f ) (12)

Recognising this deficiency in the experimental procedure,it was decided to demand the evaluation of more predictionmodels, such as Barnea and Mednick (1978) equation for fixedbeds, Eq. (13). In addition, a set of correlations available in theliterature (Yang, 2003) for estimating the minimum fluidisa-tion velocity value (umf) needed to be included for comparison.As this increases the amount of calculations, it is necessary toprovide a tool for assisting this task.

(�P

L

)B−M

=[

0.63 + 4.8Re�

]2

·{

6�f u2(1 − ε)[1 + K(1 − ε)1/3]

8gdpε2

}

where Re� = Redp

ε · exp[(5(1 − ε))/3 · ε];

K ={

2.57 if Redp < 400

2.76 otherwise(13)

3. Software platform selection

Computers have supplied the perfect platform for dataprocessing since they became available to academic institu-tions (Feisel and Rosa, 2005; Edgar, 2006; Baker and Sugden,2007). Many student-oriented modelling and simulation soft-ware tools have been developed ever since, employinglanguages and computing tools such as C++, Java, MS VisualBasic®, MATLAB®, MathCad®, COMSOLTM, and Spreadsheets(Evans, 2000; Abbas and Al-Bastaki, 2002; Erzen et al., 2003;Zheng and Keith, 2004; Coronell, 2005; Edgar, 2006; Axaopoulosand Pitsilis, 2007; Selmer et al., 2007; Stover, 2008; Kanyarusokeand Uziak, 2011; Narang et al., 2012), as well as commer-cial simulators (Dahm et al., 2002; Dahm, 2003; Wankat, 2006;Vazquez-Arenas et al., 2009). Nonetheless, some of these tools,such as MATLAB®, MathCad® and commercial simulators arecost prohibitive to most students and many institutions, par-ticularly in developing countries (Kanyarusoke and Uziak,2011). Moreover, another shortcoming of commercial simula-tors is the fact that students tend to see them as black-boxes,and may not fully understand the underlying phenomenonor process and simply accept the simulator outputs with-out further questioning (Hinestroza and Papadopoulos, 2003;Vazquez-Arenas and Pritzker, 2010).

Nowadays, spreadsheets have become universally avail-able to institutions and students and, together with currentdesktop computing capabilities, they offer a powerful andyet simple tool for accomplishing iterative, high volume andcomplex calculations, making them widely used in simula-tion and numerical methods courses (Savage, 1995; Burns andSung, 1996; Evans, 2000; Hinestroza and Papadopoulos, 2003;Coronell, 2005; Stover, 2008; Kanyarusoke and Uziak, 2011;Stamou and Rutschmann, 2011). Particularly, MS Excel®, incombination with MS Visual Basic for Applications® (VBA)has become very popular, as it provides a low cost and idealcompromise between computer programming (through VBA),built-in functions, graphical tools, data management in tablesand matrix formats and flexible user interface, through com-mand objects such as command buttons, drop boxes, check

boxes, etc. (Jacobson, 2001; Baker and Sugden, 2007; Billo, 2007;Foley, 2011; Stamou and Rutschmann, 2011).

education for chemical engineers 8 ( 2 0 1 3 ) e58–e71 e63

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mstMos

taop

Within the chemical engineering programme at the USB,tudents are trained to use MATLAB® in the Computing andumerical Methods lecture courses. They are also acquainted

o MS Excel® in the Physics Laboratory, but only to a basicevel, learning only plot experimental data and perform someimple cell operations.

Concerning about this deficiency, this author ran a smallearch through the main Venezuelan job sites and, found thatn general, employers demand familiarity and intermediate-o-high skills in the MS Office® environment, MS Excel® inarticular.

As an attempt to address such deficiency and help studentseet the job market requirements, this author decided to use

preadsheets as the programming environment for developinghe required tools for the chosen laboratory experiences. BeingS Excel® 2007 the available spreadsheet software through-

ut campus and, matching the employers’ needs, the platformelection was self made.

