steady state heat conduction heat transfer fe learning module_v1_01272011_watson.ppt

Thermal Finite Element Analysis Tutorial:Steady-State Heat Conduction

Kyle WatsonUniversity of the PacificDepartment of Mechanical [email protected]: 209.946.3081

For Use with SolidWorks Simulation 2010 Reference Text: engel and Ghajar, Heat and Mass Transfer, 4th Ed.Expected Completion Time: 30-45 minutesApplicable Courses: Heat Transfer, Finite Element Analysis

*Table of ContentsEducational ObjectivesFEA BackgroundProblem DescriptionProblem Solving StepsUsing SolidWorks to Create a 3-D ModelCreating a Thermal Study using SolidWorks SimulationDefining the Material PropertiesDefining the Thermal Boundary ConditionsMeshing the Model and Running the StudyPost-Processing the Results to Find:the Steady-State Temperature Distributionthe Temperature at a Particular LocationComparing the Results with Hand CalculationsAdditional ExercisesAcknowledgement

*Educational Objectives (1/2)The educational goal of this tutorial is to provide undergraduate engineering students with:

an understanding of a specific engineering topic (heat transfer through a semi-infinite medium)an understanding of finite element (FE) theoryan ability to apply commercial FE software (SolidWorks Simulation) to typical engineering problems.

This educational goal will be accomplished through the following four educational objectives:Table ofContents

*Educational Objectives (2/2)Engineering Topics: Understand the fundamental basis of engineering topics through the use of finite element computer modelsFE Theory: Understand the fundamental basis of FE theoryFE Modeling Practice: Be able to implement a suitable finite element model and construct a correct computer model using commercial FE softwareFE Solution Interpretation and Verification: Be able to interpret and evaluate finite element solution quality, including the importance of verificationTable ofContents

*FEA Background (1/3)FEA Theory MeshingMeshing discretizes the continuous 3-D model into finite elements. The type of elements created in this process depends upon the type of geometry involved. SolidWorks Simulation offers two types of elements: tetrahedral solid elements (for meshing solid geometry) and shell elements (for meshing surface geometry).Table ofContentsA Meshed 3-D SolidWorks Model

*FEA Background (2/3)FEA Theory Element TypesTetrahedral solid elements can be either first order (draft quality) or second order (high quality). First order tetrahedral elements have four nodes, straight edges, and flat faces. Second order tetrahedral elements have ten nodes and are more accurate in modeling problems. Each tetrahedral element, whether 4 or 10 nodes per element, has three degrees of freedom for each node.Table ofContentsFirst Order Tetrahedral Elementand Nodes

*FEA Background (3/3)FEA Theory The MathA differential equation defining the physics of the problem (the heat conduction equation for thermal analysis) is approximated and solved at specific locations on each finite element and extrapolated to each node of that element. For each meshed 3-D model, these differential equations are approximated with arrays of linear equations. The FEA software has mathematical solvers which solve these large arrays of equations for the temperature at each node of each element.Table ofContentsAn Array of Linear Equations

*Problem Description (1/3)A long bar with thermal conductivity, k, has the same fixed temperature, Ts, on the upper and lower surface. Air moves over the right surface with a temperature, T, and convection heat transfer coefficient, h, while the left side is insulated. Find the steady-state temperature distribution in the bar, T(x,y). See sketch on the next slide.

Thermal material properties: k = 1.5 W/mK (thermal conductivity) = 2300 kg/m3 (material density)Table ofContents

*Problem Description (2/3)Heat Conduction in a Long Bar with the Cross-Section ShownTsTable ofContentsTsT, hLyLxGiven:

T = 30Ch = 50 W/m2CTs = 200CLx = 40 cmLy = 60 cm

*Problem Description (3/3)SolidWorks Simulation will be used to perform the following:

determine the steady-state temperature distribution throughout the bar.determine the temperature at a particular location in the bar by using the probe tool with the results from part a).

