Steady State Heat Transfer (no mass transport) Chapter 3.

Steady State Heat Transfer (no mass transport)

Chapter 3

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Training ManualSteady-State Heat Transfer

• When the flow of heat does not vary with time, heat transfer is referred to as steady-state.

• Since the flow of heat does not vary with time, the temperature of the system and the thermal loads on the system also do not vary with time.

• From the First Law of Thermodynamics, the steady-state heat balance can be expressed simply as:

energy in - energy out = 0

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0...

qz

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zy

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yx

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x zzyyxx

QTK

Steady-State Heat TransferGoverning Equation

• For steady-state heat transfer, the differential equation expressing thermal equilibrium is:

• The corresponding finite element equation expressing nodal equilibrium is:

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Types of Thermal Loads and Boundary Conditions

• Temperature

– is a DOF constraint on a specific region of a model used to impose a known, fixed temperature.

• Uniform Temperature

– can be applied to all nodes that do not already have a temperature constraint. It may be used to set an initial temperature only, not a constraint, on all nodes in the first substep of a steady-state or transient analysis. It can also be used to evaluate initial values of temperature-dependent material properties in a non-linear analysis.

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• Heat Flow Rate

– is a concentrated nodal load. A positive heat flow rate indicates energy is being supplied to the model. Heat flow rate may also be specified on keypoints. This type of load is typically applied when convection and heat flux cannot be used. Use care when applying this load to regions with large mismatches in thermal conductivity.

• Convection

– is a surface load applied on exterior surfaces of a model to simulate heat transfer between a surface and surrounding fluid.

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• Heat Flux

– is also a surface load. It is used when the heat flow rate across a surface is known. A positive value of heat flux indicates heat flux is being supplied to the model.

• Heat Generation Rate

– is applied as a body load to represent heat generated within a body, and has units of heat flow rate per unit volume.

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• ANSYS Thermal Loads are grouped into four general categories:

1. DOF Constraint - specified DOF (temperature) value

2. Force Load - concentrated load (heat flow) applied at a point

3. Surface Load - distributed load (convection,heat flux) over a surface

4. Body Load - volumetric or field load (heat generation)

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General Notes on Thermal Loads and Boundary Conditions

• In ANSYS, boundaries that have no applied loads are treated as adiabatic (perfectly insulated) by default.

• Symmetry boundary conditions are imposed by letting the boundaries be adiabatic.

• If the temperature of a region of the model is known, then it can be fixed at that value.

• Reaction heat flow rates are only available at fixed temperature DOF’s.

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Training ManualThermal Analysis Template

• Building the Model

– Specify title and jobname.

– Record units, if desired.

– Enter the Preprocessor

• Define element type(s), check keyoptions.

• Define real constants, if required.

• Define material properties.

• Create or Import geometry.

• Mesh.

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• In the Solution Processor

– Define analysis type, check analysis options.

– Apply loads and boundary conditions.

– Specify load step options.

– Execute the solution.

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• Review the Results

– Start general postprocessor and/or time history postprocessor.

– Review results by listing, plotting, etc.

– Review appropriate error measures

– Verify the solution.

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A listing of all commands executed can be found in the jobname.log file.

A listing of all commands executed can be found in the jobname.log file.

GUI and ANSYS Commands

• ANSYS is a command driven program.

• ANSYS commands may be input manually, created using the GUI (Graphical User Interface) or both.

• The GUI provides an easy way for users to interact with the ANSYS program.

• The GUI generates ANSYS commands based on the user’s menu picks.

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Training ManualGUI and ANSYS Commands

• Review the ANSYS output window to see the execution of the commands and text output.

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Training Manual

Follow the highlighted boxes for the steps specific to this example problem.

Follow the highlighted boxes for the steps specific to this example problem.

Basic DescriptionA long steel tubewith rectangular finsreceives heat by convection from a hot gas flowinginside the tube. The outer surface is exposed to ambient air, and heat flux is being extracted at the fin tips.

An ANSYS input file for this example is provided in Appendix BAn ANSYS input file for this example is provided in Appendix B

Steady State Heat TransferExample Problem Description

• Details of each step in the analysis process will be illustrated with the use of a simple example.

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Problem Description:

• The temperature of the hot gas is 600°F. The interior film coefficient is 0.40 BTU/hr•in2•°F.