A double benefit is present here, as not only students usinghe developed tools will be benefited with the interaction, butlso the group of five students that developed the first versionf the spreadsheets, who received intensive training in VBArogramming from this author.

Fig. 7 – Screenshot of temperature pro

4. The spreadsheets

This section describes the developed spreadsheets for eachlaboratory experience, and introduces the typical final resultsfor each one of them. These final results are the kind of plotsand tables that students must present and analyse in their labreports.

Each spreadsheet is designed with an interactive, simpleand user-friendly interface in order to empower the studentfor testing different sets of data, conditions and correlations.Hence, students do not require prior computer programmingskills, just the basic familiarity the spreadsheet platform envi-ronment. In addition, attached to each spreadsheet is a simpleuser manual document.

4.1. Temperature profiles spreadsheet

For this spreadsheet, students must provide as inputs thematerial properties (check as known or not the thermal con-ductivity), geometry and the collected data set in steady-statecondition for the selected bar. After processing, the sheetpresents plots and tables showing calculated temperature pro-files, air convection coefficient values and estimated thermal

conductivity as the outputs. Fig. 7 is a screenshot of the input-data section of this sheet.

files lab experience spreadsheet.

e64 education for chemical engineers 8 ( 2 0 1 3 ) e58–e71

Table 1 – Heat transfer convection coefficient values inair calculated with different correlations and conditionsfor the metallic bars.

Bar Tsup (K) Convection coeff. h (W/(m2 K))

Morgan Churchill and Chu

Al-1 in.350a 8.1 7.4420b 9.7 8.9

Al-0.5 in.338a 9.2 8.3420b 11.6 10.5

St-1 in.326a 7.0 6.4415b 9.6 8.9

a Average temperature.b Heated end temperature.

polynomial to the first three points of the Steel’s experimentaldata set. These calculations lead to an estimated conductivity

First, students are required to evaluate convection coeffi-cient correlations in air for each metallic bar under differentconditions, as summarised in Table 1. Next, students mustcompare analytic and numeric solutions, evaluated with theobtained convection coefficient values, as shown in Fig. 8. Inaddition, students are asked to estimate by trial and error theair convection coefficient value that best adjusts the experi-mental data set for the aluminium bars, contrast it against the

Fig. 8 – Comparative analytic and numeric temper

values reported by correlations and, argue about the possiblecauses of the encountered differences.

In general, students have found that the convectioncoefficients calculated through correlations did not adjust theexperimental temperature profiles, regardless whether theanalytic or numeric solution was used. In their final reports,some students discussed about the possible causes; some ofthe proposed insights were:

• “. . .the correlations assume uniform cylinder temperature,which is not the case here. . .”

• “. . .proximity between bars might have induced and ascend-ing convective air flow, which increases the convectioncoefficient value. . .”

• “. . .an unnoticed air stream could have interfered with theexperiment, causing the convection coefficients to rise. . .”

For estimating the stainless steel bar’s thermal conduc-tivity, based on the obtained value for the 1-in. (0.0254 m)aluminium bar, students are told to assume an air convectioncoefficient value at the heated end of the steel bar similar tothe aluminium’s one, in this case, a value of 22 W/(m2 K) wastaken. The second order temperature derivative in Eq. (1) isnumerically obtained by adjusting and deriving a second grade

ature profile predictions for each metallic bar.

education for chemical engineers 8 ( 2 0 1 3 ) e58–e71 e65

Fig. 9 – Local air convection coefficient values for thea

vctvi

vcecmt(lcese

ams(ttpiiw

•

•

4

Irada

mwfi

Table 2 – Reference free convection coefficient values inwater for the selected objects calculated through theChurchill and Chu correlation (Incropera et al., 2007).

