Spreadsheets for assisting Transport Phenomena Laboratory experiences

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

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Spreadsheets for assisting Transport Phenomena Laboratory experiences Aurelio Stammitti ∗ Transport Phenomena Laboratory, Department of Thermodynamics and Transport Phenomena, Universidad Simón Bolívar, Caracas 1080A, Venezuela

a b s t r a c t Academic laboratories have been traditionally used for complementing and reinforcing in a practical way the theoretical 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, transient 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 complex 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, compare 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

1.

Introduction

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

Arenas and Pritzker, 2010; Patterson, 2011; Narang et al., 2012; Vernengo and Dahm, 2012). It is also a known issue that processing experimental data and comparing results against theoretical models can be time consuming due to iterative and complex calculations, which reduce the student’s available time for analysis and discussion 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)’ course at the Simón Bolívar University, Caracas, Venezuela (USB), is offered to the third year of the chemical engineering programme and, comprises a total of ten heat transfer and fluid mechanics experiences (Meléndez and Gutiérrez, 2005). In

∗ Correspondence address: Universidad Simón Bolívar, Dpto. Termodinámica y Fenómenos de Transferencia, Laboratorio de Fenómenos de Transporte, Edif. TYT, Ofic. 101, Apartado Postal 89000, Caracas 1080A, Sartenejas, Baruta, Edo. Miranda, Venezuela. Tel.: +58 212 906 4113; fax: +58 212 906 3743. E-mail addresses: [email protected], [email protected] Received 28 August 2012; Received in revised form 13 January 2013; Accepted 22 February 2013 1749-7728/$ – see front matter © 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ece.2013.02.005

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addition, the heat transfer lab experiences are also offered as part of the heat transfer courses for mechanical engineering. The experiences study some of the following concepts: • Heat transfer: transient heat conduction, steady-state conduction, radiation between plates, heat exchangers and viscous flow heat transfer. • Fluid mechanics: transport properties measurement, flow measurement instruments, pressure drop across pipes and fittings and, fixed and fluidised beds. These experiences have not received any updates or major revisions in the last 10 years, as neither new models nor correlations have been incorporated in the course. Laboratory instructors have also realised that reports delivered by students have become very similar, almost like a template, repeating the same discussions and conclusions due to lack of drive, the inability of testing and comparing models and correlations and wasted time in data processing. For these reasons and, in order to motivate students and challenge their conclusion drawing abilities, this author decided to propose a project for developing a software tool for each experience, with aims of assisting time consuming data processing, and granting the students the capability of quickly assessing and comparing theoretical and numerical models and correlations in different scenarios for each laboratory experience. Through the development of such powerful and yet easyto-use software tools, it is expected to close the gap between the processing task and understanding the physical concepts presented in lectures, as students would get plenty of time for comparing experimental results against models, discussing conceptually, quantitatively and qualitatively the occurring phenomenon or process and finally, understanding the effect of variables (Hinestroza and Papadopoulos, 2003; Feisel and Rosa, 2005; Vazquez-Arenas and Pritzker, 2010; Narang et al., 2012). In order to narrow the scope of the first stage of this project, a subset of the available laboratory experiences had to be chosen for developing the respective software tools. The selection criteria were discussed with laboratory instructors and other staff members in the Thermodynamics and Transport Phenomena Department at the USB. After the discussion, this author decided to choose three experiences, taking into account the following characteristics: • Mathematical and numerical complexity of theoretical models and correlations. • Experimental data volume. • Number of career programmes that employ that experience. After the analysis, one fluid mechanics and two heat transfer experiences were selected, as they will be presented in Section 2. Next, a software platform needed to be chosen for developing the tools and, as shown in Section 3, spreadsheets provide balance between simplicity, speed and availability (Kanyarusoke and Uziak, 2011; Stamou and Rutschmann, 2011) and therefore, this was the preferred platform. The actual task of developing the spreadsheet tools was carried out by two groups of fourth year chemical engineering students (five people in total), under the scope of the course named ‘Short Research Project in Chemical Engineering (EP4103)’, tutored by this author. Such course is offered within the chemical engineering programme as a means of taking students through the whole research process, from the