• The ambient air temperature is 100 °F. The exterior film coefficient is 0.025 BTU/hr•in2•°F.

• Each fin is subject to a heat flux of -20 BTU/hr•in2 at the tip.

Analysis Goals:

• Analyze the smallest repeatable section and determine the following:

1) Temperature distribution.

2) Convection heat loss from upper and lower fin surfaces.

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Training Manual

A cut cross-section is shown below.


Modeling Guidelines:

Use surface effect elements for the interior convection loads.

Use “convection on lines” to apply convection to the exterior surfaces of the fins.

Apply heat flux at the fin tip.

Assume the finned tube is LONG, and neglect effects at the ends of the tube.

Model the smallest repeatable section.

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Adiabatic symmetry boundaryAdiabatic symmetry boundary

Adiabatic symmetry boundary

Adiabatic symmetry boundary

Heat Fluxat tip of finHeat Fluxat tip of fin

ConvectionSurfacesConvectionSurfaces

ConvectionSurfacesConvectionSurfaces

Note simplification to the smallest repeatable 2D geometry.

Note simplification to the smallest repeatable 2D geometry.


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Follow the highlighted boxes for the steps specific to this example problem.Follow the highlighted boxes for the steps specific to this example problem.


Guidelines for steady-state heat transfer example:

• Use smallest repeatable section to determine the following:

– temperature distribution in the tube/fin

– convection heat loss from the tube/fin

– plot of temperature variation along the tube/fin surface.

• Mesh using axisymmetric PLANE55 elements.

• Use surface effect elements SURF151 with extra node option on the inner diameter of the tube.

• Assume constant, isotropic material properties.

• No temperature-dependent properties.

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Training ManualBuilding the Model

• The first phase of thermal analysis includes building the model and meshing.

• In this section, we will:

– Specify jobname and title.

– Record units used.

– Enter the Preprocessor

• Define element types and keyoptions.

• Review real constant definition.

• Define material properties.

• Create geometry.

• Mesh the model.

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Building the ModelSetting Preferences for the GUI

Use the Preferences option to activate GUI filtering; only menus related to thermal analysis will be visible and usable. If not set, menus for all disciplines will be active.

Activate thermal filtering for this

example,click “OK”.

Activate thermal filtering for this

example,click “OK”.

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Building the ModelSpecifying a Jobname

Define a unique jobname to distinguish one set of analysis files from another. All files will have the name jobname.ext. Click on YES to begin writing new log and error files named jobname.log and jobname.err.

Change jobname to “stltube”

Change jobname to “stltube”

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Building the ModelSpecifying a Title

Define a descriptive title for your analysis. The title will be printed at the bottom of your plots, and is written to the load step files and the results file.

Enter a Title: “Example - Steel Tube with Fins” and click “OK”.

Enter a Title: “Example - Steel Tube with Fins” and click “OK”.

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Building the Model

Units Use the /UNITS command to record units used throughout the analysis.

Record the units for this example as British/Inches, abbreviated “bin”

Record the units for this example as British/Inches, abbreviated “bin”

Except for magnetic field analysis, you do not need to “tell” ANSYS which system of units you will be using. However, you may record the system of units used using the /UNITS command.Once you have decided which system of units to use, BE CONSISTENT. ANSYS does not perform any units conversion.The system of units selected will affect your solid model, material properties, real constants, and loads.No units conversion is done if a new /UNITS command is issued.

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Training ManualBuilding the ModelUnits

For more information on the /UNITS command, use the

on-line documentation.

To access help, type “help,xxxxx” in the input window; “xxxxx” can be an element number (77), command (/units), or element class (solid). Or, use the UtilityMenu>>Help pulldown.

To access help, type “help,xxxxx” in the input window; “xxxxx” can be an element number (77), command (/units), or element class (solid). Or, use the UtilityMenu>>Help pulldown.

Enter “help, /UNITS” in the input window to access on-line documentation.

Enter “help, /UNITS” in the input window to access on-line documentation.

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Building the ModelUnits

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Now, we are ready to begin preprocessing…

Remember, follow the highlighted boxes for steps specific to the example problem.

Steady-state heat transfer example.Steady-state heat transfer example.

Building the Model

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Preprocessing: Building the ModelDefining an Element Type

Define element type(s) to be used for the analysis.

Begin element type definition for the example problem. Note there are currently no defined element types. Click “Add….” to begin.