Geometry Conv. coeff. h (W/(m2 K))a

Horizontal cylinder 1293Vertical plate (cube side) 1033Upper plate (top) 672Lower plate (bottom) 1344Cube weighted average 1025

a T0 = 296 K and T∞ = 335 K.

low Fourier numbers. Students were told to pay attention to

luminium bars.

alue of 29.5 W/(m K). It must be noticed that the estimatedonductivity value is very sensitive to the assumed convec-ion coefficient value, for instance, if a convection coefficientalue of 21 W/(m2 K) is used, a 28.1 W/(m K) conductivity values obtained.

In their final reports, students compared the obtainedalues against those reported in the literature (the actualonductivity value for the steel bar is not reported in thequipment manual, therefore it remains unknown) and, manyoncluded that this method is only useful for estimating theagnitude order of thermal conductivity, as stainless steels’

hermal conductivity values range from 14 to 25 W/(m K)Incropera et al., 2007). Some students also quoted the fol-owing possible error sources in their reports: “. . .assumedonvection coefficient value; . . .steel bar temperature readingrrors; . . .not waiting long enough in order to get a real steady-tate condition”. A sensitivity analysis was not required in thisxperience.

In this experience students are also required to evaluatend analyse the local convection coefficient values for the alu-inium bars, as presented in Fig. 9. Such values are implicitly

olved with the spreadsheet from the analytic solutions of Eq.1) for all experimental data points with each boundary condi-ion in Eq. (2). As expected, the coefficient values are higher athe heated end of the bar and decrease exponentially with theosition, having an approximate average value of 23 W/(m2 K)

n every case. Students are asked to explain such behaviourn terms of the involved variables. Some of their answersere:

“. . .it is logical as the temperature difference decreasesalong the bars. . .”

“. . .the thinner bar cools down faster as it has a lowermass/surface area ratio. . .”

.2. Transient heat conduction

n the same fashion of the former spreadsheet, here theequired inputs are material and fluid properties, geometry,nalytic solution parameters and, collected temperature/timeata set. As outputs, Biot and Fourier numbers are presented,s well as the analytic temperature profiles, as shown in Fig. 10.

For evaluating analytic solutions in Eqs. (3) and (4) it isandatory to calculate the Biot numbers for each geometry,

hich require a known value for the heat convection coef-cient in water. Students are asked to evaluate through the

spreadsheet free convection correlations for each geometry(cylinder and plates), such as the classic Churchill and Chucorrelation (Incropera et al., 2007). Table 2 summarises typicalfree convection coefficient values, evaluated at the beginningof the heating process. As the analytic solutions of the tran-sient heat conduction problem assume a unique and constantconvection coefficient value for all the object’s surfaces, aweighted average value should be calculated for the cube usingthe surface area of each side as the weighting factor. These val-ues are used as an initial reference only; since there is agitationin the water bath, convection coefficient values are expectedto be higher than stagnant ones and, students must estimatesuch quantity.

In Fig. 11 is shown a comparative analysis that studentscarry out over the known material cylinder on analytic solu-tion dependence with the number of series terms, Eqs. (4)–(6).

Before introducing the spreadsheet, students were tradi-tionally told to use the approximation of one series term forEqs. (5) and (6). In consequence, students were unaware ofthe real behaviour of the analytic solutions and, generallyfound inconsistencies between experimental data and calcu-lated values and usually, failed to provide a sound explanationto their results.

As expected, when students stared to use the spreadsheet,they realised that analytic solutions reproduce experimentaldata properly when using a high number of series terms (Foley,2011) for cylinder Fourier numbers over 0.2. The spreadsheetsupports up to 200 series terms.

On the other hand, Fig. 11 shows a remarkable differencebetween the experimental data and analytic solution for very

Fig. 11 – Analytic solution dependence with number ofseries terms for the PVC cylinder.

e66 education for chemical engineers 8 ( 2 0 1 3 ) e58–e71

Fig. 12 – Water convection coefficient trial and error

the construction of the object sample, which uses a hollowPlexiglas tube threaded into the object in order to allocate thethermocouple in its centre. Finally, taking this into consider-ation, students were asked to discuss about the effect on theobject sample conductivity around its centre. Such discussionwas never requested before, as the analytic solution with oneseries term does not reproduce the system.

