heat transfer simulation

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LM-TH-11Learning Module 1Thermal AnalysisTitle Page GuideWhat is a Learning Module?A Learning Module (LM) is a structured, concise, and self-sufficient learning resource. AnLM provides the learner with the required content in a precise and concise manner, enablingthe learner to learn more efficiently and effectively. It has a number of characteristics thatdistinguish it from a traditional textbook or textbook chapter: An LM is learning objective driven, and its scope is clearly defined and bounded. Themodule is compact and precise in presentation, and its core material contains onlycontents essential for achieving the learning objectives. Since an LM is inherentlyconcise, it can be learned relatively quickly and efficiently. An LM is independent and free-standing. Module-based learning is therefore nonsequentialand flexible, and can be personalized with ease.Presenting the material in a contained and precise fashion will allow the user t

o learneffectively, reducing the time and effort spent and ultimately improving the learningexperience. This is the first module on thermal analysis and provides the user with thenecessary tools to complete a thermal FEM study with different boundary conditions. It goesthrough all of the steps necessary to successfully complete an analysis, including geometrycreation, material selection, boundary condition specification, meshing, solution, andvalidation. These steps are first covered conceptually and then worked through directly as

they are applied to an example problem.Estimated Learning Time for This ModuleEstimated learning time for this LM is equivalent to three 50-minute lectures, or one week ofstudy time for a 3 credit hour course.How to Use This ModuleThe learning module is organized in sections. Each section contains a short explanation and alink to where that section can be found. The explanation will give you an idea of whatcontent is in each section. The link will allow you to complete the parts of the

module youare interested in, while being able to skip any parts that you might already be

familiar with.The modularity of the LM allows for an efficient use of your time.LM-TH-12Table of Contents1. Learning Objectives ................................................................................................................ 3 2. Prerequisites ............................................................................................................................ 3 3. Pre-test ....................................................................


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............................................................... 3 4. Tutorial Problem Statements................................................................................................... 4 5. Conceptual Analysis ............................................................................................................... 7 6. Abstract Modeling .................................................................................................................. 8 7. Software-Specific FEM Tutorials ........................................................................................... 8 8. Post-test .................................................................................................................................. 8 9. Practice Problems.................................................................................................................... 8 10. Assessment ............................................................................................................................ 9 Attachment A. Pre-Test ............................................................................................................ 10 Attachment B. Conceptual Analysis ......................................................................................... 12 Attachment C1. SolidWorks-Specific FEM Tutorial 1............................................................. 15 Attachment C2. SolidWorks-Specific FEM Tutorial 2............................................................. 27 Attachment C3. SolidWorks-Specific FEM Tutorial 3...............................

.............................. 49 Attachment D. CoMetSolution-Specific FEM Tutorials .............................

............................. 64 Attachment E. Post-Test ........................................................................................................... 65 Attachment F. Practice Problems .............................................................................................. 68 Attachment G. Solutions to Practice Problems ......................................................................... 74 Attachment H. Assessment ....................................................................................................... 81 LM-TH-13

1. Learning ObjectivesThe objective of this module is to introduce the user to the process of static structural analysisusing FEM. Upon completion of the module, the user should have a good understanding of thenecessary logical steps of an FEM analysis, and be able to perform the following

tasks: Creating the solid geometry Assigning material properties Applying thermal boundary conditions Meshing Running the analysis Verifying model correctness

Processing needed results2. PrerequisitesIn order to complete the learning module successfully, the following prerequisites are required: By subject area:o Heat Transfero Thermal Analysis By topic:knowledge ofo convection


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o conductiono radiationo thermal resistanceo temperature distributiono temperature gradiento heat fluxo steady state analysiso transient analysiso energy balance3. Pre-testThe pre-test should be taken before taking other sections of the module. The purpose of the pretestis to assess the user's prior knowledge in subject areas relevant to heat transfer and thermalanalysis. Questions are focused towards fundamental concepts including temperaturedistribution, heat flux, thermal properties, and various boundary conditions.The pre-test for this module given in Attachment I. Link to Pre-testLM-TH-144. Tutorial Problem StatementsA good tutorial problem should focus on the logical steps in FEM modeling and demonstrate as

many aspects of the FEM software as possible. It should also be simple in mechanics with ananalytical solution available for validation. Three tutorial problems are covered in this learningmodule.Tutorial Problem 1A 2.25x1.5x1.5 meter table frame made of AISI 304 steel is subjected to four differenttemperatures at the bottom of each of its legs as shown below. Use FEM analysisto find thetemperature at points A, B, C, and D.AB

CD305 C200 C30 C10 CLM-TH-15Tutorial Problem 2A flanged pipe made of plain carbon steel is subjected to both convective and conductiveboundary conditions. Fluid inside the pipe is at a temperature of 130C and has aconvection

coefficient of hi = 160 W/m2-K. Air on the outside of the pipe is at 20C and hasa convectioncoefficient of ho = 70 W/m2-K. The right and left ends of the pipe are at temperatures of 450Cand 80C, respectively. There is a thermal resistance between the two flanges of 0.002 K-m2/W.Use FEM analysis to analyze the pipe under both steady state and transient conditions.LM-TH-16


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Tutorial Problem 3A square block with a thin cutout inside is exposed to radiation from a source of 100C andemissivity of 0.8. The outer faces are exposed to convective boundaries with h =

5 W/m2-K andT = 27C. The cutout is 0.01m deep, has a thermal conductivity of k = 1.5 W/m-K, and the restof the dimensions are given in the figure below. Use FEM analysis to find the temperaturedistribution throughout the model and plot the heat flux through the block.0.4m0.16m0.05mLM-TH-175. Conceptual AnalysisConceptual analysis is the abstraction of the logical steps in performing a task

or solving aproblem. Conceptual analysis for FEM simulation is problem type dependent but softwareindependent,and is fundamental in understanding and solving the problem.Conceptual analysis for static structural analysis reveals the following general

logical steps:1. Pre-processing

o Geometry creationo Material property assignmento Boundary condition specificationo Mesh generation2. Solution3. Post-processing4. ValidationAttachment II discusses the conceptual analysis for the tutorial problem in this

module. Link to Conceptual AnalysisLM-TH-186. Abstract Modeling

Abstract modeling is a process pioneered by CometSolutions Inc. Abstract modeling enables allattributes of an FEM model (such as material properties, constraints, loads, mesh, etc.) to bedefined independently in an abstract fashion, thus reducing model complexity without affectingmodel accuracy with respect to the simulation objective. It detaches attributesfrom one another,and emphasizes conceptual understanding rather than focusing on software specifics. Evidently,abstract modeling is independent of the specific software being used. This is afundamentaldeparture from the way most FEM packages operate.

Conceptual analysis focuses on the abstraction of steps necessary for an FEM simulation, whileabstract modeling focuses on the abstraction and modularization of attributes that constitute anFEM model. They are powerful enabling instruments in FEM teaching and learning. Link to Abstract Modeling7. Software-Specific FEM TutorialsIn software-specific FEM tutorial section, the tutorial problem is solved step by step in aparticular software package. This section fills in the details of the conceptual


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analysis as outlinedin previous section. It provides step by step details that correspond to the pre-processing,solution, post-processing and validation phases using a particular software package.Two commercial FEM packages are covered in this module: SolidWorks and CometSolution.Below are the two links: Link to SolidWorks FEM Tutorial 1 Link to SolidWorks FEM Tutorial 2 Link to SolidWorks FEM Tutorial 3 Link to CometSolution FEM Tutorials8. Post-testThe post-test will be taken upon completion of the module. The first part of the

post-test is fromthe pre-test to test knowledge gained by the user, and the second part is focused on the FEMsimulation process covered by the tutorial. Link to Post-Test9. Practice ProblemsThe user should be able to solve practice problems after completing this module.