Begin element type definition for the example problem. Note there are currently no defined element types. Click “Add….” to begin.

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• Use the HELP button to get more information on the element library.

• By default, the first element type defined is assigned Element Type Reference Number 1.

• Since GUI Preferences were set for thermal analysis, only thermal elements are shown.

Then choose an element type within that categoryThen choose an element type within that category

First choose a categoryFirst choose a category

Select Thermal Solid PLANE55 for element type 1, click “Apply”.Select Thermal Solid PLANE55 for element type 1, click “Apply”.

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Preprocessing: Building the ModelReviewing and Choosing Keyoptions

Keyoptions

• Keyoptions or KEYOPTs are options associated with element types.

• Review or change the keyoptions for the element type defined by choosing “Options” as shown:

Check default keyoptions for this element type, PLANE55.Check default keyoptions for this element type, PLANE55.

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Use the menu pull-downs to reveal options available for a particular element, and pick the appropriate value.

Change element behavior setting. This example requires axisymmetric element behavior. The default is planar.

Change element behavior setting. This example requires axisymmetric element behavior. The default is planar.

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Preprocessing: Building the ModelSurface Effect Elements

Surface Effect Elements - An Introduction

• Surface effect elements act as a “skin” on the faces of solid elements and are frequently used to apply loads.

• Surface effect elements provide added flexibility when defining a surface load, particularly when both convection and heat flux occur on the same region.

• An optional discrete node, offset from the surface of the model, can be used to represent the bulk temperature of a surrounding fluid. This “extra” node is also convenient for results evaluation.

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Surface Effect Elements - An Introduction

• Surface effect elements can be used to apply heat generation loads.

• Surface effect elements are convenient to use when the film coefficient varies with temperature; keyoption settings provide different options for their evaluation.

NOTE: Surface effect elements will be discussed in greater detail in Chapter 7.NOTE: Surface effect elements will be discussed in greater detail in Chapter 7.

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Surface Effect Elements and Convection

• A convection load may be applied directly to the surface effect elements, the solid elements, or the solid model entities.

• Using the “extra node” option with SURF151 allows specification of a nodal temperature at the “extra node”, which actually represents the bulk fluid temperature.

NOTE: This example problem does not actually require the use of surface effect elements because there is only constant convection (with known Hf and Tb) on each surface. However, the use of the surface effect elements on the inner diameter of the pipe will allow us to more easily evaluate the heat loss/gain by convection during postprocessing.

NOTE: This example problem does not actually require the use of surface effect elements because there is only constant convection (with known Hf and Tb) on each surface. However, the use of the surface effect elements on the inner diameter of the pipe will allow us to more easily evaluate the heat loss/gain by convection during postprocessing.

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Note the second element type defined is assigned Element Type Reference Number 2 automatically.

Define thermal surface effect element, SURF151. This is the second element type used in the example problem.Define thermal surface effect element, SURF151. This is the second element type used in the example problem.

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Check the default settings for the SURF151element. Highlight Type 2, and click “Options”.Check the default settings for the SURF151element. Highlight Type 2, and click “Options”.

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Change element behavior from planar to axisymmetric. Note changes to K4, removal of midside nodes and K5, including an extra node for convection calculations. Click “Close” when finished.

Change element behavior from planar to axisymmetric. Note changes to K4, removal of midside nodes and K5, including an extra node for convection calculations. Click “Close” when finished.

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Preprocessing: Building the ModelDefining and Checking Real Constants

Real Constants

• Real constants are geometric properties specific to a given element type.

• Not all element types require real constants.

• Some element types may require real constants only if certain keyoptions are activated.

• Use ANSYS on-line help to get more information about real constants that may be required for your analysis.

• The first real constant set defined is assigned Reference Number 1 by default.

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Check required real constants. Note there arecurrently none defined. Click “Add….” to begin.

Check required real constants. Note there arecurrently none defined. Click “Add….” to begin.

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• To define real constants:

– first highlight the element type with which the real constant set is associated

– then, define the real constant set by filling in values in the dialog box provided.

No real constants are required for eitherelement type for the example problem.No real constants are required for eitherelement type for the example problem.

NOTE: Thickness must be specified if HGEN loads are applied to surface effect elements.

NOTE: Thickness must be specified if HGEN loads are applied to surface effect elements.