After observing the dependence on the number of seriesterms, students are indicated to set this number in 100, inorder to provide accurate solutions without compromisingspeed. Next, by trial and error, students must estimate the con-vection coefficient value that minimises the Quadratic Errorbetween the experimental data and the analytic solution forthe PVC cylinder Eq. (14), as noticed in Fig. 12. The convectioncoefficient value predicted by Churchill and Chu correlation(Incropera et al., 2007) marks the limit where the QuadraticError becomes asymptotic. It must be clarified here that veryhigh convection coefficient values produce extremely highBiot numbers, which cause numerical problems when solvingthe n roots for Eqs. (5) and (6), in consequence, it was estab-lished an upper limit of 600 for the Biot number within thespreadsheet.

E2 =∑

(TEXPi − TAnal.

i )2

(14)

i

Fig. 10 – Spreadsheet for transient h

estimation for the PVC cylinder.

Once the final estimated convection coefficient value isaccepted by students for the PVC cylinder, the experimentis repeated with the ‘Unknown Material’ cylinder (which is aTeflon® type material), having the same dimensions of the PVCone. Assuming the convection coefficients to be equal for bothcylinders, it can be estimated the thermal conductivity of the

‘Unknown Material’ by trial and error. Fig. 13 displays the trialand error evaluation process carried out by students. Before

eat conduction lab experience.

education for chemical engineers 8 ( 2 0 1 3 ) e58–e71 e67

Fig. 13 – Estimated thermal conductivity for the ‘unknownmaterial’ cylinder.

tip

udo(

ttc‘c

•

•

•

Fm

Fig. 15 – Comparative results for the solid–liquid system.

he introduction of the spreadsheet, the estimated conductiv-ty values by students were usually inconsistent and off-range,reventing them from doing a valuable discussion.

Next, in Fig. 14 are presented the comparative solutionssing different series terms for the ‘Unknown Material’ cylin-er. This plot visually confirmed to the students the validityf the approximation of using one series terms in Eqs. (5) and

6) for high Fourier numbers.In their final reports, students were able to discuss on solu-

ion sensitivity and computational cost on number of serieserms used and the effect of the chosen convection coeffi-ient value over the estimated thermal conductivity of theUnknown Material’. Some discussions offered the followingomments:

“These analytic solutions are complex, as it takes over 1 minto run when 200 terms are used.”

“The one series term approximation is not always valid, onlyfor high Fourier numbers for the cylinder.”

“The thermal conductivity for the ‘Unknown Material’ canonly be guessed through this method, as it depends uponthe selected convection coefficient value, it has a large asso-

ciated error.”

ig. 14 – Comparative analytic solutions for the ‘unknownaterial’ cylinder.

4.3. Fixed and fluidised beds

This spreadsheet is very similar to the former one. It requiresas inputs the fluid properties, particle geometry and density,and pressure drop vs. bed height data set. The outputs arethe different flow parameters, Eqs. (7)–(10), minimum fluidis-ation velocities, calculated from several correlations and thecorresponding plots.

In the original version of this laboratory experience, onlythe Ergun (1952) pressure drop equation was consideredand, it was constantly observed that it does not faithfullyreproduce the experimental data. Therefore, in this projectwas introduced the Barnea and Mednick (1978) model forcomparison purposes. Moreover, minimum fluidisation veloc-ity correlations were not included in the lab’s booklet norrequested for the discussion. Hence, some selected simplecorrelations have been incorporated into the spreadsheet.

Figs. 15 and 16 illustrate comparative results for eachfluid–solid system. The dash-dotted lines have been manu-ally added in order to highlight the observed transition regionon each system.