The practiceproblems provide a good reinforcement of the knowledge and skills learned in the

module, and

LM-TH-19can be assigned as homework problems in teaching or self study problems to enhance learning.These problems are similar to the tutorial problems worked in the module, but they involvedifferent geometries and thermal boundary conditions. Link to Practice Problems Link to Solutions for Practice Problems10. AssessmentThe assessment is provided as a way to receive feedback about the module. The user evaluatesseveral categories of the learning experience, including interactive learning, t

he module format,its effectiveness and efficiency, the appropriateness of the sections, and the overall learningexperience. There is also the opportunity to give suggestions or comments aboutthe module. Link to AssessmentLM-TH-110Attachment A. Pre-Test1. Heat transfer through a solid body is referred to aso Conductiono Convectiono Radiation

o Generation2. The temperature gradient is defined aso Temperature rate of change per unit lengtho Heat flow through a bodyo Temperature rate of change per unit volumeo Temperature rate of change per unit area3. Heat flux is defined byo The amount of heat generated per unit volumeo The heat transfer rate per unit areao The amount of heat stored in a control volume


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o The temperature change per unit length4. Heat transfer between a solid body and a fluid is referred to aso Conductiono Convectiono Radiationo Generation5. Which behavior best describes a material with a high thermal conductivity compared to amaterial will a smaller thermal conductivity?o Temperature change is smaller through the solido Heat flux is higher through the solido Thermal resistance is lower through the solido All of the aboveLM-TH-1116. The convection coefficient is related too The rate that heat is transferred between a solid and fluido The rate that heat is transferred between two solidso The emissive power of the materialo The heat generation capability of the material7. The amount of heat transferred by radiation is directly related too The Stephan-Boltzmann constanto The surface temperatureo The emissivity of the material

o All of the above8. If no heat is transferred to or from a surface, it is referred to aso Isothermalo Exothermalo Adiabatico Isobaric9. When all temperatures are in equilibrium, the problem is assumed to beo Transiento Steady-Stateo Laminaro None of the above10. Which of the following terms is not part of the energy balance for heat transfer?

o Generated energyo Stored energyo Energy into the systemo Energy destroyed Click to continueLM-TH-112Attachment B. Conceptual AnalysisConceptual Analysis of Thermal SimulationConceptual analysis for a thermal problem using finite element analysis revealsthat thefollowing logical steps and sub-steps are needed:1. Pre-processing (building the model)

1. Geometry creation2. Material property assignment3. Boundary condition specification4. Mesh generation2. Solution (running the simulation)3. Post-processing (getting results)4. Validation (checking)The above steps are explained in some detail as follows.1. Pre-processingThe pre-processing in FEM simulation is analogous to building the structure or m


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aking thespecimen in physical testing. Several sub-steps involved in pre-processing are geometry creation,material property assignment, boundary condition specification, and mesh generation.The geometry of the structure to be analyzed is defined in the geometry creation

step. After thesolid geometry is created, the material properties of the solid are specified in

the materialproperty assignment step. The material properties required for the FEM analysisdepends on thetype of analysis. Some common material properties for thermal analysis are thermalconductivity, mass density, and specific heat.For most novice users of FEM, the boundary condition specification step is probably the mostchallenging of all pre-processing steps. Within a thermal analysis problem, there are variousboundary conditions that must be applied according to the problem statement. Ina thermalanalysis, heat can flow by means of conduction, convection and radiation. Conduction is the primary source of heat transfer through a solid body. Heat istransferred by conduction from higher temperatures in the solid to lower temperatures in

the solid and the temperature variation is linear. Heat transfer by conduction is dependenton the material s thermal conductivity (k) as well as the cross sectional area and

thetemperature gradient (change in temperature/change in distance). Convection is the primary source of heat transfer between one or more fluids. Forexample, heat can travel by convection between a solid body and a fluid such asair orwater. The convection heat transfer coefficient (h) defines how quickly heat travels fromone boundary to the next. Heat transfer by convection is also dependent on the surface

area exposed to the fluid as well as the ambient and surface temperatures.LM-TH-113 A solid body can lose or absorb thermal energy due to radiation. Radiation can occurbetween two different bodies or from a surface to ambient air. The heat transfer

rate forradiation is dependent on: the emissivity of the body, the exposed surface area,

theStephan-Boltzmann constant, and the surface and ambient temperatures.Other boundary conditions and properties also exist in a thermal analysis including: Adiabatic There is no heat transfer through an adiabatic boundary condition. A s

urfacecan be assumed to be adiabatic if there is no other boundary conditions appliedto it. Heat flux The heat transfer rate per unit area. Heat generation The amount of heat generated within a system. Usually expressedinunits of W/m3. Thermal energy balance The sum of all heat entering, exiting and generated is equal tothe amount of heat stored in a control volume.


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Steady-state analysis All temperatures and results are assumed to be in equilibrium andnot changing over time. Transient analysis An initial temperature is given and the problem is analyzed as thetemperature changes over time.Mesh generation is the process of discretizing the body into finite elements and

assembling thediscrete elements into an integral structure that approximates the original body. Most FEMpackages have their own default meshing parameters to mesh the model and run the

analysiswhile providing ways for the user to refine the mesh.2. SolutionThe solution is the process of solving the governing equations resulting from the discretizedFEM model. Although the mathematics for the solution process can be quite involved, this stepis transparent to the user and is usually as simple as clicking a solution button or issuing thesolution command.3. Post-processingThe purpose of an FEM analysis is to obtain wanted results, and this is what the

post-processing

step is for. Typically, various components or measures of temperature, heat flux, or temperaturegradient at any given location in the structure are available. The way a quantity is outputteddepends on the FEM software.4. ValidationAlthough validation is not a formal part of the FEM analysis, it is important to

be included.Blindly trusting a simulation without checking its correctness can be dangerous.

The validationusually involves comparing FEM results at one or more selected positions with exact orapproximate solutions using classical approaches learned in heat transfer or the

rmal analysiscourses. Going through validation strengthens conceptual understanding and enhances learning.Conceptual Analysis of a Given ProblemLM-TH-114This section will give an example of conceptual analysis that will be applied to

the first tutorialproblem. The goal of the FEM simulation is to correctly set up the boundary conditions and thenfind the temperature at various nodes. The problem shows a table frame with a given materialand four temperature boundaries applied to the legs. Conceptual analysis of the

current problemis described as follows.1. Pre-processing (building the model)The geometry of the structure is first created using the design feature of the FEM package. Next,a material is assigned to the solid model. In this problem, the material of theframe is given asAISI 304 steel. Depending on the software, the material is either directly selected as steel fromthe material library, or the properties of the material given in the problem are


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inputted directly.After assigning the material properties, the boundary conditions are specified.This problem has4 different temperature boundaries that need to be applied. The rest of the faces and edges of theframe are assumed to be adiabaticThe next step is to mesh the solid to discretize it into finite elements. Generally, commercialFEA software has automatic default meshing parameters such as average element size of themesh, quality of the mesh, etc. Here the default parameters provided by the software are used.2. Solution (running the simulation)The next step is to run the simulation and obtain a solution. Usually the software providesseveral solver options. The default solver usually works well. For some problems, a particularsolver may be faster or give more accurate results.3. Post-processing (getting results)After the analysis is complete, the post-processing steps are performed. Results

suchtemperature, heat flux, and temperature gradient can be viewed. In this example,

thetemperatures can be checked at the 4 nodes of interest.

4. Validation (checking)Validation is the final step in the analysis process. In this step, the temperatures at nodes 1-4 arecalculated by hand. These analytical solutions are compared with the software generated resultsto check the validity of the analysis.This completes the Conceptual Analysis section. Click the link below to continue

with thelearning module. Click to continueLM-TH-115Attachment C1. SolidWorks-Specific FEM Tutorial 1

Overview: In this section, three tutorial problems will be solved using the commercial FEMsoftware SolidWorks. Although the underlying principles and logical steps of anFEM simulationidentified in the Conceptual Analysis section are independent of any particularFEM software,the realization of conceptual analysis steps will be software dependent. The SolidWorks-specificsteps are described in this section.This is a step-by-step tutorial. However, it is designed such that those who are

familiar with thedetails in a particular step can skip it and go directly into the next step.Tutorial Problem 1. A four legged table frame is subjected to different temperat

ures at eachof its legs0. Launching SolidWorksSolidWorks Simulation is an integral part of the SolidWorks computer aided design softwaresuite. The general user interface of SolidWorks is shown in Figure 1.Figure 1: General user interface of SolidWorks.In order to perform FEM analysis, it is necessary to enable the FEM component, calledSolidWorks Simulation, in the software.