Table ofContents

*Problem Solving StepsUsing SolidWorks to Create a 3-D ModelCreating a Thermal Study using SolidWorks SimulationDefining the Material PropertiesDefining the Thermal Boundary ConditionsMeshing the Model and Running the StudyPost-Processing the Results to Find:the Steady-State Temperature Distributionthe Temperature at a Particular LocationComparing the Results with Hand CalculationsAdditional ExercisesTable ofContents

*Using SolidWorks to Createa 3-D Model (1/6)

Create a new part by clicking the New icon from the dropdown menu

Select the Part option from the New SolidWorks Document window

Click OKProblemSolvingStepsTable ofContents


Set the units to CGS (Centimeter Gram Second) by clicking the Tools dropdown menu and selecting OptionsSelect the Document Properties tabSelect UnitsSelect CGSClick OKProblemSolvingStepsTable ofContents


Draw the part by selecting the Sketch tab

Select the Rectangle icon and select the Front PlaneProblemSolvingStepsTable ofContents

*Change to Front view and sketch a rectangle in the center of the graphics window

Dimension your rectangle by selecting the Smart Dimension iconProblemSolvingStepsTable ofContentsUsing SolidWorks to Create a 3-D Model (4/6)


Click on a horizontal line from your rectangle and enter its dimension (the width of the bar is 40 cm) and repeat for a vertical line from your rectangle (the height of the bar is 60 cm)

Click the Zoom to Fit icon in order to resize your drawing to fit in the drawing windowProblemSolvingStepsTable ofContents


To make your part 3-D, select the Features tab and select the Extruded Boss/Base icon

Extrude the part as a Blind extrusion. This is a 2-D heat transfer problem so you may enter any dimension for this depth (Note: less processing time will be required for a smaller dimension)

Click the green checkmark and note the creation of a 3-D modelProblemSolvingStepsTable ofContents

*Creating a Thermal StudyUsing SolidWorks Simulation (1/3)

Load SolidWorks Simulation onto your computer by clicking the Tools dropdown menu and selecting Add-insSelect SolidWorks Simulation if it is not already selected and click OKNote the creation of the Simulation tabProblemSolvingStepsTable ofContents


Select the Simulation tab

Select New Study under the Study Advisor icon

Select Thermal for the study type and click the green checkmark

Note the creation of a Study Manager

ProblemSolvingStepsTable ofContents


Specify that this is a Steady-State thermal study by right-clicking on the Study icon in the Study Manager and selecting Properties

Select the Steady-State option and select FFEPlus for the Solver

Click OKProblemSolvingStepsTable ofContents

*Defining the Material Properties (1/2)

ProblemSolvingStepsTable ofContentsRight-click on the Part icon under the Study Manager and select Apply/Edit Material

Scroll down to the Custom Materials folder and right-click on this folder and select New Category

Right-click on New Category and select New Material (note that this new material will be labeled Default)

*Defining the Material Properties (2/2)

ProblemSolvingStepsTable ofContentsSelect this New Material (labeled as Default) and enter the density and thermal conductivity of the bar as listed on Slide #8

Click Apply. Note the checkmark that appears over the Part icon in the Study Manager indicating a material has been defined

Click Close

*Defining the ThermalBoundary Conditions (1/7)

Specify the convection boundary condition on the right side:Highlight the right surface (in blue) by clicking on that surface

Right-click on Thermal Loads under the Study Manager and select ConvectionProblemSolvingStepsTable ofContents


Enter the fluid temperature (Bulk Ambient Temperature) for this study (30C = 303 K) and the Convection Coefficient (50 W/m2K) and click the green checkmark

Note the entry that appears under Thermal Loads in the Study ManagerProblemSolvingStepsTable ofContents


Specify the temperature at the top and bottom boundaries:Highlight the top and bottom surfaces of the part (in blue) by clicking on those surfaces (it will be necessary to rotate the view of the object). Make sure both surfaces are highlighted

Right-click on Thermal Loads under the Study Manager and select TemperatureProblemSolvingStepsTable ofContents


Select Temperature and enter the temperature of these surfaces (200C) and click the green checkmark

Note the second entry that appears under Thermal Loads in the Study ManagerProblemSolvingStepsTable ofContents


Specify the insulated boundary condition on the left side:Highlight the left surface of the part (in blue) by clicking on that surface (it will be necessary to rotate the view of the object)