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Preprocessing: Building the ModelDefining and Checking Material Properties

• General Notes on Material Properties for Steady-State Thermal Analysis

– For a steady state analysis, thermal material property data must be input for thermal conductivity “k” as KXX, and optionally KYY, KZZ.

– KYY and KZZ default to KXX if not defined by the user.

– Density (DENS) and specific heat (C) or enthalpy (ENTH) are not required for a steady-state analysis without mass transport of heat.

– Temperature-dependent material conductivity, k, makes a thermal analysis non-linear.

– Temperature-dependent film coefficients are treated as material properties.

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• Options for Definition of Material Properties in ANSYS:

– Fill in values in the appropriate dialog boxes after selecting a material behavior option.

– Read in material properties from the standard ANSYS material library, or a user-defined material library.

• After defining material properties, you may also write material data to a file for future use.

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• To read material properties from a Material Library, simply indicate the directory and file containing the data.

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• To input material data manually, first select Material Models and double-click the tree structure to get to the material behavior required for this analysis (Thermal, Conductivity, Isotropic) …

The material type used for this example is constant isotropic. The first material defined is assigned reference number 1 by default.

The material type used for this example is constant isotropic. The first material defined is assigned reference number 1 by default.

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• Then, fill in required value in the dialog box …

For a steady-state thermal analysis with constant isotropic properties, only KXX is required.

Thermal conductivity of steel used in thisexample is 0.75 BTU/hr-in-°F

Thermal conductivity of steel used in thisexample is 0.75 BTU/hr-in-°F

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Preprocessing: Building the ModelTemperature-Dependent Material Properties • For temperature-dependent material properties, click Add

Temperature to include additional temperature dependent values…

Sample only. Do not use this data.Sample only. Do not use this data.

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Preprocessing: Building the ModelTemperature-Dependent Material Properties

• Click the Graph button to plot a graph of Property v. Temperature…

Sample only. Do not use this data.Sample only. Do not use this data.

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Preprocessing:Building the ModelUsing Temperature-Dependent Material Properties

How does ANSYS use this data?

• Temperature-dependent material properties are evaluated once per element. The material properties are assumed to be constant over the volume of the element.

• The temperature used for a given element is:

res temperatunodal

elementfor that centroid at the evaluatedelement of functions shape done is evaluationproperty material heat which t re temperatuthe

:

0

T0

TN

Twhere

TNT

c

c

res temperatunodal

elementfor that centroid at the evaluatedelement of functions shape done is evaluationproperty material heat which t re temperatuthe

:

0

T0

TN

Twhere

TNT

c

c

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Preprocessing: Building the ModelListing Material Properties

• Material properties may be easily listed by making the following menu selections…

Temperature dependent material properties can also be listed

Temperature dependent material properties can also be listed

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Preprocessing: Building the ModelDeleting Material Properties

• Material properties may be deleted individually, or for multiple materials by using the Material Model GUI:

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Training ManualPreprocessing: Building the ModelUsing Imported Geometry

• Geometry may be imported from CAD program part files or standard data exchange formatted files. To import geometry, use the File>>Import menu picks:

NOTE: The sample dialog box shown here corresponds to one method of IGES file import.

NOTE: The sample dialog box shown here corresponds to one method of IGES file import.

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Preprocessing: Building the ModelCreating the Geometry

• Geometry may be created in ANSYS. Here primitives are used to generate geometry for our example problem.

Create two independent areas using primitives, and input the dimensions as shown in the problem description.

Create two independent areas using primitives, and input the dimensions as shown in the problem description.

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Preprocessing: Building the ModelCreating Geometry

Enter the coordinates of the corners of each rectangle. ANSYS will create the rectangle and its associated lines, and keypoints. Choosing “Apply” keeps the dialog box open. Choosing “OK”closes the dialog box.

Enter the coordinates of the corners of each rectangle. ANSYS will create the rectangle and its associated lines, and keypoints. Choosing “Apply” keeps the dialog box open. Choosing “OK”closes the dialog box.

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Area plot

• This plot is produced automatically by ANSYS after creating the two independent rectangles. The image is automatically sized to fit into the graphics window.


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• Boolean operations such as intersect, add, subtract, divide, glue, overlap, and partition can also be used to manipulate geometry.

Apply the Booleans>>Overlap>>Areas command to produce the desired geometry.

Apply the Booleans>>Overlap>>Areas command to produce the desired geometry.