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literature review, experimental or development procedure, collecting and processing data, analysing and drawing conclusions and finally, preparing a report with a technical paper format, followed by an oral presentation before the department staff, using a congress meeting session setting (Coordinación Ingeniería Química, 2008). The developed spreadsheets were reviewed and debugged by this author and then, introduced into the ‘Transport Phenomena Laboratory I’ course and tested with a group of fifteen students. Lastly, for assessing the effect on learning, students’ response, usefulness and quality of the developed tools, a simple survey was developed and applied to these students after delivering each respective report (Abbas and Al-Bastaki, 2002; Erzen et al., 2003; Domingues et al., 2010), as presented in Section 5. This paper summarises the selected laboratory experiences and the criteria for their selection. Next, each spreadsheet is described; typical results are displayed alongside with the observations and comments derived from their introduction into the lab course. Remarks and conclusions expressed by students in their reports are also included in this work. The applied survey is then discussed and, despite it was only applied to a small group of students; results are positive and promising and, together with the conclusions drawn by students, the continuation and improvement of this project are encouraged.

2. Selected Transport Phenomena Laboratory experiences As mentioned in Section 1, for the initial stage of this project, only three laboratory experiences were chosen. The selection criteria, discussed with staff members and instructors, considered the experimental data volume to be processed, the mathematical and numerical complexity of classic analytic theoretical models and correlations used for describing each phenomenon, and last but not least, the impact related to the number of students to be benefited with this initiative. As the set of heat transfer exercises available serve both chemical and mechanical engineering programmes, it was decided to take two heat transfer exercises and one fluid mechanics exercise. Now, considering the topics covered in heat transfer theoretical courses, steady state and transient heat conduction subjects are widely discussed, however, usually simplified analytic solutions are presented and short time is given to the numerical approach. Therefore, the lab experiences dedicated to studying these phenomena are selected, as they pose relative complexity in their theoretical and numerical models. It should be clarified that traditionally, in the lab, students were required to code these solutions, and frequently failed to accomplish the task for several reasons, such as poor time management and insufficient computer programming skills, even though the ‘Applied Numerical Methods in Engineering’ course is a prerequisite for enrolling in the laboratory. On the other hand, within the fluid mechanics course, the topic of flow through fixed and fluidised beds is not covered and yet, there is a lab experience that studies it. As this experience has never been updated, typically, students fail to fully understand the underlying concepts due to lack of theoretical background and insufficient information available in the lab booklet (Meléndez and Gutiérrez, 2005), just one simple model and no correlations at all. This is the third experience chosen for this project. The selected experiences are summarised as follows.

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Fig. 1 – Temperature profiles experience laboratory equipment.

2.1.

Temperature profiles

This experience studies the heat conduction through solid metallic bars (aluminium and stainless steel) of different cross section diameters. The experimental apparatus is shown in Fig. 1. The main objectives of this experience are (Meléndez and Gutiérrez, 2005): • Visualising bars’ temperature profile evolution when heated at one end exposed to air. • Comparing air convection coefficient values estimated through correlations and analytic models. • Estimating steel’s thermal conductivity. Students record temperature readings for each bar until reaching a steady state condition. An example of the typical data set obtained is shown in Fig. 2. In order to fulfil the lab objectives, students must quantitative contrast data against models. Eq. (1) shows the classic Differential Equation (DE) that models the temperature profile for a constant cross-section area fin. For this DE there are sets of combinations of Boundary Conditions (BC), as presented in Eq. (2) (Incropera et al., 2007): d2 T hP − (T − T∞ ) = 0 kAc dx2

x=0:

x=L:

T = TBase

(1)

dT = 0 (insulated end) dx

Transient heat conduction

In this lab experience is studied the heating process of solid objects of different non-metallic homogeneous materials. The main goals are (Meléndez and Gutiérrez, 2005): • Estimating and comparing water’s heat convection coefficient values around different object shapes. • Estimating the thermal conductivity of an ‘Unknown Material’ sample. The experimental laboratory equipment consists of a regulated temperature water bath where the sample objects are submerged as shown in Fig. 3. Students measure the temperature at the centre of the sample object and record time/temperature until reaching a close-to-equilibrium condition. Typical experimental results are presented in Fig. 4. The classic analytic solutions of transient temperature profiles are shown in Eqs. (3)–(6) (Incropera et al., 2007).

T∞ − T0

k

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

CUBE

3 = fPlate (Bip , Fop , xp∗ ) where xp∗ =

Fop =

(2)

⎪ ⎪ ⎪   ⎪ ⎪ ⎩ dT = (T∞ − T) · h (convective end) dx

2.2.

