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Understanding Transport Phenomena Concepts in Chemical Engineeringwith COMSOL Multiphysics Erick S. Vasquez*Department of Chemical and Materials Engineering, University of Dayton, Dayton, OH, USA*Corresponding author: evasquez1@udayton.eduABSTRACTTransport Phenomena in Chemical Engineeringinvolves three key aspects: Momentum, Heat andMass Transport. These areas are described bydifferential equations which are solved for aparticular problem using independent or a set ofcombined equations (e.g., water flowing in a heatedpipe). At an undergraduate level class, the advancedmathematics of partial differential equations, tensorsand the specific applications of conservations lawsfor a differential element are challenging concepts tounderstand.Nonetheless, Transport phenomenarepresent the basis of Chemical Engineeringfundamentals. For example, fluid velocitydistribution, temperature distribution, and fluxes(momentum flux, heat flux, and Mass/Molar Fluxes)are core concepts in Chemical Engineering.Although analytical solutions exist for verysimplified problems that are solved in class usingmathematics, the students are usually eager tounderstand the effect of velocity change in more thanone dimension and/or with respect to time. In thiswork, a unique approach is presented to develop anapplied Transport Phenomena course that involvessimulations using COMSOL Multiphysics . Thespecific models from the applications library used forenhancing students learning are (a) shell and tubeheat exchanger and (b) flow past a cylinder.Additionally, the Fluid Flow module, Heat Transfermodule, and Chemicals species Transport modulesare used to understand laminar/turbulent flow in apipe. As an outcome, it is expected that acombination of analytical solutions and theirrepresentation in COMSOL Multiphysics can beutilized to enhance students’ learning. A survey hasbeen developed to be used in the assessment oflearning outcomes from this class.The ultimate goal is to develop a project-basedcourse so that the students can obtain a practicalunderstanding of Transport Phenomena and connectthe importance of computational tools in manyChemical Engineering processes.Keywords: Engineering Education, TransportPhenomena, Student Creativity, Hands-onlearning.1. IntroductionMomentum, heat, and mass transfer are the three coreconcepts involved in Transport Phenomena. InChemical Engineering, the fundamental concepts areusually taught using the traditional BS&L textbook.1,2Typically, at an undergraduate level in our institution,this subject is divided into two courses and acomplementary laboratory. The first course involves1-D and steady-state problems for the Navier-Stokesequation and the equation of energy, and Fick’s 2ndlaw of Diffusion at steady state for Newtonian fluids.The second course involves unsteady state problemswhich are also solved mathematically with changes inone dimension. For example, when using the errorfunction to predict heating of a semi-infinite slab. Inthe second course, additional emphasis is placed oninterphase transport processes and turbulent flow.Lastly, the Transport Phenomena Laboratoryinvolves measurements of flow, temperature, .Recently, it has been shown that coupling computersimulations with theory lead to a better understandingof a topic.3,4 Due to the required use of PDEs andvarious assumptions needed to solve Transportphenomena problems, COMSOL Multiphysics is apotential tool that can enhance students’ learning ofthis topic. In fact, other researchers have alreadyfocused on the implementation of COMSOLMultiphysics to foster Transport Phenomenaunderstanding.5–8In this study, simple and easy-to-solve problems,including models from the application library, wereimplemented at the end of the second TransportPhenomena course at an undergraduate level. Duringa traditional lecture, analytical solutions of ODEs andPDEs are presented using a sequence of steps until aproblem is solved. Hence, the students found aconnection between the steps shown in class and onsetting up a study with the software interface.Students’ surveys were used to assess theunderstanding of transport phenomena after computersimulations, and a preliminary discussion of theseresults along with the survey questions is discussed.Excerpt from the Proceedings of the 2017 COMSOL Conference in Boston