Students were explained that the experimental equip-ment beds have a rectangular shape with simple upwardflow plenums (Fig. 5) and they observed that such arrange-ments actually cause non-uniform particle distributions. Inthe solid–liquid bed is usually observed a counter–clockwiseparticle circulation and, in the gas–solid bed it is observed abubble flow, with the bubbles tending to lean on the right side

at high air flows. Students were also told that pressure dropmodels have been developed for cylindrical bed systems and

e68 education for chemical engineers 8 ( 2 0 1 3 ) e58–e71

Fig. 16 – Comparative results for the solid–gas system.

asked to compare the pressure drop predictions against theexperimental data and argue on the effect of the rectangularshape of the experimental equipment on pressure drop. Suchdiscussion was never done before, as not enough informationwas available.

In their discussions, students pointed out that both pres-sure drop models consistently predicted the location of thetransition regions, though, these models over predicted andunder predicted pressure drop values for the solid–liquid andthe solid–gas systems respectively. In addition, they acknowl-edged the fact that bed geometry affects pressure drop, butwithout further explanation.

Students were also able to identify the transition regions foreach system through the Bed porosity, Eq. (8), and K�P param-

Table 3 – Minimum fluidisation velocity predictions by selected

Correlation Restrictions

System Particle sh

Carman (1937) (S–G) Spheres onlyErgun (1952) (S–G) Spheres onlyLeva (1959) (S–G) –

Rowe (1961) (S–L) Spheres onlyWen and Yu (1966) (S–G) and (S–L) –

Richardson (1971) (S–L) Spheres onlyRiba et al. (1978) (S–L) Spheres onlyGrace (1982) (S–G) and (S–L) –

Chyang and Huang (1988) (S–L) Granular

Tannous et al. (1994) (S–L) –

Average

eter, Eq. (9), plots in Figs. 15 and 16. For this data set, theminimum fluidisation velocities (umf) observed were around0.08 m/s and 0.13 m/s for the solid–liquid and solid–gas sys-tems respectively. Such values should be compared againstpredictions of selected correlations, as listed in Table 3.

Despite the observed discrepancies among models andexperimental data, students realised that values predictedby the most recent correlations for the solid–liquid systemare closer in magnitude order to the measured value. On theother hand, the predicted values for the solid–gas system arevery distant from the observed one. Regretfully, students wereunable to provide an explanation to this behaviour; some justmentioned that: “. . .it might be attributed to the rectangu-lar shape”; “. . .the non-uniform flow distribution may causehigher pressure drops”. Ultimately, these findings make therectangular bed system worthy of further research.

5. Students’ survey

For evaluating students’ response to the introduction ofthe spreadsheets in the laboratory, a survey was developed(Stubington, 1995; Abbas and Al-Bastaki, 2002; Erzen et al.,2003; Domingues et al., 2010). The survey has a total of sixteenquestions, grouped in four categories, as compiled in Table 4.The questions are to be answered in a 1–5 Likert scale, where1 stands for “Fully disagree” and 5 stands for “Fully agree”.

The spreadsheets were tested at the USB, in the ‘TransportPhenomena Laboratory I’ course during the fall quarter of 2011with 15 students of chemical engineering. Students workedin groups of three people during the entire course, and had1 week for delivering the final report after each lab session.Students were surveyed at the moment of report delivery. Itshould be clarified that each group worked on the lab experi-ences in a different sequence. Table 5 summarises the surveyresults for all three spreadsheets.

Although these results are to be considered only as prelim-inary, because of the small population, in general, the threespreadsheets were welcomed by students.

Balancing section A results, students agreed that thespreadsheets are attractive, user-friendly and easy-to-use,being the ‘Transient Heat Conduction’ the most complex one.On the other hand, the user manuals were not as useful andclear as expected, evidently indicating that they require majorimprovements, as some students quoted in the open endedsection.

Section B shows some interesting and contradictoryresults. Firstly, students agreed in question B.3 that all spread-

correlations (Yang, 2003).