 T−T  0

(heated end)

⎧ T = T∞ (infinite fin) ⎪ ⎪ ⎪ ⎪ ⎪ ⎨

numerically through the finite difference method (Billo, 2007). Students were usually told to evaluate only the analytic solutions. The numerical counterpart was frequently left aside, as students needed to code the solutions each time and, repeatedly faced coding problems, which delayed data processing and, making them sometimes even fail to deliver the report on time.

 T−T  0 T∞ − T0

CYL

x Lp

˛·t L2p

(3)

= fPlate (Bip , Fop , xp∗ ) · fCylinder (Bic , Foc , rc∗ )

where rc∗ =

r ˛·t Foc = 2 Rc Rc

Fig. 2 – Temperatures profiles experience typical experimental data.

(4)

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fPlate (Bip , Fop , xp∗ ) =

∞ 

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

(5)

n=1

fCylinder (Bic , Foc , rc∗ ) =

∞ 

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

(6)

n=1

Fig. 3 – Transient heat conduction experience laboratory equipment.

The  n parameters are the positive n roots of the respective transcendental equations for plate and cylinder, which depend 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 and cumbersome 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, numerically inconsistent results that students were unable to neither explain nor speculate upon the error source. Therefore, more series terms must be incorporated in order to improve the quality of estimated convection coefficients. So, here becomes necessary the use of computational tools for performing such complex calculations in reasonable time.

2.3.

Fig. 4 – Transient heat conduction experience typical experimental data.

Fixed and fluidised beds

This lab session encourages students to observe and compare the behaviours of fixed and fluidised beds for the solid–gas and solid–liquid systems. The goal for this experience is to evaluate the main parameters that describe this phenomenon, such as pressure drop, Froude and Reynolds numbers, bed void fraction and minimum fluidisation velocity (Meléndez and Gutiérrez, 2005). The experimental equipment consists of two rectangular Plexiglas columns filled with bed pellets, as shown in Fig. 5. For each fluid–solid system, starting from the fixed bed condition (ε0 ≈ 0.38), students gradually increase the fluid flow rate and record bed pressure drop and bed height until reaching

Fig. 5 – Fixed and fluidised beds experience laboratory equipment.

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 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 prediction models, such as Barnea and Mednick (1978) equation for fixed beds, Eq. (13). In addition, a set of correlations available in the literature (Yang, 2003) for estimating the minimum fluidisation velocity value (umf ) needed to be included for comparison. As this increases the amount of calculations, it is necessary to provide a tool for assisting this task.



 P  L

B−M

= 0.63 +

where Re =

K=

4.8 Re

2  ·

6f u2 (1 − ε)[1 + K(1 − ε)

Redp ε · exp[(5(1 − ε))/3 · ε]

1/3

]



8gdp ε2 ;

2.57 if Redp < 400

(13)

2.76 otherwise

3.

Fig. 6 – Fixed and fluidised beds experience typical experimental data. the fluidisation condition. Typical experimental data for both systems are presented in Fig. 6. Students are here required to plot Froude number Eq. (7), bed porosity Eq. (8), pressure drop and the Wilhelm–Kwauk parameter Eq. (9) vs. Reynolds number Eq. (10) (McCabe et al., 2005) in order to identify the transition regions. Finally, they are asked to compare the experimental pressure drop values against the Ergun (1952) equation for fixed beds, Eqs. (11) and (12) for fluidised beds. No other models or correlations are requested. u20

Frdp =

ε=1−

KP =

Redp =

(7)

gdp

L  0

L

d3p f

 P 

22f

L0

(8)

(9)

f u0 dp

(10)

f



 P  L

(1 − ε0 )

Ergun

= 150

f u20 (1 − ε) gdp ε3 Redp

2

+ 1.75

f u20 (1 − ε) gdp ε3

(11)