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“Pick All” selects both areas for overlapping and executes the command.

“Pick All” selects both areas for overlapping and executes the command.

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Use the PlotControls>>Numbering commands, to turn on plotting of area numbers. Show with both colors and numbers (/NUM).Use the PlotControls>>Numbering commands, to turn on plotting of area numbers. Show with both colors and numbers (/NUM).

• To see individual entities clearly, turn on numbering using the Utility Menu.

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• Plot of areas after overlap, with area numbering turned on, and shown with both colors and numbers.

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Preprocessing: Building the ModelGeneral Notes on Boolean Operations

• By default, input entities of a Boolean operation are deleted after the operation.

• Deleted entity numbers become “free”. That is, they will be reassigned to new entities created after the Boolean operation, starting with the lowest available number.

• When overlapping areas, a new area is created which is equal to the common area of the original entities. New areas are created by trimming the original areas to make room for the new area. All areas share common lines and keypoints.

• To review procedures for Boolean Operations, check the following documentation:

– ANSYS On-line Help

– ANSYS Modeling and Meshing Guide

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Preprocessing: Building the ModelDefining Attributes

Element Attributes

• Element attributes are model characteristics that must be assigned prior to meshing. They include:

– Material properties

– Element types

– Real constants

– Element coordinate systems

• Each specific type of attribute defined in a model will have a unique reference number.

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Element Attributes (continued)

• Element attributes can be easily assigned under Attributes>>Define, or using the MeshTool. The MeshTool is often a more convenient approach since meshing controls, which are normally the next step in the processing sequence, are also set using the MeshTool.

• When using multiple element types, material or real constants, be sure to match attributes to the appropriate region of the model.

• Element attributes may be listed and plotted for model checking.

• Attributes can be set globally, or assigned to specific volumes, areas, lines, and keypoints prior to meshing.

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To set Attributes using the MeshTool:

Select an item then SET attributes.Select an item then SET attributes.

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Preprocessing: Building the ModelDefining Model Attributes

• When setting attributes, use the pull-down menus to reveal options, and pick the appropriate values.

NOTE: You must already have defined element type, material and real constants prior to this operation.

NOTE: You must already have defined element type, material and real constants prior to this operation.

NOTE: ESYS is mainly used for orthotropic material definition.NOTE: ESYS is mainly used for orthotropic material definition.

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Meshing involves the following

steps:

1) Assign element attributes.

(element types, real constants, material properties)

2) Set mesh controls.

Set the controls that govern the size (mesh density) and shape of the elements to be created during the meshing operation.

3) Save the database (optional).

4) Generate the Mesh.

Preprocessing: Building the ModelSetting Mesh Controls

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Preprocessing: Building the ModelSetting Mesh Controls

Meshing in ANSYS (continued):

• If a solid model is meshed without setting any controls, the mesh will have the following characteristics:

– it will be free meshed, not mapped.

– element sizes will be determined automatically by ANSYS (which may be OK for a first approximation ).

– element type will be determined by the dimensionality of the geometry and element types defined (default=1)

– element attributes will default to material 1 and real constant set 1.

• There are many ways to set mesh controls. Refer to the ANSYS Modeling and Meshing Guide for more information.By default meshing attributes are set to element type 1, material 1 and real set 1, therefore, they do not need to be redefined at this point in the sample problem.By default meshing attributes are set to element type 1, material 1 and real set 1, therefore, they do not need to be redefined at this point in the sample problem.

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Training ManualPreprocessing: Building the ModelSetting Mesh Controls

• The next step is to set controls that govern the size (mesh density) of the elements that will be created during the meshing operation. Global size is used to create a mesh of uniform element size.

Set a global element edge length value of 0.06 for the sample problem.Set a global element edge length value of 0.06 for the sample problem.

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Preprocessing: Building the ModelMeshing the Model

Using the MeshTool, specify:1) Mesh: areas2) Shape: quad3) Mesher: mapped; 3 or 4 sided4) Select “Pick All” in the picking menu5) Close the MeshTool

Using the MeshTool, specify:1) Mesh: areas2) Shape: quad3) Mesher: mapped; 3 or 4 sided4) Select “Pick All” in the picking menu5) Close the MeshTool

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The resulting element plot is shown below.

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Continue meshing; generate surface effect elements

Notes on generating the surface effect elements:

• Before generating the surface effect elements, we must do some additional preprocessing :

– set attributes to use element type 2, SURF151.