COMSOL Multiphysics is a powerful tool forsolving a multitude of research projects; here, it isshown that it can also be used to motivate students tounderstand the concepts of Momentum, Heat, andMass Transport at an undergraduate level. Also, itgives a first-hand experience to computational toolsthat complement the lectures and the laboratoryexperiments.2. Methods and Examples using COMSOLMultiphysics COMSOL Multiphysics v.5.2 was used for all theclass examples. The students had complete access tothe software and performed the simulations withguidance from the instructor simultaneously. Thefollowing examples were implemented during classsessions [Note: * indicates a problem found in theapplication library]:A. Flow in a pipeB. Flow Between Parallel PlatesC. Heat Conduction through a planeD. Flow Past a Cylinder*E. Transient Diffusion or Tubular Reactor*.For Examples A-C, the students learned the selectionof space dimension, setup boundary conditions,steady vs. non-steady steady solutions, drawgeometries, and define mesh types. This connectionalso helped the students to identify the steps followedin-class for simplified problems.A project-type assignment was given to the studentsbased on the shell and tube heat exchanger*simulation at the end of the course. The assignmentconsisted of changing one variable of their choiceand compare it with the results provided originally.This assignment was left to connect concepts that aretaught in following courses: Fluid Flow and HeatTransfer and the Chemical Engineering UnitOperations Laboratory.Continuity Equation𝜌 . (𝐮) 0(1)Navier-Stokes Equation𝜌(𝐮. )𝐮 . [p𝐈 𝜇( 𝐮 ( 𝐮)𝑇 ] F(2)Fourier’s law of Heat Conduction𝐪 𝑘 𝐓(3)Energy Equation 𝐓𝜌𝐶𝑝 𝜌𝐶𝑝 𝐮. 𝐓 . 𝐪 Q Q ted(4) 𝑡Fick’s Laws𝐍𝒊 𝐷𝑖 𝑐𝑖 c𝑖 𝑡 . ( 𝐷𝑖 𝑐𝑖 ) 𝑅𝑖(5)(6)4. Simulation Results and Major TransportConcepts Illustrated in Class.4.1 Flow in a pipeLaminar flow was illustrated using flow in a pipe(Fig. 1). For this example, a Newtonian fluid wasselected at a constant temperature. The primary goalof this example consisted of identifying the velocityprofile, the maximum velocity at the center of thepipe, and the symmetry of the solution based ondefining an average velocity at the entrance of thepipe. The same examples was solved in classanalytically. However, using simulations, studentswere able to see the importance of assumptions andthe effects on the results from a 3-D point of view.3. Governing Equations and NumericalModelStationary and Time-Dependent studies wereimplemented in the class. Laminar flow andTurbulent flow (k-ϵ) were used to demonstrate thedifferent velocity profiles obtained in fluid flow. Heattransport was illustrated only using conductionthrough a wall. For Diffusion studies, transport ofdiluted species was utilized. Materials were selectedfrom the applications library and are specified foreach example in the next sections. The primaryequations used for each problem are the following:Figure 1. A) Top view of a pipe with a maximum velocityof 2 m/s and B) isometric view of the velocity profile.4.2 Flow between parallel platesA second concept illustrated with COMSOLMultiphysics involves pressure drop betweenparallel plates (Fig. 2). In this example, studentsdefined different boundary conditions such as inletand outlet pressure and determine the velocity profileat different sections of the system. Overall, theExcerpt from the Proceedings of the 2017 COMSOL Conference in Boston

students gained a better understanding of therelationship between pressure drop and fluid flow,which is typically covered by the Hagen-Poiseuilleequation for flow in a pipe. This example alsoillustrated fluid flow transitions between laminar andturbulent velocity profiles based on the gap betweenthe plates and the inlet pressure.Figure 2. A) Velocity magnitude for flow between parallelplates and B) Turbulent velocity profile (inset) and pressuredrop illustration.4.3 Heat conduction through a planeThis example was used to illustrate Fourier’s law ofheat conduction in one direction by defining thenecessary boundary conditions. By using a planegeometry, the students were able to connect theimportance of defining a coordinate system thatcorrelates with the direction of the heat flow. In thisexample (Fig. 3), the x-direction was used toillustrate the temperature drop across a