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Main menu Frequently used command icons Help iconRoll over todisplayFile,Tools andother menusLM-TH-116Step 1: Enabling SolidWorks Simulationo Click "Tools" in the main menu. Select "Add-ins...". The Add-ins dialog windowappears, as shown in Figure 2.o Check the boxes in both the Active Add-ins and Start Up columns correspondingto SolidWorks Simulation.o Checking the Active Add-ins box enables the SolidWorks for the current session.Checking the Start Up box enables the SolidWorks for all future sessions wheneverSolidWorks starts up.Figure 2: Location of the SolidWorks icon andthe boxes to be checked for adding it to the panel.1. Pre-ProcessingPurpose: The purpose of pre-processing is to create an FEM model for use in thenext step of thesimulation, Solution. It consists of the following sub-steps: Geometry creation Material property assignment

Boundary condition specification Mesh generation.1.1 Geometry CreationThe purpose of Geometry Creation is to create a geometrical representation of the solid object orstructure to be analyzed in FEM. In SolidWorks such a geometric model is calleda part. In thistutorial, the necessary part has already been created in SolidWorks. The following steps willopen up the part for use in the FEM analysis.Step 1: Opening the part for simulation. One of the following two options can be

used.o Option1: Double click the following icon to open the embedded part file, Table

Frame.SLDPRT, in SolidWorks.CheckSolidWorksSimulation boxesLM-TH-117Click SolidWorks part file icon to open it ==> o Option 2: Download the part file Table Frame.SLDPRT from the web sitehttp://www.femlearning.org/. Use the File menu in SolidWorks to open thedownloaded part.The SolidWorks model tree will appear with the given part name at the top. Above

the model

tree, there should be various tabs labeled Features, Sketch, etc. If the Simulation tab is notvisible, go back to steps 1 and 2 to enable the SolidWorks Simulation package.Step 2: Creating a Studyo Click the Simulation tab above the model treeo Under the drop-down menu select New Studyo In the box under Name type in Thermal Conduction Studyo Select Thermal underneath Type as in Figure 3o Click to create the studyFigure 3: Creating a thermal study


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LM-TH-1181.1 Material Property AssignmentThe next step in FEM analysis is to apply the material properties to the frame.The material isgiven in the problem as AISI 304 and the SolidWorks libraries can be used to apply the materialproperties.Step 3: Applying the materialo Select in the upper left hand cornero In the Select material source section, select the From library files optiono Expand the Steel section and choose AISI 304o Make sure Linear Elastic Isotropic option is selected under Model Type andunits are in SIo Verify the settings with Figure 4 and click OKFigure 4: Material property manager in SolidWorks1.3 Boundary Condition SpecificationSince this is a conduction study, the boundary conditions will be the temperatures at the fourlegs. In a thermal study in SolidWorks, the boundary conditions are called thermal loads. Thenext steps will apply the four different temperatures to the frame using thermal

loads. Thetemperatures need to be applied to the back faces of the frame so the figure nee

ds to be rotated tosee the correct face.LM-TH-119Step 4: Rotating the figureo Click on the View Orientation icon in the top of the workspaceo Select the Back option as in Figure 5Figure 5: Rotating the viewNote: The figure can also be rotated by pressing the scroll button the mouse and

moving itaround. However, in this problem it is much easier to refer to the four faces from the backorientation.

The part should now be oriented so the back four faces are visible. The boundaryconditiontemperatures can now be applied.Step 5: Applying a temperature boundary to the upper right faceo Click on the icon in the upper left corner of the screen to drop down thethermal loads menuo Select Temperatureo With the green box highlighted, select the upper right face of the frame as in

Figure 6o In the Temperature menu, change the units to Celsiuso Enter 30 in the numeric box next to ito Click to create the boundary temperatureLM-TH-1

20Figure 6: Setting a temperature boundaryStep 6: Applying a temperature boundary to the lower right faceo Click on the icon in the upper left corner of the screen to drop down thethermal loads menuo Select Temperatureo With the green box highlighted, select the lower right face of the frameo In the Temperature menu, change the units to Celsiuso Enter 200 in the numeric box next to ito Click to create the boundary temperature


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Step 7: Applying a temperature boundary to the lower left faceo Click on the icon in the upper left corner of the screen to drop down thethermal loads menuo Select Temperatureo With the green box highlighted, select the lower left face of the frameo In the Temperature menu, change the units to Celsiuso Enter 10 in the numeric box next to ito Click to create the boundary temperatureStep 8: Applying a temperature boundary to the upper left faceLM-TH-121o Click on the icon in the upper left corner of the screen to drop down thethermal loads menuo Select Temperatureo With the green box highlighted, select the upper left face of the frameo In the Temperature menu, change the units to Celsiuso Enter 305 in the numeric box next to ito Click to create the boundary temperatureThe frame is now fully defined with the four boundary conditions and can be move

on to meshgeneration and getting results.1.4 Mesh GenerationPurpose: The purpose of the Mesh Generation sub-step is to discretize the part into elements.

The mesh consists of a network of these elements. In this example, large elementsizes will causethe software to run incorrectly so there needs to be a fine mesh.Step 9: Meshing the modelo Right click on the icon in the model treeo Select Create Mesho Under the Mesh Parameters menu, change the units to cmo Underneath the units, type 3.5cm in the Global Size box as in Figureo Click to create the mesh2. SolutionPurpose: The Solution is the step where the computer solves the simulation problem andgenerates results for use in the Post-Processing step.

Step 1: Running the simulationo At the top of the screen, clicko When the analysis is finished, the icon will appear on the model tree3. Post-ProcessingPurpose: The purpose of the Post-Processing step is to process the results of interest. For thisproblem, the temperatures at four nodes will need to be acquired from the temperature plot.LM-TH-122To solve the problem, a thermal plot needs to be defined. This plot will show the temperature atany given element in the model.

Step 1: Defining a temperature ploto Right click on the icon in the model treeo Select Define Thermal Ploto Under the Display menu, select TEMP: Temperature in the first box andCelsius in the second box as in Figure 7o Click to create the plotFigure 7: Creating a temperature plotA plot should appear on the frame that shows the temperature distribution at the

different nodesas well as a legend. By default, the numbers in the legend are in scientific for


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mat. To make thelegend and probe results easier to read, the plot will be changed to a floatingnumber format.Step 2: Formatting the ploto Right click on the plot icon under in the model treeo Select Chart Optionso Inside the Position/Format section, change scientific(e) to floating(f) as inFigure 8o Click to accept the changesLM-TH-123Figure 7: Plot settings and how it affects the legendAnother formatting step that needs to be taken is to display the mesh along with

the temperaturedistribution on the plot.Step 3: Displaying the mesh on the plot along with the temperatureo Right click on the plot and select Settingso Click on the drop down menu underneath Boundary Options and change to Mesho Click to accept changes.Now that the plot is defined and formatted correctly, it can be probed to find the temperatures atthe four points of interest.Step 4: Selecting the probeo Right click on the temperature plot icon and select Probe

The probe property manager will appear with the options of At location and On SelectedEntities. When At location is selected under the Options menu, the probe can be usedtoclick on individual elements and it will display the temperature on the plot aswell as underneaththe Results section. If On selected entities is selected, the probe can be used to find thetemperature at all the elements on a face, edge or vertex.Step 5: Using the probeo Choose At location from the Options menuo Select the four corners of the frame as in Figure 8o The software gives temperatures for corners A, B, C and D as 111.6, 181.2, 108

.7,and 143.2, respectivelyLM-TH-124Figure 8: Probing the temperature plot at the four nodesThese answers will be verified in the next section.Hand CalculationsTo check the validity of the SolidWorks answers, a control volume needs to be defined aroundeach of the four nodes and an energy balance needs to be applied to find the theoreticaltemperatures. Nodes A, B, C, and D will all have conduction heat transfer from three different

directions. Assume all heat transfer is coming into the node and use a control volume as inFigure 9.LM-TH-125Figure 9: Sketch of the table frame with boundary conditions and control volumeFigure 9 shows the control volume and energy balance for node A. Heat transfer for conductionis given by the following equation:


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Where q is the heat transfer rate, k is the material s thermal conductivity, A isthe cross sectionalarea, TA is the temperature at node A, T is the temperature from the neighboring

node, and L isthe distance from the neighboring node to node A.Starting with an energy balance gives: Since there is no energy generation or stored energy in this problem, the last two terms can beneglected. Also, we assumed all the energy was going into node A so the energy out is zero. Thisleaves: Plugging in variables for q into the energy balance gives:

q1q2q3ABD C10C305C200C

30CLM-TH-126Since the cross sectional area and the thermal conductivity are the same for the

material, theycancel out. Plugging in values for the length then gives:

The equation has three unknowns, so it cannot be solved without applying an energy balance tothe other three nodes. Once an energy balance has been applied to all four nodes, the variablescan be put into a matrix and solved for. From the above equation for node A, the

coefficients foreach temperature are as follows:


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Repeating this process three more times gives:


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Using a matrix to solve the four equations gives the following:

The results are tabulated in the table, along with the simulation results and the percent difference.SolidWorks Hand Calculations Percent DifferenceTA 111.6 110.2 1.3TB 181.2 182.0 0.4TC 108.7 107.6 1.0TD 143.2 143.0 0.1LM-TH-127Attachment C2. SolidWorks-Specific FEM Tutorial 2Tutorial Problem 2. A pipe connected with a flange is subjected to convection, c

onduction,and a thermal resistance0. Launching SolidWorksIn order to perform FEM analysis, it is necessary to enable the FEM component, calledSolidWorks Simulation, in the software.Step 1: Enabling SolidWorks Simulationo Click "Tools" in the main menu. Select "Add-ins...". The Add-ins dialog windowappears, as shown in Figure 1.o Check the boxes in both the Active Add-ins and Start Up columns corresponding


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to SolidWorks Simulation.o Checking the Active Add-ins box enables the SolidWorks for the current session.Checking the Start Up box enables the SolidWorks for all future sessions wheneverSolidWorks starts up.Figure 1: The Add-Ins manager and Simulation boxes1. Pre-ProcessingPurpose: The purpose of pre-processing is to create an FEM model for use in thenext step of thesimulation, Solution. It consists of the following sub-steps:LM-TH-128 Geometry creation Material property assignment Boundary condition specification Mesh generation.1.1 Geometry CreationThe purpose of Geometry Creation is to create a geometrical representation of the solid object orstructure to be analyzed in FEM. In SolidWorks such a geometric model is calleda part. In thistutorial, the necessary part has already been created in SolidWorks. The following steps willopen up the part for use in the FEM analysis.Step 1: Opening the part for simulation. One of the following two options can be

used.o Option1: Double click the following icon to open the embedded part file FlangedPipe.SLDASM in SolidWorks.Click SolidWorks part file icon to open it ==> o Option 2: Download the part file Flanged Pipe.SLDASM and flange.SLDPRTfrom the web site http://www.femlearning.org/. Use the File menu in SolidWorks toopen the downloaded part.This problem will involve both steady state and transient heat transfer conditions. To study a heattransfer problem in SolidWorks, a thermal study needs to be created.

Step 2: Creating a Studyo Click the Simulation tab above the model treeo Under the drop-down menu select New Studyo In the box under Name type in Flanged Pipe Steady State Studyo Select Thermal underneath Type as in Figure 2o Click to create the studyLM-TH-129Figure 2: Creating a thermal study1.2 Material Property AssignmentThe next step in FEM analysis is to apply the material properties to the pipe and flange. Thematerial is given in the problem as plain carbon steel and the SolidWorks librar

ies can be used toapply the material properties.Step 3: Applying the materialo Select in the upper left hand cornero In the Select material source section, select the From library files optiono Expand the Steel section and choose Plain Carbon Steelo Make sure Linear Elastic Isotropic option is selected under Model Type and unitsare in SIo Verify the settings with Figure 3 and click OKLM-TH-1


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30Figure 3: The material property manager and SolidWorks libraries1.3 Boundary Condition SpecificationIn the Boundary Condition Specification sub-step, the restraints and loads on the part aredefined. In this problem there are multiple boundary conditions. The pipe experiences convectionon both the outer and inner faces as well as conduction through the metal. There

is also a smallthermal resistance between the two flanges that will need to be considered in the FEMsimulation. The SolidWorks Simulation software assumes that if no boundary conditions areapplied the surface is adiabatic. First the two temperature boundary conditionswill be applied onthe ends of the pipe.Step 4: Applying the 80C temperature boundaryo Click on the icon in the upper left corner of the screen to drop down thethermal loads menuo Select Temperatureo With the green box highlighted, select the left face of the pipe as in Figure4o In the Temperature menu, change the units to Celsiuso Enter 80 in the numeric box next to it

o Click to create the boundary temperatureLM-TH-131Figure 4: Setting the first temperature boundaryStep 5: Applying the 450C temperature boundaryo Click on the icon in the upper left corner of the screen to drop down thethermal loads menuo Select Temperatureo Rotate the assembly so that the right face of the pipe can be viewedo With the green box highlighted, select the right face of the pipe as in Figure

5o In the Temperature menu, change the units to Celsiuso Enter 450 in the numeric box next to it

o Click to create the boundary temperatureLM-TH-132Figure 5: Setting the second temperature boundaryIn the next step the convective boundary will be applied to the outer face of the pipe. Half of thepipe is well insulated, so the convection conditions will only be applied to the

section of the pipethat is exposed to air. For convection, two pieces of information are needed, the convectioncoefficient (h) and the temperature of the ambient air (T ). In this case h = 70 W/m2-K and T =20C (293 K).

Step 6: Applying the outer convection boundaryo Click on the icon in the upper left corner of the screen to drop down thethermal loads menuo Select Convectiono Highlight the green box under Selected Entities and select the four outer facesofthe pipe and flange as in Figure 6o Enter 70 in the Convection Coefficient boxo Enter 293 in the Bulk Ambient Temperature boxo Click to create the boundary


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LM-TH-133Figure 6: Applying the outer convective boundaryThis problem also has convection on the inside of the pipe from the fluid. In this case, h = 160W/m2-K and T = 130C (403 K).Step 7: Applying the inner convective temperature boundaryo Click on the icon in the upper left corner of the screen to drop down thethermal loads menuo Select Convectiono Highlight the green box under Selected Entities and select both inner faces of thepipe as in Figure 7o Enter 160 in the Convection Coefficient boxo Enter 403 in the Bulk Ambient Temperature boxo Click to create the boundaryLM-TH-134Figure 7: Applying the inner convective boundaryThe final boundary condition for this problem is the thermal resistance betweenthe flanges.Applying a thermal resistance is accomplished in SolidWorks by using the connections feature.The connections manager in SolidWorks requires the user to select two faces and

set the thermalresistance. In this case, the two faces of the flange cannot be seen so an exploded view will haveto be created that will allow the two faces to be selected.Step 8: Creating an exploded viewo Click on the Assembly tab in the command managero Click on to bring up the exploded view property managero Highlight the Settings box and select flange from the model treeo Select the z-axiso Type 100mm into the Explode distance boxo Verify the settings with Figure 8 and click to acceptLM-TH-135

Figure 8: Property manager for creating an exploded viewNow that the two inner faces of the flanges can be seen, the thermal resistancecan be applied.Step 9: Applying the thermal resistanceo Click on the icon in the upper left hand corner of the screen to dropdown the connections menuo Select Contact Seto Under Type, select Thermal Resistanceo Highlight the green box and select one of the flange faceso Highlight the pink box and select the other face of the flanges as in Figure 9o Select Distributed under the Thermal Resistance menuo Enter .002 (K-m^2)/W in the Thermal Resistance sectiono Click to apply the thermal resistance

LM-TH-136Figure 9: Applying a thermal resistance to the faces of the flangeThe assembly is now fully defined according to the problem statement. The exploded viewcreated earlier can be collapsed and separated at any time and will not affect the simulation. Thenext step is an optional step that will go over how to suppress an exploded view. The explodedview will be needed later in the post processing section to find the temperature