– create the “extra node” ( reference KEYOPT5).

• Surface effect elements will be created using the existing nodes on the surface, and reference the “extra node”.

Continue meshing; generate surface effect elements

Notes on generating the surface effect elements:

• Before generating the surface effect elements, we must do some additional preprocessing :

– set attributes to use element type 2, SURF151.

– create the “extra node” ( reference KEYOPT5).

• Surface effect elements will be created using the existing nodes on the surface, and reference the “extra node”.

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Define attributes for meshing using the preprocessor menu picks Attributes>>Define as shown:

Set element type number to : 2 SURF151

Set element type number to : 2 SURF151

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Change the display to a node plot. NOTE: Since we will be using existing nodes for surface effect element definition, switching to a node plot will make it very easy to select nodes on the surface we are interested in.

Change the display to a node plot. NOTE: Since we will be using existing nodes for surface effect element definition, switching to a node plot will make it very easy to select nodes on the surface we are interested in.

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Training ManualPreprocessing: Building the ModelMeshing the Model

Create the “extra node” required for SURF151 definition.NOTE: Use direct generation to create the extra node. The active coordinate system is global cartesian.

Create the “extra node” required for SURF151 definition.NOTE: Use direct generation to create the extra node. The active coordinate system is global cartesian.

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NOTE: Here, randomly assigning a node number of 1000, which is greater than any existing node number, makes it easy to identify the “extra” node. If this field was left blank, the next available node number would be automatically assigned to the new node.

NOTE: Here, randomly assigning a node number of 1000, which is greater than any existing node number, makes it easy to identify the “extra” node. If this field was left blank, the next available node number would be automatically assigned to the new node.

NOTE: Location of the “extra” node is arbitrary. We selected x=1.0, y=0.25.

NOTE: Location of the “extra” node is arbitrary. We selected x=1.0, y=0.25.

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The node plot is automatically updated to include the new node. Use Box Zoom or any Zoom command to get a better view of the region of interest.The node plot is automatically updated to include the new node. Use Box Zoom or any Zoom command to get a better view of the region of interest.

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Now we are ready to create the surface effect elements.

Create surface effect elements.Create surface effect elements.

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Use the Box picking option to select only the nodes on the inner tube surface for surface effect element definition.

Use the Box picking option to select only the nodes on the inner tube surface for surface effect element definition.

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Verify that all nine nodes are selected; click “Apply”Verify that all nine nodes are selected; click “Apply”

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Use graphical picking to select the extra node, or enter 1000 in the input window. Then, click “OK”.

Use graphical picking to select the extra node, or enter 1000 in the input window. Then, click “OK”.

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Preprocessing: Building the ModelChecking Attributes by Plotting

Attributes may be checked by plotting using the NumberingControls. Simply toggle the on/off buttons to specify which entities should be numbered and with what style.

To verify the element types were properly specified, turn on numbering based on element type number.

To verify the element types were properly specified, turn on numbering based on element type number.

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Training ManualPreprocessing: Building the ModelChecking Attributes by Plotting

For the sample problem, check element attribute numbering by plotting to verify element types were correctly specified.

NOTE: In this example, we could not have produced type 2, SURF151 elements without changing element attributes prior to meshing.

For the sample problem, check element attribute numbering by plotting to verify element types were correctly specified.

NOTE: In this example, we could not have produced type 2, SURF151 elements without changing element attributes prior to meshing.

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Here, switching to a vector plot will produce a wire-frame plot of elements.Here, switching to a vector plot will produce a wire-frame plot of elements.


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Example showing elements plotted in vector mode, with element types shown with both colors and numbers turned on.

Example showing elements plotted in vector mode, with element types shown with both colors and numbers turned on.

Issue the command /SHOW to reset plotting.Issue the command /SHOW to reset plotting.

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• Solution Processing

• Now we are ready to begin the next phase of the analysis process as described in the Thermal Analysis Template; Solution Processing

• In this phase, we will:

– Define the analysis type, and check analysis options

– Apply loads and boundary conditions.

– Execute the solution.

In the Solution Processor

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In the Solution ProcessorDefining the Analysis Type

Specify that this is a new analysis, and a steady-state problem. (This is the default).

Specify that this is a new analysis, and a steady-state problem. (This is the default).