Minimum Fluidisation Velocity umf (m/s)

ape Solid–liquid Solid–gas

– 24.45 – 2.23

– 9.23 0.23 –

0.04 1.75 0.04 – 0.16 –

0.05 1.780.04 –0.05 –

0.09 7.89

education for chemical engineers 8 ( 2 0 1 3 ) e58–e71 e69

Table 5 – Survey results for the spreadsheets as percentage of respondents for each question.

Q Temperature profiles Transient heat conduction Fixed and fluidised beds

1 + 2 3 4 + 5 1 + 2 3 4 + 5 1 + 2 3 4 + 5

A.1 0 13 87 0 20 80 0 20 80A.2 0 13 87 0 40 60 0 0 100A.3 0 0 100 20 20 60 0 0 100A.4 0 13 87 0 20 80 0 20 80A.5 0 20 80 20 20 60 0 20 80A.6 0 33 67 20 20 60 20 40 40A.7 0 73 27 0 40 60 20 40 40B.1 0 13 87 20 0 80 0 40 60B.2 67 0 33 40 20 40 60 20 20B.3 0 0 100 0 20 80 0 40 60B.4 0 13 87 0 0 100 0 60 40C.1 13 0 87 20 0 80 0 0 100C.2 0 13 87 0 40 60 20 20 60C.3 13 0 87 0 0 100 0 20 80C.4 0 13 87 0 40 60 0 20 80C.5 0 13 87 0 40 60 0 20 80

1 + 2: fully disagree + disagree; 3: neutral; 4 + 5: agree + fully agree.

Table 4 – Survey questions.

Question A – Simulator characteristics and GUI designA.1 GUI Design is attractiveA.2 GUI is user-friendlyA.3 The spreadsheet is easy to useA.4 Size of Texts, Charts and Graphics is easy to readA.5 Results’ display quality is appropriateA.6 User manual is easy to understandA.7 User Manual was useful for learning how to use the

spreadsheet

Question B – User experienceB.1 I’m comfortable with MS Excel before the LaboratoryB.2 Instructor assistance was required for using the

spreadsheetB.3 Interaction degree between user and spreadsheet

was goodB.4 Amount of required knowledge on the Laboratory

experience required for using the spreadsheet

Question C – Contribution to learningC.1 Spreadsheet was useful for performing calculationsC.2 Spreadsheet contributed to the understanding of

the lab sessionC.3 It is justified the use of the spreadsheet in the

laboratory sessionC.4 Spreadsheet provided important time reduction in

calculationsC.5 Spreadsheet facilitates fulfilling more easily the

objectives

D – Comments

sstttmftwsfwt

yses quality as students had the new possibility of quickly

heets are well interactive, attaining the ‘Temperature Profiles’heet the highest score. This can be attributed to the fact thathis sheet has more drop boxes, checkboxes, command but-ons, etc. than the other two. It also has an illustrative imagehat changes according to the selected boundary condition,

aking of it an attractive and playful tool. Secondly, resultsor questions B.1 and B.2 appear to be somehow contradic-ory. Even though many students claimed to be comfortableith the MS Excel® 2007 environment before the laboratory

ession, over 30% required assistance for using the sheet. Suchact might be attributed to several factors as: user manualsere not clear enough; students did not fully understand the

ask and, some other students actually turned to be unfamiliar

with the spreadsheet platform. Ultimately, question B.4 par-tially confirms that the developed tools are neither virtual-labsnor didactic simulators, which are tools used for introducingnew concepts or procedures. Here, students require some the-oretical background in order to process the experimental dataand properly estimating parameters via trial and error runs.