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at the flanges.Step 10: Suppressing the exploded viewo Click the Configuration Manager icono Expand all the tabs on the configuration tree by clicking the [+]o Right click on ExplView1 and select Collapse1.4 Mesh GenerationIn this step the specific mesh parameters for the model will be defined.Step 11: Meshing the modelo Right click on the icon in the model treeo Select Create Mesho Under the Mesh Parameters menu, change the units to cmo Underneath the units, type 1cm in the Global Size box as in Figure 10o Click to create the meshLM-TH-137Figure 10: Mesh settings for the model2. SolutionNow that the boundary conditions and mesh have been specified, the simulation needs to run andget data for post-processing.Step 1: Running the simulationo Run the analysis by clicking at the top of the screeno When the analysis is finished, the icon should appear3. Post-Processing

The post-processing step of this problem will involve creating two different plots for the steadystate solution and then looking at the transient solution. The first plot to create will show thetemperature distribution throughout the pipe.Step 1: Creating a temperature ploto Right click on the icono Select Define Thermal Ploto In the first box underneath Display, select TEMP: Temperatureo Select Celsius in the next boxo Click to accept the changesLM-TH-138

The next two steps will format the plot to make it easier to read. First, the number formatting willbe changed from scientific to floating.Step 2: Formatting the ploto Right click on the plot icon under in the model treeo Select Chart Optionso Inside the Position/Format section, change scientific(e) to floating(g) as inFigure 11o Click to accept the changesFigure 11: Changing the chart options to display floating numbersAnother formatting step that needs to be taken is to display the mesh along with

the temperaturedistribution on the plot.

Step 3: Displaying the mesh on the plot along with the temperatureo Right click on the plot and select Settingso Click on the drop down menu underneath Boundary Options and change to Mesho Click to accept changes.The next plot will look at the temperature gradient in the pipe. This plot willbe a vector plotinstead of a contour plot to better show how the direction and magnitude of thetemperaturechanges in the pipe.Step 4: Creating a temperature gradient plot


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o Right click on the icono Select Define Thermal Ploto In the first box underneath Display, select GRADN: Resultant Temp GradientLM-TH-139o Select C/cm in the next boxo Expand the Advanced Options tab and check the box next to Show as vector ploto Click to accept the changesThe next step will format the plot to make it easier to read.Step 5: Formatting the ploto Right click on the plot icon under the tabo Select Vector plot optionso In the first box under Options, type in 500o In the next box, type 80o Click to accept the changesThe first box in the vector plot options controls the size of the arrows and the

second boxcontrols the density of the arrows. These two numbers can be adjusted for any thermal analysisto make a vector plot more readable. The direction of the arrows represents theincreasingtemperature and the size of the arrows represents the magnitude. The next two figures show thevector plot at various points of interest.

Figure 12: Temperature gradient at the flangeLM-TH-140Figure 13: Temperature gradient on the insulated side of the pipeNotice how on the convective side the resultant arrows are vertical as well as horizontal. On theinsulated side the arrows at the top and bottom are strictly horizontal. This is

because no heat canescape out of the insulation and the temperature gradient does not change direction. The arrowsare the largest near the 450C boundary condition because the temperature is increasing rapidlyaround that area. Look at various areas on the pipe and flange and see how the t

emperaturegradient various at different boundary conditions and geometries.To verify the solution, the probe will be used to find temperatures at three locations on the pipethat will be compared to theoretical hand calculations. The three locations will

be on either sideof the flange and in the middle of the insulated section of the pipeStep 6: Probing the pipeo Rotate the part to the top orientation by using the icono Double click on the temperature plot to activate ito Right click on the temperature plot and select Probeo Under Options choose At locationo Select a node in the middle of the insulated side as in Figure 14

o SolidWorks gives the temperature to be 136.9LM-TH-141Figure 14: Using the probe to find the temperature in the middle of the pipeStep 7: Probing the flangeso Select On selected entitieso Highlight the inside circumference of a flange and click Updateo Look for the Avg under the Summary tab as in Figure 15o Right click on Edge under Results and select Clear Selectionso Repeat the process for the other flange


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o SolidWorks gives the temperatures to be 91.5 and 100.8o Click to exit the probeLM-TH-142Figure 15: Probing the average temperature along the inside of the flangeThese points will be verified in the next section. Now, the transient solution will be looked at tosee how transient analysis can be used in SolidWorks. The transient solution will show how thetemperature changes over time and the simulation software allows the user to specify the totaltime and the time steps. The current study can be used to look at the transientsolution, but theproperties of the current study need to be changed.Step 8: Setting up the transient studyo Right click on Flanged Pipe Steady State Study in the model treeo Select Propertieso Under Solution type, change from Steady State to Transiento Type 2000 in Total timeo Type 200 in Time increment as in Figure 16o Check the box next to Initial temperatures from thermal studyo Click OKLM-TH-143

Figure 16: Changing from a steady state to transient study using initial temperaturesWhen the simulation ran earlier in the tutorial, it solved for the steady statesolution only. To getthe transient results, the analysis needs to be run again.Step 9: Running the simulation for a transient studyo Run the analysis by clicking in the top of the screenThe study will give a solution at every 200 seconds for a total of 2000, which gives a total of 10sets of data. SolidWorks Simulation has several ways of examining the data and the next twosteps will go over how to watch the temperature change over time and how to graph it.

Step 10: Animating the ploto Right click on the temperature plot icon under the tabo Select Animateo Click the Play button under Basics to start the animationThe animation can be sped up or slowed down depending on user preference. Use the dial next toSpeed to control how fast the animation runs through its steps. Also, the start, end andincrement time can be adjusted by going back into the property manager. The next

step will plotvalues over time.LM-TH-144

Step 11: Graphing temperature over timeo Right click on the temperature plot icon under the tabo Select Probeo Choose At location from the probe property managero Click various nodes on the pipe and flange to get a variety of data pointso Click the Response icon under Report OptionsA graph similar to Figure 17 should pop up after a few moments.Figure 17: Various nodes as the temperature changes over timeFigure 17 shows the response of the system over time. In this case, the initialtemperature of the


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pipe was not specified so the data started at 0 K and increased to its steady state solution. Thesoftware also allows the user to specify an initial temperature for a transientstudy. The next stepwill set the initial temperature for all faces of the pipe to be 30C.Step 12: Modifying the transient studyo Right click on Flanged Pipe Steady State Study in the model treeo Select Propertieso Uncheck the box labeled Initial temperatures from thermal studyo Click OKNow, a temperature boundary condition needs to be used to specify the initial temperature of allthe faces. The whole body needs to be set at an initial temperature of 30C. By default,LM-TH-145SolidWorks is set to select exposed faces instead of entire bodies. The software

has a selectionfilter that allows the user to change between selecting faces, edges, solid bodies, etc.Step 13: Using the selection filter toolo In the main menu, go to View -> Toolbars -> Standardo When the Standard toolbar appears, selecto Select the Filter Solid Bodies icon

This will allow the selection of an entire body when applying the initial temperature. The variousfilters can be turned on and off as needed. The software will often revert to its default settings sothe filters may need to be applied multiple times.Step 14: Setting an initial temperatureo Click on the icon in the upper left corner of the screen to drop down thethermal loads menuo Select Temperatureo Choose Initial temperature under Typeo Apply the selection filter as in Step 13o Select the two pieces of the assemblyo In the Temperature menu, change the units to Celsius

o Enter 30 in the numeric box next to ito Click to set the initial temperatureThe boundary condition markers in SolidWorks can make the model hard to read. To

get rid ofthe markers, right click on the icons under Thermal Loads and select Hide. The boundaryconditions will still be evaluated in the simulation but the markers will be hidden. Now that theboundary conditions have changed, the study must be run again to get the results.Step 15: Running the simulation for a transient study Run the analysis by clicking in the top of the screenRepeat Steps 10 and 11 to see how the temperature graphs have changed over time

with an initialtemperature set to 30C instead of 0K. The animation can also be run for the graphof the

temperature gradient. Activate the temperature gradient plot and run the animation to see howthe vector magnitudes change over time.VerificationLM-TH-146In this section the temperatures acquired from the SolidWorks steady state tempe