plane. Inaddition, the linear temperature drop obtained in classfor panels was demonstrated. Another conceptillustrated with this example includes the calculationof heat flux and heat flow through an area usingsimulations. The students were able to observe theconvenience and the powerful use of computationalsimulations when predicting these quantities.After illustrating basic concepts and how to useCOMSOL Multiphysics in the classroom, thestudents were introduced to transient/unsteady statestudies using two examples.4.4 Flow past a cylinderThe concepts of streamlines, boundary layers, eddies,and turbulent flow were explained using an examplefrom the application library: Flow past a cylinder.The students demonstrated understanding on thistopic after running the simulations (Fig.4). Moreover,the students also changed the size or the position ofthe cylinder to obtain a better idea of the effects ofdisturbances in fluid flow. While these topicsenhanced students understanding, the mostinteresting outcome from this simulation was thegeneration of small video that showed the fluid flowas a function of time. This example fulfilled theexpectations of students on getting a betterunderstanding of transient fluid flow from asimulation point of view. Without experiments toconfirm transitional regimes—laminar to turbulentflow—simulations are an excellent alternative forthese topics.Figure 4. Fluid Flow past a cylinder at different Renumbers.4.5 Transient DiffusionDiffusion in 1- and 2-Dimensions was analyzed usingCOMSOL Multiphysics . These examples illustratedconcentration gradients as a function of time in morethan one dimension (Fig. 5). In fact, the importanceof Fick’s first and second law of diffusion wasemphasized. In the classroom, the students learnedabout the effects of 2-D concentration gradients asillustrated in Fig. 5C. Moreover, the students wereable to generate concentration profiles with respect totime which is comparable to mathematical models for1-D examples (Fig. 5B). Similar to the previoustransient example, the students were fascinated aboutthe generation of a small video to illustrate transienttransport phenomena processes.Figure 3. Temperature distribution across a concrete planefrom 160 to 20 C.Excerpt from the Proceedings of the 2017 COMSOL Conference in Boston

Figure 6. Shell and tube heat exchanger simulationsshowing temperature streamline with air(top) andFreon(bottom) as the materials under the same conditions.5. Students Assessment and FeedbackFigure 5. A) 1-D concentration drop as function of time,B)Concentration profiles for 1-D simulations and C) 2-Dconcentration drops for a plane.4.6 Students’ projects: Shell and tube heatexchangerProblem solving and creativity are key components inan engineering class.9 In this study, the creativity ofthe students was tested by allowing them to switchparameters of their choice using the shell and tubeheat exchanger application library example. While nomajor modifications were done on the geometry ofthe system, interesting results were obtained whenother materials were used or the fluid allocation (hotto cold) was switched. For example, instead of usingair to cool the system, Freon was selected from thematerials library. As a result, a new temperatureprofile and a different heat transfer coefficient wereobtained. Examples of the temperature streamlinesresults are shown in Fig. 6. As expected, Heat wastransferred a faster rate with this fluid.After spending class time and a take-home projectusing COMSOL Multiphysics , a survey wasprovided to the student for the assessment of theefficacy of using this software in a TransportPhenomena Course (Table 1).The main learning objective pursued in this coursewas to use a modeling software to help the studentsunderstand Transport phenomena topics using aninteractive platform. To develop the survey, a seriesof questions were introduced to the students in thefollowing order: (1) importance of computationalsimulation in Transport phenomena (Q1-Q3), (2)Specific questions regarding COMSOL Multiphysics as a software (Q4-Q7), and (3) examplesevaluation of the concepts illustrated in class and intheir project (Q8-Q11). The specific questions arelisted in Table 1.Results from this survey (Table 1) were mostly agreeand/or strongly agree for the majority of thequestions. However, some exceptions includedneutral answers, which were obtained mostly forquestion 4 (Table 1). In this survey, it is clear that thestudents could not connect some of the mathematicalpredictions and translate the use of simulations forthe design of an equipment.Excerpt from the Proceedings of the 2017 COMSOL Conference in Boston