Software platform selection

Computers have supplied the perfect platform for data processing since they became available to academic institutions (Feisel and Rosa, 2005; Edgar, 2006; Baker and Sugden, 2007). Many student-oriented modelling and simulation software tools have been developed ever since, employing languages and computing tools such as C++, Java, MS Visual Basic® , MATLAB® , MathCad® , COMSOLTM , and Spreadsheets (Evans, 2000; Abbas and Al-Bastaki, 2002; Erzen et al., 2003; Zheng and Keith, 2004; Coronell, 2005; Edgar, 2006; Axaopoulos and Pitsilis, 2007; Selmer et al., 2007; Stover, 2008; Kanyarusoke and Uziak, 2011; Narang et al., 2012), as well as commercial 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 are cost prohibitive to most students and many institutions, particularly in developing countries (Kanyarusoke and Uziak, 2011). Moreover, another shortcoming of commercial simulators is the fact that students tend to see them as black-boxes, and may not fully understand the underlying phenomenon or process and simply accept the simulator outputs without further questioning (Hinestroza and Papadopoulos, 2003; Vazquez-Arenas and Pritzker, 2010). Nowadays, spreadsheets have become universally available to institutions and students and, together with current desktop computing capabilities, they offer a powerful and yet simple tool for accomplishing iterative, high volume and complex calculations, making them widely used in simulation and numerical methods courses (Savage, 1995; Burns and Sung, 1996; Evans, 2000; Hinestroza and Papadopoulos, 2003; Coronell, 2005; Stover, 2008; Kanyarusoke and Uziak, 2011; Stamou and Rutschmann, 2011). Particularly, MS Excel® , in combination with MS Visual Basic for Applications® (VBA) has become very popular, as it provides a low cost and ideal compromise between computer programming (through VBA), built-in functions, graphical tools, data management in tables and matrix formats and flexible user interface, through command objects such as command buttons, drop boxes, check boxes, etc. (Jacobson, 2001; Baker and Sugden, 2007; Billo, 2007; Foley, 2011; Stamou and Rutschmann, 2011).

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Within the chemical engineering programme at the USB, students are trained to use MATLAB® in the Computing and Numerical Methods lecture courses. They are also acquainted to MS Excel® in the Physics Laboratory, but only to a basic level, learning only plot experimental data and perform some simple cell operations. Concerning about this deficiency, this author ran a small search through the main Venezuelan job sites and, found that in general, employers demand familiarity and intermediateto-high skills in the MS Office® environment, MS Excel® in particular. As an attempt to address such deficiency and help students meet the job market requirements, this author decided to use spreadsheets as the programming environment for developing the required tools for the chosen laboratory experiences. Being MS Excel® 2007 the available spreadsheet software throughout campus and, matching the employers’ needs, the platform selection was self made. A double benefit is present here, as not only students using the developed tools will be benefited with the interaction, but also the group of five students that developed the first version of the spreadsheets, who received intensive training in VBA programming from this author.

4.

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The spreadsheets

This section describes the developed spreadsheets for each laboratory experience, and introduces the typical final results for each one of them. These final results are the kind of plots and tables that students must present and analyse in their lab reports. Each spreadsheet is designed with an interactive, simple and user-friendly interface in order to empower the student for testing different sets of data, conditions and correlations. Hence, students do not require prior computer programming skills, just the basic familiarity the spreadsheet platform environment. In addition, attached to each spreadsheet is a simple user manual document.

4.1.

Temperature profiles spreadsheet

For this spreadsheet, students must provide as inputs the material properties (check as known or not the thermal conductivity), geometry and the collected data set in steady-state condition for the selected bar. After processing, the sheet presents plots and tables showing calculated temperature profiles, air convection coefficient values and estimated thermal conductivity as the outputs. Fig. 7 is a screenshot of the inputdata section of this sheet.

Fig. 7 – Screenshot of temperature profiles lab experience spreadsheet.

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Table 1 – Heat transfer convection coefficient values in air calculated with different correlations and conditions for the metallic bars. Bar

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

Churchill and Chu

a

Al-1 in.

350 420b

8.1 9.7

7.4 8.9

Al-0.5 in.

338a 420b

9.2 11.6

8.3 10.5

St-1 in.

326a 415b

7.0 9.6

6.4 8.9

a b

Average temperature. Heated end temperature.

First, students are required to evaluate convection coefficient correlations in air for each metallic bar under different conditions, as summarised in Table 1. Next, students must compare analytic and numeric solutions, evaluated with the obtained convection coefficient values, as shown in Fig. 8. In addition, students are asked to estimate by trial and error the air convection coefficient value that best adjusts the experimental data set for the aluminium bars, contrast it against the

values reported by correlations and, argue about the possible causes of the encountered differences. In general, students have found that the convection coefficients calculated through correlations did not adjust the experimental temperature profiles, regardless whether the analytic or numeric solution was used. In their final reports, some students discussed about the possible causes; some of the proposed insights were: • “. . .the correlations assume uniform cylinder temperature, which is not the case here. . .” • “. . .proximity between bars might have induced and ascending convective air flow, which increases the convection coefficient value. . .” • “. . .an unnoticed air stream could have interfered with the experiment, causing the convection coefficients to rise. . .” For estimating the stainless steel bar’s thermal conductivity, based on the obtained value for the 1-in. (0.0254 m) aluminium bar, students are told to assume an air convection coefficient value at the heated end of the steel bar similar to the aluminium’s one, in this case, a value of 22 W/(m2 K) was taken. The second order temperature derivative in Eq. (1) is numerically obtained by adjusting and deriving a second grade polynomial to the first three points of the Steel’s experimental data set. These calculations lead to an estimated conductivity

Fig. 8 – Comparative analytic and numeric temperature profile predictions for each metallic bar.