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rature studywill be verified. The transient solution is much more complicated to solve so only the steadystate solution will be verified. To calculate the temperatures at the nodes, three control volumesaround the unknowns need to be set up as in the following figure.Figure 18: Control volumes for the three unknown temperaturesThe following dimensions will be needed to solve the problem: the outside diameter of the pipe(Do), inside diameter (Di), diameter of the flange (Dflange), and the length ofeach section of pipe(L). The dimensions are listed below along with the units. Do = .08m Di = .06m Dflange = .15m L = .40mEach control volume will have an energy balance applied to it. There is both convection andconduction heat transfer going in and out of each node so the following two equations areneeded:Conduction

Where q is the heat transfer rate, k is the thermal conductivity, Ac is the cross sectional area, Tis the change in temperature from one node to the next, and is the change in distance betweenthe two points.Convection Where q is the heat transfer rate, h is the convection coefficient, A is the surface area, T is thetemperature, and T is the ambient temperature.T1 T2 T3 T4 T5CV 3 CV 2 CV 1

LM-TH-147Also, the thermal resistance between the flanges needs to be accounted for. Thermal resistance isrelated to the heat transfer rate by the following equation: Since all energy is assumed to be entering the node, the energy balance reducesto the followingequation: For the first control volume, there is conduction on the left and right of the n

ode and convectionon the inside of the pipe. The outer edge is adiabatic so no heat enters or leaves from the outside.When using a temperature for the convection equations, use the temperature in the middle of thenode. For CV 1, it is just T4 but the other two control volumes need a center temperature that isrelated to the neighboring nodal temperatures. The energy balances for the three

control volumesare below.


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CV 1: CV 2: CV 3:

Substituting in numbers and solving for coefficients for T2, T3, and T4 gives the following threeequations: LM-TH-148Solving for the three unknown temperatures and comparing to the simulation results gives:T2 = 93.1CT3 = 102.5CT4 = 149.8C

SolidWorks (C) Hand Calculations (C) Percent Difference (%)T2 91.5 93.1 1.7T3 100.8 102.5 1.7T4 136.9 149.8 9.4The hand calculations compare well with the results from the simulation. Differences in thenumbers could be due to some of the assumptions made in the analysis such as neglecting themissing area of the bolts when calculating resistance. Also, the area surrounding T4 has a high


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temperature gradient so the results will not be as accurate when only one node is used torepresent the right side of the pipe. More accurate results could be obtained if

more nodes wereused in this area.LM-TH-149Attachment C3. SolidWorks-Specific FEM Tutorial 3Tutorial Problem 3. A square box with a thin cutout in the middle exposed toradiation and convection0. Launching SolidWorksIn order to perform FEM analysis, it is necessary to enable the FEM component, calledSolidWorks Simulation, in the software.Step 1: Enabling SolidWorks Simulationo Click "Tools" in the main menu. Select "Add-ins...".o Check the boxes in both the Active Add-ins and Start Up columns correspondingto SolidWorks Simulation.o Checking the Active Add-ins box enables the SolidWorks for the current session.Checking the Start Up box enables the SolidWorks for all future sessions wheneverSolidWorks starts up.1. Pre-ProcessingPurpose: The purpose of pre-processing is to create an FEM model for use in thenext step of the

simulation, Solution. It consists of the following sub-steps: Geometry creation Material property assignment Boundary condition specification Mesh generation.1.1 Geometry CreationThe purpose of Geometry Creation is to create a geometrical representation of the solid object orstructure to be analyzed in FEM. In SolidWorks such a geometric model is calleda part. In thistutorial, the necessary part has already been created in SolidWorks. The following steps willopen up the part for use in the FEM analysis.

Step 1: Opening the part for simulation. One of the following two options can beused.o Option1: Double click the following icon to open the embedded part file Plate withCutout.SLDPRT in SolidWorks.Click SolidWorks part file icon to open it ==> LM-TH-150o Option 2: Download the part file Plate with Cutout.SLDPRT from the web sitehttp://www.femlearning.org/. Use the File menu in SolidWorks to open thedownloaded part.

Only of the block has been modeled instead of the whole piece. This is because the block issymmetric about the center and adiabatic boundary conditions can be used to mirror the rest ofthe block. Notice also that there is a square plate above the block that will be

used to help createthe radiation boundary condition.Step 2: Creating a thermal studyo Click the Simulation tab above the model treeo Under the drop-down menu select New Study


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o In the box under Name type in Radiation Studyo Select Thermal underneath Type as in Figure 1o Click to create the studyFigure 18: Creating a thermal study1.1 Material Property AssignmentThe next step in FEM analysis is to apply the material properties to the plate.The materialproperties are given in the problem as k = 1.5 W/m-K and mass density equal to 7000 kg/m3.Step 3: Applying the materialLM-TH-151o Select in the upper left hand cornero In the Select material source section, select the Custom defined optiono Type 7000 next to Mass densityo Type 1.5 next to Thermal conductivityo Make sure Linear Elastic Isotropic option is selected under Model Type and unitsare in SIo Verify the settings with Figure 2 and click OKFigure 19: Material property manager1.3 Boundary Condition SpecificationIn this example there are three boundary conditions: radiation, convection, andadiabatic. Bydefault, SolidWorks Simulation assumes any undefined surfaces to be adiabatic so

thoseboundary conditions do not need to be defined. First, the convection boundary conditions will beapplied.Step 4: Applying a convective boundaryLM-TH-152o Click on the icon in the upper left corner of the screen to drop down thethermal loads menuo Select Convectiono Highlight the green box under Selected Entities and select the four outer facesofthe box as in Figure 3

o Enter 5 in the Convection Coefficient boxo Enter 300 in the Bulk Ambient Temperature boxo Click to create the boundaryFigure 20: Convection property manager and selected faces for the problemThe next boundary condition for the box involves radiation. In SolidWorks, radiation can besimulated from surface to surface or surface to ambient air. In this case, there

is a thin plateradiating to the box so the open system option will be selected. First, the temperature of theflat plate needs to be defined. The next step will apply the boundary conditionto the thin plate.Step 5: Applying a temperature to the plate

o Click on the icon in the upper left corner of the screen to drop down thethermal loads menuo Select TemperatureLM-TH-153o Highlight the green box and select the lower face of the plateo Type 100 underneath the Temperature menu and change the units to Celsius asin Figure 4o Click to create the boundaryFigure 21: Setting the temperature for the lower face of the plate


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Now that the plate has a defined temperature, the software can be instructed toradiate to the box.To accomplish this, a radiation boundary must be defined. In this example, the plate will radiatefrom the plate s lower surface to the box s upper face as well as radiate from the plate to theambient air. This is considered an open system by the software.Step 6: Defining a radiation boundaryo Click on the icon in the upper left corner of the screen to drop down thethermal loads menuo Select RadiationLM-TH-154o Underneath the Type section, select Surface to surfaceo Highlight the green box and select the faces of the plate and the box as in Figure 5o Check the box labeled Open systemo Type 27 in the temperature box and change the units to Co Type 0.8 for the emissivityo Click to create the boundaryFigure 22: Applying the radiation boundary between the two facesAll of the boundary conditions are now defined in the model and it is ready to be meshed.1.4 Mesh Generation

In this step we will define specific mesh parameters for the model.Step 7: Creating the mesho Right click on the icon in the model treeo Select Create MeshLM-TH-155o Under the Mesh Parameters menu, change the units to ino Underneath the units, type .4in in the Global Size box as in Figure 6o Click to create the meshFigure 23: Mesh parameters for the model2. SolutionPurpose: The Solution is the step where the computer solves the simulation problem and

generates results for use in the Post-Processing step.Step 1: Running the simulationo Run the analysis by clicking at the top of the screeno When the analysis is finished, the icon will appear on the model tree3. Post-ProcessingPurpose: The purpose of the Post-Processing step is to process the results of interest.The post-processing for this problem involves creating a temperature plot as well as a vector plotof the heat flux.Step 1: Creating a temperature ploto Right click on the iconLM-TH-1

56o Select Define Thermal Ploto In the first box underneath Display, select TEMP: Temperatureo Select Celsius in the next boxo Click to accept the changesThe default settings for the temperature plot make it difficult to read becausethe temperature ofthe box does not vary much from top to bottom. The top plate is at 100C and the box averagesaround 35C. To see the effect of the cutout section on the temperature distributi