Table 1. Students survey to evaluate their experience of learning Transport Phenomena with COMSOL Multiphysics StronglyStronglyDisagree Disagree Neutral Agree Agree1. Transport Phenomena helped me to connect various topics learned in myprevious Eng. Classes2. Simulations helped me to obtain a better understanding of TransportPhenomena3. The in-class examples helped me to visualize results in 3-D4. COMSOl modeling helped me to understand the relationship between actualexperiments and equipment design/ mathematical predictions5. COMSOL results are easy to understand and manipulate6. COMSOL is a software with a user friendly interface7. By using COMSOL , I am more interested in Transport phenomena8. Simulations/videos were useful to connect with the theory and understandmultidimensional flow9. The following modules were useful for my learning:a. flow in a pipe/ flow between two plates/ Heat conduction through a planeb. Flow past a cylinderc. Diffusion/Tubular reactor10. The project (Shell and tube HX) was effective in connecting new conceptsin Chemical Engineering11. The instructor should spend more class time with computer simulations toenhance my learning6. ConclusionsOverall, the students surveyed in this course weresatisfied by the implementation of a modelingsoftware in the Transport Phenomena class. One ofthe major concerns when implementing this type ofsimulations involves the ability to work with a userfriendly software interface. For this study, thestudents were completely satisfied on usingCOMSOL Multiphysics for this class based on thesurvey results (Q6; Table 1). In future courses, bothsimulations and mathematical results will be coveredat the same time to compare mathematical orexperimental results with simulation values.Similarly, as part of the suggestions, COMSOLMultiphysics could potentially be used formodeling the equipment in the Transport Phenomenalaboratory and in the Unit Operations laboratory inorder to validate simulations results. Thesesuggestions will be implemented in future sections aspart of the outcomes arising from this study.References1. Bird, B., Steward, W. & Lightfoot, E. TransportPhenomena (revised 2nd edition) John Wiley &Sons. New York (2007).2. Bird, R. B. Transport phenomena. Appl. Mech.Rev. 55, R1–R4 (2002).3. Bozkurt, E. & Ilik, A. The effect of computersimulations over students’ beliefs on physics andphysics success. Procedia-Soc. Behav. Sci. 2,4587–4591 (2010).4. Sarabando, C., Cravino, J. P. & Soares, A. A.Contribution of a computer simulation tostudents’ learning of the physics concepts ofweight and mass. Procedia Technol. 13, 112–121(2014).5. Geike, R. & Berlin, T. F. H. COMSOLmultiphysics in education–chemical reactions,heat and mass transfer. Proceedings of theCOMSOL Conference 1, (2008).6. Mills, P. L., Vasilev, M. & Sharma, P.Application of COMSOL Multiphysics Software in Transport Phenomena EducationalProcesses. Proceedings of the COMSOLConference in Boston, (2015)7. Pieper, M. & Schulz, S. Teaching SimulationMethods with COMSOL Multiphysics .Proceedings of the COMSOL Conference inCambridge, (2014)8. Plawsky, J. L. Transport phenomenafundamentals. CRC Press, (2014).9. Adams, J., Kaczmarczyk, S., Picton, P. &Demian, P. Problem solving and creativity inengineering: conclusions of a three year projectinvolving reusable learning objects and robots.Eng. Educ. 5, 4–17 (2010).AcknowledgementsThe author would like to acknowledge theDepartment of Mechanical Engineering and theDepartment of Electrical Engineering at theUniversity of Dayton for access to the computerlaboratory.Excerpt from the Proceedings of the 2017 COMSOL Conference in Boston

understanding of Transport Phenomena and connect the importance of computational tools in many Chemical Engineering processes. Keywords: Engineering Education, Transport Phenomena, Student Creativity, Hands-on learning. 1. Introduction . Momentum, heat, and mass transfer are the three core concepts involved in Transport Phenomena. In

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