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Table 2 – Reference free convection coefficient values in water for the selected objects calculated through the Churchill and Chu correlation (Incropera et al., 2007). Geometry Horizontal cylinder Vertical plate (cube side) Upper plate (top) Lower plate (bottom) Cube weighted average a

Fig. 9 – Local air convection coefficient values for the aluminium bars. value of 29.5 W/(m K). It must be noticed that the estimated conductivity value is very sensitive to the assumed convection coefficient value, for instance, if a convection coefficient value of 21 W/(m2 K) is used, a 28.1 W/(m K) conductivity value is obtained. In their final reports, students compared the obtained values against those reported in the literature (the actual conductivity value for the steel bar is not reported in the equipment manual, therefore it remains unknown) and, many concluded that this method is only useful for estimating the magnitude order of thermal conductivity, as stainless steels’ thermal conductivity values range from 14 to 25 W/(m K) (Incropera et al., 2007). Some students also quoted the following possible error sources in their reports: “. . .assumed convection coefficient value; . . .steel bar temperature reading errors; . . .not waiting long enough in order to get a real steadystate condition”. A sensitivity analysis was not required in this experience. In this experience students are also required to evaluate and analyse the local convection coefficient values for the aluminium bars, as presented in Fig. 9. Such values are implicitly solved with the spreadsheet from the analytic solutions of Eq. (1) for all experimental data points with each boundary condition in Eq. (2). As expected, the coefficient values are higher at the heated end of the bar and decrease exponentially with the position, having an approximate average value of 23 W/(m2 K) in every case. Students are asked to explain such behaviour in terms of the involved variables. Some of their answers were:

Conv. coeff. h (W/(m2 K))a 1293 1033 672 1344 1025

T0 = 296 K and T∞ = 335 K.

spreadsheet free convection correlations for each geometry (cylinder and plates), such as the classic Churchill and Chu correlation (Incropera et al., 2007). Table 2 summarises typical free convection coefficient values, evaluated at the beginning of the heating process. As the analytic solutions of the transient heat conduction problem assume a unique and constant convection coefficient value for all the object’s surfaces, a weighted average value should be calculated for the cube using the surface area of each side as the weighting factor. These values are used as an initial reference only; since there is agitation in the water bath, convection coefficient values are expected to be higher than stagnant ones and, students must estimate such quantity. In Fig. 11 is shown a comparative analysis that students carry out over the known material cylinder on analytic solution dependence with the number of series terms, Eqs. (4)–(6). Before introducing the spreadsheet, students were traditionally told to use the approximation of one series term for Eqs. (5) and (6). In consequence, students were unaware of the real behaviour of the analytic solutions and, generally found inconsistencies between experimental data and calculated values and usually, failed to provide a sound explanation to their results. As expected, when students stared to use the spreadsheet, they realised that analytic solutions reproduce experimental data properly when using a high number of series terms (Foley, 2011) for cylinder Fourier numbers over 0.2. The spreadsheet supports up to 200 series terms. On the other hand, Fig. 11 shows a remarkable difference between the experimental data and analytic solution for very low Fourier numbers. Students were told to pay attention to

• “. . .it is logical as the temperature difference decreases along the bars. . .” • “. . .the thinner bar cools down faster as it has a lower mass/surface area ratio. . .”

4.2.

Transient heat conduction

In the same fashion of the former spreadsheet, here the required inputs are material and fluid properties, geometry, analytic solution parameters and, collected temperature/time data set. As outputs, Biot and Fourier numbers are presented, as well as the analytic temperature profiles, as shown in Fig. 10. For evaluating analytic solutions in Eqs. (3) and (4) it is mandatory to calculate the Biot numbers for each geometry, which require a known value for the heat convection coefficient in water. Students are asked to evaluate through the