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on, the colorrange for the graph needs to be adjusted. The next two steps will format the plot to make it easierto read. First, the number formatting will be changed from scientific to floating and then thecolor range will be adjusted.Step 2: Formatting the ploto Right click on the plot icon under in the model treeo Select Chart Optionso Under Display Options change from Automatic to Definedo In the boxes underneath Defined, type 34 and 40 as in Figure 7o Inside the Position/Format section, change scientific(e) to floating(g)o Click to accept the changesFigure 24: Modifying the chart options to make the temperature variation more visibleNow the temperature variation can be seen easier on the box. Another formattingstep is todisplay the mesh elements along with the temperature distribution on the plot.LM-TH-157Step 3: Displaying the mesho Right click on the temperature plot icon and select Settingso Under Boundary Options, change to Mesho Click to accept the changes

Before creating the next plot, various points on the model will be gathered fromthe temperatureplot by using the probe.Step 4: Using the probeo Right click on the temperature plot icon and select Probeo Choose At location under Optionso Select the four nodes near the cutout as in Figure 8o The probe gives 38.46, 37.70, 36.30, and 35.47Figure 25: Acquiring temperatures at various points of interest using the probeAlthough the temperatures are all within a few degrees of another, the box has some unusualtemperature distribution around the cutout. To get a better idea of how the temperature varies

around the cutout, the other option in the probe menu will be used to graph thetemperature alongthe top and bottom edges.Step 5: Using the probe to graph the temperature along the top edgeo Choose On selected entities from the probe managero Highlight the top edge of the boxo Click Update to generate the datao Click the plot icon under Report OptionsLM-TH-158Figure 26: Temperature variation along the top edge starting at the corner withthe cutoutFigure 9 shows the temperature distribution along the edge. Without a cutout, th

e temperaturealong the edge would vary linearly. In this case, the temperature is higher thannormal in the first

45% of the graph and then levels off to an even slope after the cutout ends. Next, the bottomedge will be graphed to see its variation.Step 6: Using the probe to graph the temperature along the bottom edgeo Choose On selected entities from the probe managero Highlight the bottom edge of the boxo Click Update to generate the data


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o Click the plot icon under Report OptionsLM-TH-159Figure 27: Temperature variation along the bottom edge starting at the corner underneath thecutoutThis time, Figure 10, is showing the bottom edge of the box. Again, the temperature does notfollow the linear pattern that it normally would if there was no cutout. The bottom corner of thebox underneath the cutout is the coldest part off the model and the temperaturegoes back upbefore it levels off into a linear slope around 65%. To better understand why the small cutout isskewing the temperature, a plot of the heat flux through the box will be created. Instead of colorcontrast, this will be a vector plot to make it easier to understand.Step 7: Creating a vector plot of the heat fluxo Right click on the icono Select Define Thermal Ploto In the first box underneath Display, select HFLUX: Resultant Heat Fluxo Select W/m^2 in the next boxo Expand the Advanced Options tab and check the box next to Show as vector ploto Click to accept the changes

The next step will format the plot to make it easier to read. The SolidWorks Simulation softwarehas options that can vary the vector size and density.Step 8: Formatting the ploto Right click on the plot icon under the tabo Select Vector plot optionsFigure 28: Modifying thevector plotLM-TH-160o In the first box under Options, type in 300o In the next box, type 80 as in Figure 11o Click to accept the changes

Switch the view to the left orientation and zoom in on the area of the cutout. Theplot shouldresemble Figure 12.Figure 29: Left side view of the heat flux around the cutoutFigure 12 shows the direction and magnitude of the heat flux moving through thebox. From thispicture, it is clear why the coldest part of the box was the bottom corner and why the temperaturewas skewed around the cutout. This is because the heat has to flow by conduction

through thebox. However, there is no conduction through the cutout and so the heat has to flow around it,which makes it a take longer path to the bottom corner. The front view of the bo

x can be seen inFigure 13.Figure 30: Front view of the heat flux around the cutoutLM-TH-161Again, the heat is flowing normally through most of the box with the exception of the heat flowaround the cutout. The lack of conduction creates a sort of kink in the flow ofheat that forces itto magnify in the areas immediately around the cutout. This increases the temper


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ature along theedges of the cutout, which is why temperatures in Figure 10 were highest at areas around thecutout.VerificationTo verify the simulation solution, temperatures will be calculated at four points on the box. Inthis problem there are nodes that have radiation, convection, and conduction. For the threemodes of heat transfer, the following three equations are needed for the energybalance.Convection Where q is the heat transfer rate, h is the convection coefficient, A is the surface area, T is thetemperature, and T is the ambient temperature.Conduction Where q is the heat transfer rate, k is the thermal conductivity, A is the cross

sectional area, and x is the change in distance from one node to the next.Radiation

Where q is the heat transfer rate, is the Stefan-Boltzmann constant (5.67x10-8), is theemissivity, A is the surface area being radiated, and Ts is the temperature of the surface emittingradiation. In this case, q represents the rate of heat leaving the upper plate with a surfacetemperature of 100C (373 K) and =0.8. The surface it is radiating to does not absorb all of theradiation from the plate. The amount of heat transferred to the second surface is also dependenton the distance the plates are from each other and the surface temperatures of b

oth plates. If theradiating plate is assumed to be a point source with radiation emitting equallyin a hemisphere tothe plate, the diagram would look like Figure 14.A2 = L2A1 = 2 r2LM-TH-162Figure 14: Surface areas of the radiation and boxIn this case, the amount of heat transferred to the bottom surface is related to

total heat by an arearatio.

Figure 15 shows the four control volumes that will be applied to the box. Note the differences insurface area when calculating the heat transfer from convection. Also account for the missingspace in the box by subtracting the missing area for the conduction equations. Use the remainingsection as the cross sectional area, Ac,2.


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Figure 15: Control volumes for the energy balanceAssuming all of the heat transfer is going into the node, the energy balance reduces to: For the first control volume, there is radiation, conduction and convection.CV 1 CV 2 CV 3

T1T2T3T4CV 1CV 2CV 3CV 2LM-TH-163

CV 4 Plugging in values and rearranging the equation to solve for the coefficients gives: The hand calculations along with simulation results and percent differences are

given below.Hand Calculations(C)SolidWorks (C) Percent Difference(%)T1 40.61 38.4 5.7T2 39.72 37.7 5.3T3 39.21 36.3 8.0T4 38.38 35.5 8.1The differences in this case could be due to the geometry assumptions made in wh


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en performingthe hand calculations or the irregular temperature distribution in areas aroundthe cutout.LM-TH-164Attachment D. CoMetSolution-Specific FEM TutorialsLM-TH-165Attachment E. Post-Test1. What is a plot that uses arrows of various sizes instead of contrasting colors called?o Vector Ploto Contour Ploto Linear Ploto None of the above2. What parameters need to be defined in convection boundary?o Convection coefficient and surface temperatureo Convection coefficient and ambient temperatureo Ambient temperature and surface temperatureo Surface temperature and thermal conductivity3. The amount of heat transfer per unit area is referred to aso Temperature gradiento Heat fluxo Temperature distribution

o Temperature flow4. Which direction does heat flow between two different temperatures?o Cold to hoto Hot to coldo Into the systemo Out of the system5. A surface with no specified boundary condition is assumed have what kind of boundaryo Initial temperatureo Adiabatico Convectiono RadiationLM-TH-1

666. What extra parameters are required for a transient study as opposed to steady-state?o Time stepo Final temperatureo Initial temperatureo Both I and III7. How does temperature approximately vary through a solid with no heat generation?o Linearo Logarithmico Exponentialo Parabolic

8. What material properties are needed for a thermal analysis?o Thermal conductivityo Specific heato Densityo All of the above9. Which option is radiation heat transfer not dependent on?o Emissivityo Distance from sourceo Thermal conductivityo Surface temperature


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10. Thermal resistance is inversely related too Heat fluxo Temperature changeo Heat generationo All of the aboveLM-TH-16711. Which of the following is not a boundary condition in SolidWorks?o Temperatureo Convectiono Conductiono Radiation12. Which post-processing options are available in a transient study?o Animating the ploto Looking at the time response of a certain node on a ploto Plotting a certain time stepo All of the above13. What are the heat transfer equations for conduction, convection, and radiation?14. What tool must be used to acquire data from a thermal plot?15. Describe how to apply a thermal resistance between two faces.LM-TH-168Attachment F. Practice Problems

Problem 1A metal sphere of diameter d = 30mm is initially at temperature Ti = 700 K. At t=0, the sphere isplaced in a fluid environment that has properties of T = 300 K and h = 50 W/m2-K.