Right-click on Thermal Loads under the Study Manager and select Heat FluxProblemSolvingStepsTable ofContents


Enter the heat flux at this surface (insulated implies heat flux = 0) and click the green checkmark

Note the third entry that appears under Thermal Loads in the Study Manager ProblemSolvingStepsTable ofContents


Note the appearance of symbols indicating all of the different boundary conditionsThese symbols can be hidden by right-clicking on Thermal Loads under the Study Manager and selecting Hide All ProblemSolvingStepsTable ofContents

*Meshing the Model andRunning the Study (1/2)

Right-click on Mesh under the Study Manager and select Create Mesh

You can vary the coarseness of the mesh in the Mesh window that opens; the default value is typically adequate (a finer mesh will require more processing time)

Click the green checkmark to create the mesh; note the meshed model that appears

To view statistics about the meshed model, right-click Mesh and select Details; the number of nodes (~10k) and elements (~6k) can be seen


*Meshing the Model andRunning the Study (2/2)

Right-click on Mesh under the Study Manager and select Mesh and RunA solver status window will briefly appear for this fast steady-state study; note the elapsed timeNote that a Results folder is created in the Study Manager with the thermal results and a temperature plot of the object is displayedProblemSolvingStepsTable ofContents

*Post-Processing the Results to Find(1/2)

the Steady-State Temperature DistributionProblemSolvingStepsTable ofContentsRight-click on Thermal1 under the Results folder and select Edit DefinitionA Thermal Plot window will appear where you can select the temperature unitsClick the green checkmark


the Steady-State Temperature DistributionProblemSolvingStepsTable ofContentsThe temperature distribution throughout the bar appears along with the temperature scale; this scale can be changed to decimal form (instead of scientific) by double-clicking on the scale and changing the Number Format under the Chart Options window that appears


the Temperature at a Particular LocationProblemSolvingStepsTable ofContentsRight-click on Thermal1 under the Results folder and select ProbeA Probe Result window will appear; if you select a location on the object, the x, y, z coordinates, node number, and temperature at that location will appear

*Comparing the Results withHand Calculations (1/2)

The Finite Difference Method can be used to solve this problem by hand. Symmetry can be used to reduce the number of nodes, and therefore the number of algebraic equations that need to be solved.

ProblemSolvingStepsTable ofContentsUtilizing symmetry and a square mesh results in 15 nodes of unknown temperatureThe finite difference solutionfor these 15 unknown temperatures(C)

*Comparing the Results withHand Calculations (2/2)

ProblemSolvingStepsTable ofContents= Node #3 of the hand calculations177C 176.387C= Node #2 of the hand calculations161C 159.798C= Node #1 of the hand calculations155C 153.928C= Node #8 of the hand calculations137C 137.023C= Node #7 of the hand calculations129C 129.424C= Node #9 of the hand calculations161C 160.678CHAND CALCULATIONS AND FEA PRODUCE RESULTS WITHIN ~ 1C

*Additional Exercises (1/3)

Exercise #1

Redo this study but change to a Coarse mesh.Compare the number of elements and nodes that result from this Coarse mesh with your initial trial.Does the Coarse mesh result in the same temperature distribution? Why or why not?



Exercise #2

Redo this study but change to a material that has a higher thermal conductivity.What happens to the minimum temperature in the bar?Explain what has happened as a result of changing the thermal conductivity.ProblemSolvingStepsTable ofContents


Exercise #3

Use the Iso Clipping feature by right-clicking on Thermal1 under the Results folder to visualize isotherms (lines of constant temperature).You can select any temperature and the corresponding isotherm will show on the temperature plot (an arrow will indicate this temperature on the legend).View multiple isotherms on the same plot by clicking the Iso 2 box and entering another temperature; this can be repeated multiple times for additional isotherms.What happens to the isotherms at the insulated boundary?ProblemSolvingStepsTable ofContents

*Acknowledgement

This work is partially supported by the National Science Foundation Division of Undergraduate Education grant, Transforming Undergraduate Education in Science, Technology, Engineering and Mathematics (TUES) Phase 2; Award Numbers: 1023034 and 1023064Table ofContents

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steady state heat conduction heat transfer fe learning module_v1_01272011_watson.ppt

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