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

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the construction of the object sample, which uses a hollow Plexiglas tube threaded into the object in order to allocate the thermocouple in its centre. Finally, taking this into consideration, students were asked to discuss about the effect on the object sample conductivity around its centre. Such discussion was never requested before, as the analytic solution with one series term does not reproduce the system. After observing the dependence on the number of series terms, students are indicated to set this number in 100, in order to provide accurate solutions without compromising speed. Next, by trial and error, students must estimate the convection coefficient value that minimises the Quadratic Error between the experimental data and the analytic solution for the PVC cylinder Eq. (14), as noticed in Fig. 12. The convection coefficient value predicted by Churchill and Chu correlation (Incropera et al., 2007) marks the limit where the Quadratic Error becomes asymptotic. It must be clarified here that very high convection coefficient values produce extremely high Biot numbers, which cause numerical problems when solving the n roots for Eqs. (5) and (6), in consequence, it was established an upper limit of 600 for the Biot number within the spreadsheet. E2 =

 i

(TiEXP − TiAnal. )

2

(14)

Fig. 12 – Water convection coefficient trial and error estimation for the PVC cylinder. Once the final estimated convection coefficient value is accepted by students for the PVC cylinder, the experiment is repeated with the ‘Unknown Material’ cylinder (which is a Teflon® type material), having the same dimensions of the PVC one. Assuming the convection coefficients to be equal for both cylinders, it can be estimated the thermal conductivity of the ‘Unknown Material’ by trial and error. Fig. 13 displays the trial and error evaluation process carried out by students. Before

Fig. 10 – Spreadsheet for transient heat conduction lab experience.

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

the introduction of the spreadsheet, the estimated conductivity values by students were usually inconsistent and off-range, preventing them from doing a valuable discussion. Next, in Fig. 14 are presented the comparative solutions using different series terms for the ‘Unknown Material’ cylinder. This plot visually confirmed to the students the validity of 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 solution sensitivity and computational cost on number of series terms used and the effect of the chosen convection coefficient value over the estimated thermal conductivity of the ‘Unknown Material’. Some discussions offered the following comments:

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

4.3. • “These analytic solutions are complex, as it takes over 1 min to run when 200 terms are used.” • “The one series term approximation is not always valid, only for high Fourier numbers for the cylinder.” • “The thermal conductivity for the ‘Unknown Material’ can only be guessed through this method, as it depends upon the selected convection coefficient value, it has a large associated error.”

Fig. 14 – Comparative analytic solutions for the ‘unknown material’ cylinder.

Fixed and fluidised beds

This spreadsheet is very similar to the former one. It requires as inputs the fluid properties, particle geometry and density, and pressure drop vs. bed height data set. The outputs are the different flow parameters, Eqs. (7)–(10), minimum fluidisation velocities, calculated from several correlations and the corresponding plots. In the original version of this laboratory experience, only the Ergun (1952) pressure drop equation was considered and, it was constantly observed that it does not faithfully reproduce the experimental data. Therefore, in this project was introduced the Barnea and Mednick (1978) model for comparison purposes. Moreover, minimum fluidisation velocity correlations were not included in the lab’s booklet nor requested for the discussion. Hence, some selected simple correlations have been incorporated into the spreadsheet. Figs. 15 and 16 illustrate comparative results for each fluid–solid system. The dash-dotted lines have been manually added in order to highlight the observed transition region on each system. Students were explained that the experimental equipment beds have a rectangular shape with simple upward flow plenums (Fig. 5) and they observed that such arrangements actually cause non-uniform particle distributions. In the solid–liquid bed is usually observed a counter–clockwise particle circulation and, in the gas–solid bed it is observed a bubble flow, with the bubbles tending to lean on the right side at high air flows. Students were also told that pressure drop models have been developed for cylindrical bed systems and

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eter, Eq. (9), plots in Figs. 15 and 16. For this data set, the minimum fluidisation velocities (umf ) observed were around 0.08 m/s and 0.13 m/s for the solid–liquid and solid–gas systems respectively. Such values should be compared against predictions of selected correlations, as listed in Table 3. Despite the observed discrepancies among models and experimental data, students realised that values predicted by the most recent correlations for the solid–liquid system are closer in magnitude order to the measured value. On the other hand, the predicted values for the solid–gas system are very distant from the observed one. Regretfully, students were unable to provide an explanation to this behaviour; some just mentioned that: “. . .it might be attributed to the rectangular shape”; “. . .the non-uniform flow distribution may cause higher pressure drops”. Ultimately, these findings make the rectangular bed system worthy of further research.

5.