Theproperties of the steel are k = 35 W/m-K, = 7500 kg/m3, and c = 550 J/kg-K. Find

the surfacetemperature of the sphere after 500 seconds.Click the icon below to open the part T = 300 Kh = 50 W/m2-KTi = 700 K

LM-TH-169Problem 2An infinite wall with thickness t = 20mm is exposed to different temperatures on

each side of thewall as in Figure 2. The wall has a thermal conductivity of 5.0 W/m-K and density of 6000kg/m3.a) Find the heat flux through the wallb) Find the surface temperature on each side of the wallClick the icon below to open the part T i, =10C

hi = 20 W/m2-KT o, =70Cho = 50 W/m2-K tLM-TH-170Problem 3A plane wall is exposed to convection on both sides. The wall is split into twoparts with theinside wall made of AISI 304 steel and the other made of a material with properties k = . 25, =


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100, and c = 1200. There is a thermal resistance between the two sides of .005 m2-K/W. Find theheat flux through the walls and the surface temperatures T1, T2, T3, and T4.Click the assembly icon below to open the part T ,i = 50Chi = 15CT ,o = -20Cho = 40CT1 T2 T3 T4LM-TH-171Problem 4A thin brass loop of diameter d = 15 cm has 6 different legs of 7.5cm each and is exposed to thetemperature boundary conditions below. Nodes 4-6 are also exposed to convectionalong thecross sectional area at the end of each leg leg (T = 50C, h = 80 W/m2-K). Find the

temperaturesat nodes 1-9.Click the icon below to open the part 78

920C50C100C123456LM-TH-172

Problem 5A thin aluminum plate (1060 alloy) is exposed to a radiation from a surface 100mm away, withTs = 200C, = 0.7. A second plate is exposed to radiation from the same surface but at adistance of 300mm. Both plates are 10x100x200mm and are exposed to convection on

all sideswith h = 15 W/m2-K and T = 27C. Find the surface temperatures of each plate (assumeconstant surface temperatures throughout the plates and a closed system for radiation).Click the icon below to open the part

Ts = 200C.1m.3mLM-TH-173Problem 6Three aluminum (1060 alloy) plates are exposed to radiation from a source with Ts = 200C and = 0.7. The plates have a cross sectional area of .0025 m2 and are oriented at 200 mm away from


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the source as shown in the figure below. Find the surface temperature of each plate (assumeconstant surface temperatures throughout the plates and a closed system for radiation).Click the icon below to open the part r = .2 m123460 45LM-TH-174Attachment G. Solutions to Practice Problems Solution to Problem 1 Solution to Problem 2 Solution to Problem 3 Solution to Problem 4 Solution to Problem 5 Solution to Problem 6LM-TH-175Solution 1

Assume Lumped Capacitance Method From SolidWorksT(500) = 435.1 KPercent Difference

LM-TH-176Solution 2a) heat flux


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b) surface temperatures Check T Hand Calculation SolidWorks Percent Error (%)q 810.8 810.8 0.0T1 53.8 53.64 0.29T2 50.5 50.39 0.22LM-TH-177Solution 3Heat flux

Temperatures


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Hand Calculations SolidWorks Percent Differenceq 77.51 77.53 0.03T1 44.83 44.68 0.3T2 44.34 44.20 0.3T3 43.96 43.81 0.3T4 -18.05 -18.21 0.9LM-TH-178Solution 4Length of each arc Length of each leg0.075 mNode equations

Since the area is equal in all the node equations it has been ignored in the coefficientscalculations. Thermal conductivity cancels in all equations except at nodes with

convection (4-6). Plugging in values gives the following coefficient matrix.Temperature1 2 3 4 5 6 7 8 938.81 -12.74 0 -13.33 0 0 -12.74 0 0 0-12.74 38.81 -12.74 0 -13.33 0 0 0 0 00 -12.74 38.81 0 0 -13.33 0 0 -12.74 0-1467 0 0 1547 0 0 0 0 0 40000 -1467 0 0 1547 0 0 0 0 4000

0 0 -1467 0 0 1547 0 0 0 4000-12.74 0 0 0 0 0 38.81 -12.74 0 9310 0 0 0 0 0 -12.74 38.81 -12.74 1330 0 -12.74 0 0 0 0 -12.74 38.81 1995Node Hand Calculations SolidWorks Percent Difference1 72.66 73.1 0.602 79.65 80.28 0.783 88.42 89.23 0.914 71.48 71.9 0.585 78.11 78.75 0.816 86.44 87.2 0.877 66.90 66.83 0.108 58.04 59.29 2.11

9 99.48 99.61 0.13LM-TH-179Solution 5


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1st plateAbsorbed radiation, r = 0.1 m 2nd plateAbsorbed radiation, r = 0.3 m Temperature Hand Calculations SolidWorks Percent DifferenceTs,1 45.3 42.0 7.8

Ts,2 29.0 30.7 5.5LM-TH-180Solution 6

Temperature Hand Calculations SolidWorks Percent DifferenceT2 28.0 28.96 3.3T3 29.0 31.23 7.1T4 28.7 29.77 3.5LM-TH-181Attachment H. AssessmentPlease rank the following 3 questions on the order of 1 to 51- Little or no experience2- Some experience


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3- Moderate experience4- Much experience5- Used almost dailyBefore completing this learning module:1 2 3 4 5How much experience have you had with the FEM method?How much experience have you had with this specific topic?How much experience have you had with the specificsoftware?How has your knowledge of the FEM method improved between the pre-test and the end of themodule?o No improvemento Minor improvements, still have many questionso Moderate improvements, still have few questionso Major improvementsDo you feel the pre and post test questions accurately tested the most important

learning topics inthis subject?o Yeso Noo NeutralHow useful were the practice problems?o Very helpful

o Helpfulo Indifferento Unhelpfulo Very unhelpfulLM-TH-182Do you feel there was sufficient material contained in the learning module to answer all the posttest questions and complete the FEM analysis of the practice problems?o Yeso No If yes, did you acquire help from an outside source or complete the module on your

own? If not, which problems/concepts did you struggle with?Do you feel it was bad to not have a teacher there to answer any questions you might have?o It didn t mattero It would have been niceo I really wanted to ask a questionHow did the interactivity of the program affect your learning?o Improved it a loto Improved it someo No differenceo Hurt it someo Hurt it a lot

The six levels of Bloom s Taxonomy are listed below. Rank how well this learning modulecovers each level, with 5 meaning exceptionally well and 1 meaning very poor.1. Knowledge (remembering previously learned material)O 5O 4O 3O 2O 12. Comprehension (the ability to grasp the meaning of the material and give exam


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ples)LM-TH-183O 5O 4O 3O 2O 13. Application (the ability to use the material in new situations)O 5O 4O 3O 2O 14. Analysis (the ability to break down material into its component parts so that

itsorganizational structure may be understood)O 5O 4O 3O 2O 15. Synthesis (the ability to put parts together to form a new whole)O 5

O 4O 3O 2O 16. Evaluation (the ability to judge the value of the material for a given purpose)O 5O 4O 3O 2O 1Do you think the mixed text and video format works well?o Yes

o Indifferento NoDo you think the module presents an effective method of learning FEA?LM-TH-184o Yeso Indifferento NoDid you prefer this module over the traditional classroom learning experience? Why or why not.How accurate would it be to call this module self-contained and stand-alone?o Very accurateo Accurate

o Indifferento Inaccurateo Very inaccurateWhat specifically did you like and/or dislike about the module.Was there any part of the module that you felt was unnecessary of redundant? Was

there a needfor any additional parts?Please list any suggestions for improving this module.LM-TH-185


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Overall, how would you rate your experience taking this module?o Excellento Fairo Averageo Pooro Awful

heat transfer simulation

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