In section C students considered the spreadsheets as use-ful and their incorporation justified (questions C.1 and C.3).Results for question C.2 are in some way confusing, spe-cially for the ‘Fixed and Fluidised Beds’ experience, which hadthe lowest score. This could be related to the students’ lackof background, as this subject is not covered in theoreticalundergraduate courses. Now, regarding questions C.4 and C.5,students perceived time savings when using the spreadsheetsconsidering the workload and, on the whole, acknowledgedthat the sheets contributed to fulfilling laboratory experiences’objectives. It should be reminded here that in contrast to thetraditional approaches, instructors requested more complexcalculations and analyses.

Students also submitted valuable comments and sugges-tions, such as incorporating more heat convection coefficientcorrelations, as the available ones did not fully reproduceddata; including spherical geometry for transient heat conduc-tion, as such sample objects are available in the laboratory;incorporating error bars in the graphics of fixed and fluidisedbeds, because actual readings tend to be unstable and fluctu-ating, and finally, incorporating calculation examples withinthe user-manuals.

6. Conclusions and future work

Three spreadsheets were presented in this project. They weredesigned for assisting the data processing and complex modelevaluation tasks of selected experiences of the ‘TransportPhenomena Laboratory I (TF-2281)’ course at the USB. Thesespreadsheets comprise analytical and numerical solutions ofdifferent models, as well as correlations available in the liter-ature. Fifteen chemical engineering students who tested thespreadsheets were surveyed, showing that spreadsheets wereconsidered useful for reducing workload and boosting anal-

rehearsing with diverse correlations and models. Students

e70 education for chemical engineers 8 ( 2 0 1 3 ) e58–e71

also submitted valuable suggestions for improving the spread-sheet experience, such as incorporating more correlations andmodels and examples into the user manuals, which will beconsidered for the next stage of this project, which is to cre-ate a spreadsheet for each lab experiment available in theTransport Phenomena Laboratory courses. Finally, the goal ofupdating the teaching and learning experience of chemicalengineering students at the Laboratory through computerswas fulfilled by the introduction of these spreadsheets, with-out the need for students to acquire any programming skills tobe able to use them. This can be considered a practical advan-tage, as it would allow other fellow communities to benefitfrom this work.

Spreadsheets freely available upon request to the corre-sponding author.

List of symbols and notation

Al aluminiumBi Biot number [1]C constant for plate or cylinder analytic solutiond diameter [m]E errorFo Fourier number [1]Fr Froude number [1]g acceleration of gravity [9.81 m/s2]h heat convection coefficient [W/(m2 K)]K Barnea and Mednick (1978) constant (Eq. (13)) [1]K�P Wilhelm–Kwauk parameter [1]k thermal conductivity [W/(m K)]L bar length; bed height [m]PVC polyvinyl chloride materialr radial position [m]R cylinder radius [m]Re Reynolds number [1]St steel (stainless)t time [s]T temperature [K]u velocity [m/s]x axial position [m]

Greek letters˛ thermal diffusivity [m2/s]�P pressure drop [Pa]ε bed porosity [1]� density [kg/m3]� dynamic viscosity [Pa s]� root of transcendental equation for plate or cylinder

[1]

Subscripts and superscriptsAnal. analyticBase bar heated endB–M Barnea and Mednick (1978)c cylinderdp particle diameterEXP experimentalFB fluidised bedf fluidi countermf minimum fluidisation

n series term numberp plate; particle

0 initial value* dimensionless coordinate∞ surrounding fluid

Acknowledgements

Firstly, the author wishes to thank the undergraduate studentsAlejandra Van-Dewalle, Rómulo Rothe, Elizabeth Rischbeck,Migueddy Pérez and Jesús Tezara for their valuable con-tributions in the first development of the spreadsheetsalpha-versions as ‘Short Research Projects in Chemical Engi-neering’ at the USB, tutored by this author. Finally, thanks toall the “Transport Phenomena Laboratory I” course studentsand instructors that participated in the assessment processof the spreadsheets.

Appendix A. Supplementary data

Supplementary data associated with this article can befound, in the online version, at http://dx.doi.org/10.1016/j.ece.2013.02.005.

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