Fig. 16 – Comparative results for the solid–gas system. asked to compare the pressure drop predictions against the experimental data and argue on the effect of the rectangular shape of the experimental equipment on pressure drop. Such discussion was never done before, as not enough information was available. In their discussions, students pointed out that both pressure drop models consistently predicted the location of the transition regions, though, these models over predicted and under predicted pressure drop values for the solid–liquid and the solid–gas systems respectively. In addition, they acknowledged the fact that bed geometry affects pressure drop, but without further explanation. Students were also able to identify the transition regions for each system through the Bed porosity, Eq. (8), and KP param-

Students’ survey

For evaluating students’ response to the introduction of the 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 sixteen questions, grouped in four categories, as compiled in Table 4. The questions are to be answered in a 1–5 Likert scale, where 1 stands for “Fully disagree” and 5 stands for “Fully agree”. The spreadsheets were tested at the USB, in the ‘Transport Phenomena Laboratory I’ course during the fall quarter of 2011 with 15 students of chemical engineering. Students worked in groups of three people during the entire course, and had 1 week for delivering the final report after each lab session. Students were surveyed at the moment of report delivery. It should be clarified that each group worked on the lab experiences in a different sequence. Table 5 summarises the survey results for all three spreadsheets. Although these results are to be considered only as preliminary, because of the small population, in general, the three spreadsheets were welcomed by students. Balancing section A results, students agreed that the spreadsheets 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 and clear as expected, evidently indicating that they require major improvements, as some students quoted in the open ended section. Section B shows some interesting and contradictory results. Firstly, students agreed in question B.3 that all spread-

Table 3 – Minimum fluidisation velocity predictions by selected correlations (Yang, 2003). Restrictions

Correlation System Carman (1937) Ergun (1952) Leva (1959) Rowe (1961) Wen and Yu (1966) Richardson (1971) Riba et al. (1978) Grace (1982) Chyang and Huang (1988) Tannous et al. (1994)

(S–G) (S–G) (S–G) (S–L) (S–G) and (S–L) (S–L) (S–L) (S–G) and (S–L) (S–L) (S–L)

Particle shape

Minimum Fluidisation Velocity umf (m/s) Solid–liquid

Solid–gas

Spheres only Spheres only – Spheres only – Spheres only Spheres only – Granular –

– – – 0.23 0.04 0.04 0.16 0.05 0.04 0.05

24.45 2.23 9.23 – 1.75 – – 1.78 – –

Average

0.09

7.89

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

A.1 A.2 A.3 A.4 A.5 A.6 A.7 B.1 B.2 B.3 B.4 C.1 C.2 C.3 C.4 C.5

Temperature profiles

Transient heat conduction

Fixed and fluidised beds

1+2

3

4+5

1+2

3

4+5

1+2

0 0 0 0 0 0 0 0 67 0 0 13 0 13 0 0

13 13 0 13 20 33 73 13 0 0 13 0 13 0 13 13

87 87 100 87 80 67 27 87 33 100 87 87 87 87 87 87

0 0 20 0 20 20 0 20 40 0 0 20 0 0 0 0

20 40 20 20 20 20 40 0 20 20 0 0 40 0 40 40

80 60 60 80 60 60 60 80 40 80 100 80 60 100 60 60

0 0 0 0 0 20 20 0 60 0 0 0 20 0 0 0

3

4+5

20 0 0 20 20 40 40 40 20 40 60 0 20 20 20 20

80 100 100 80 80 40 40 60 20 60 40 100 60 80 80 80

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

Table 4 – Survey questions. Question A.1 A.2 A.3 A.4 A.5 A.6 A.7

A – Simulator characteristics and GUI design GUI Design is attractive GUI is user-friendly The spreadsheet is easy to use Size of Texts, Charts and Graphics is easy to read Results’ display quality is appropriate User manual is easy to understand User Manual was useful for learning how to use the spreadsheet

Question B.1 B.2

B – User experience I’m comfortable with MS Excel before the Laboratory Instructor assistance was required for using the spreadsheet Interaction degree between user and spreadsheet was good Amount of required knowledge on the Laboratory experience required for using the spreadsheet

B.3 B.4

Question C.1 C.2 C.3 C.4 C.5

C – Contribution to learning Spreadsheet was useful for performing calculations Spreadsheet contributed to the understanding of the lab session It is justified the use of the spreadsheet in the laboratory session Spreadsheet provided important time reduction in calculations Spreadsheet facilitates fulfilling more easily the objectives D – Comments

sheets are well interactive, attaining the ‘Temperature Profiles’ sheet the highest score. This can be attributed to the fact that this sheet has more drop boxes, checkboxes, command buttons, etc. than the other two. It also has an illustrative image that changes according to the selected boundary condition, making of it an attractive and playful tool. Secondly, results for questions B.1 and B.2 appear to be somehow contradictory. Even though many students claimed to be comfortable with the MS Excel® 2007 environment before the laboratory session, over 30% required assistance for using the sheet. Such fact might be attributed to several factors as: user manuals were not clear enough; students did not fully understand the task and, some other students actually turned to be unfamiliar

with the spreadsheet platform. Ultimately, question B.4 partially confirms that the developed tools are neither virtual-labs nor didactic simulators, which are tools used for introducing new concepts or procedures. Here, students require some theoretical background in order to process the experimental data and properly estimating parameters via trial and error runs. In section C students considered the spreadsheets as useful and their incorporation justified (questions C.1 and C.3). Results for question C.2 are in some way confusing, specially for the ‘Fixed and Fluidised Beds’ experience, which had the lowest score. This could be related to the students’ lack of background, as this subject is not covered in theoretical undergraduate courses. Now, regarding questions C.4 and C.5, students perceived time savings when using the spreadsheets considering the workload and, on the whole, acknowledged that the sheets contributed to fulfilling laboratory experiences’ objectives. It should be reminded here that in contrast to the traditional approaches, instructors requested more complex calculations and analyses. Students also submitted valuable comments and suggestions, such as incorporating more heat convection coefficient correlations, as the available ones did not fully reproduced data; including spherical geometry for transient heat conduction, as such sample objects are available in the laboratory; incorporating error bars in the graphics of fixed and fluidised beds, because actual readings tend to be unstable and fluctuating, and finally, incorporating calculation examples within the user-manuals.

6.

Conclusions and future work

Three spreadsheets were presented in this project. They were designed for assisting the data processing and complex model evaluation tasks of selected experiences of the ‘Transport Phenomena Laboratory I (TF-2281)’ course at the USB. These spreadsheets comprise analytical and numerical solutions of different models, as well as correlations available in the literature. Fifteen chemical engineering students who tested the spreadsheets were surveyed, showing that spreadsheets were considered useful for reducing workload and boosting analyses quality as students had the new possibility of quickly rehearsing with diverse correlations and models. Students

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also submitted valuable suggestions for improving the spreadsheet experience, such as incorporating more correlations and models and examples into the user manuals, which will be considered for the next stage of this project, which is to create a spreadsheet for each lab experiment available in the Transport Phenomena Laboratory courses. Finally, the goal of updating the teaching and learning experience of chemical engineering students at the Laboratory through computers was fulfilled by the introduction of these spreadsheets, without the need for students to acquire any programming skills to be able to use them. This can be considered a practical advantage, as it would allow other fellow communities to benefit from this work. Spreadsheets freely available upon request to the corresponding author.

Firstly, the author wishes to thank the undergraduate students Alejandra Van-Dewalle, Rómulo Rothe, Elizabeth Rischbeck, Migueddy Pérez and Jesús Tezara for their valuable contributions in the first development of the spreadsheets alpha-versions as ‘Short Research Projects in Chemical Engineering’ at the USB, tutored by this author. Finally, thanks to all the “Transport Phenomena Laboratory I” course students and instructors that participated in the assessment process of the spreadsheets.

List of symbols and notation

Appendix A. Supplementary data

Al Bi C d E Fo Fr g h K KP k L PVC r R Re St t T u x

aluminium Biot number [1] constant for plate or cylinder analytic solution diameter [m] error Fourier number [1] Froude number [1] acceleration of gravity [9.81 m/s2 ] heat convection coefficient [W/(m2 K)] Barnea and Mednick (1978) constant (Eq. (13)) [1] Wilhelm–Kwauk parameter [1] thermal conductivity [W/(m K)] bar length; bed height [m] polyvinyl chloride material radial position [m] cylinder radius [m] Reynolds number [1] steel (stainless) time [s] temperature [K] velocity [m/s] axial position [m]

Greek letters thermal diffusivity [m2 /s] ˛ pressure drop [Pa] P ε bed porosity [1] density [kg/m3 ]  dynamic viscosity [Pa s]  root of transcendental equation for plate or cylinder  [1] Subscripts and superscripts Anal. analytic bar heated end Base B–M Barnea and Mednick (1978) c cylinder particle diameter dp EXP experimental FB fluidised bed fluid f i counter mf minimum fluidisation series term number n plate; particle p

0 * ∞

initial value dimensionless coordinate surrounding fluid

Acknowledgements

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

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