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In the Solution ProcessorDefining Analysis Options

Analysis Options

• For a linear, steady-state, thermal analysis with a single load step, the only analysis option that may need to be set is the Equation Solver.

• NOTE: In ANSYS 5.5 and above, when Solution Control is On, the sparse solver is selected by default.

• Other analysis options such as Newton-Raphson options and Temperature Offset specifications, required for non-linear radiation problems will be discussed in the chapters that follow.

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Change to Iterative solver for large, 3-D models.Change to Iterative solver for large, 3-D models.

Check temperature offset; often required for radiation problems.

Check temperature offset; often required for radiation problems.

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* provided there are no mass transport of heat effects


Solvers:

• Any of the following solvers can be selected *:• Frontal solver (default)

• Jacobi Conjugate Gradient Solver (JCG)

• JCG out-of-memory solver

• Incomplete Cholesky Conjugate Gradient Solver (ICCG)

• Preconditioned Conjugate Gradient Solver (PCG)

• PCG out-of-memory solver

• Iterative (Fast Solution; automatic solver selection option)

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Iterative (Fast Solution) Option

• The Fast Solution option can be used for any linear, nonlinear, steady-state or transient thermal analysis with the following exceptions:

– may not be used for radiation analysis

– not recommended for heat transfer problems involving phase change.

NOTE: This option saves time and disk space by eliminating the need to create the jobname.emat, jobname.erot files. Analysis restarts are not possible when using the Fast Solution Option.

NOTE: This option saves time and disk space by eliminating the need to create the jobname.emat, jobname.erot files. Analysis restarts are not possible when using the Fast Solution Option.

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• When using the Fast Solution Option, you must specify an accuracy level.

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Temperature Offset

• The temperature offset defines the difference between absolute zero and the zero of the temperature system used.

• Temperature offset can be specified in the Analysis Options menu, or by using the command TOFFST,value.

• Temperature offset is optional, but MUST be used when

– radiation effects are present, and °F or °C are used.

– temperature-dependent heat generation rate (MASS71) is used.

The example problem uses BIN units, and degrees Fahrenheit. The Fahrenheit scale is offset 460 degrees from the Rankine scale.The example problem uses BIN units, and degrees Fahrenheit. The Fahrenheit scale is offset 460 degrees from the Rankine scale.

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In the Solution ProcessorApplying Thermal Loads and Boundary Conditions

Solid Model Loads and Finite Element Model Loads

• Thermal loads may be applied to either the solid model, or the FE model, or both.

• Solid model loads are independent of the mesh. The mesh can be changed but the loads will remain the same.

• Solid model loads are generally easier to apply than FE loads, especially when using graphical picking.

• Be careful when applying temperature values to keypoints. Use the expansion option to allow the temperature to be applied to all nodes on the line, rather than just the endpoints.

• Solid model loads take precedence over FE loads on the same region.

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Constant Values and Tabular Input

• To apply loads using TABLE type array parameters, the same commands and menu paths shown for each type of load are still used. However, instead of specifying an actual value for a particular load, the name of a table array parameter is specified.

• A new table can be defined during interactive load application by specifying the “new table” option. A series of dialog boxes prompts the user for table definition.

• These features work with both solid model and finite element model loads.

• For more details on tabular input, see Chapter 6.

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Nodal Temperature Specification

• Temperature constraints (DOF constraints) are specified in the model where the temperatures are known.

• Temperatures specified on solid model entities (keypoints, lines, and areas) will be applied to nodes for solution.

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NOTE: With GUI Preferences set to thermal only thermal loads appear in the “Apply” menu.

NOTE: With GUI Preferences set to thermal only thermal loads appear in the “Apply” menu.


Nodal Temperature Specification

• Temperature constraints (DOF constraints) are specified in the model where the temperatures are known.

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Initial Uniform Temperature

General Notes:

• A uniform temperature can be applied to nodes that do not have temperature constraints.

• There are two primary reasons to set an initial temperature:

– as a starting temperature in the first substep of a transient analysis.

– to evaluate initial values for temperature dependent material properties in a nonlinear analysis.

NOTE: Chapters 4 and 5 cover initial conditions and initial uniformtemperature specification in greater detail.

NOTE: Chapters 4 and 5 cover initial conditions and initial uniformtemperature specification in greater detail.

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Nodal Heat Flow Rates

• Heat flow rates are represented as heat flow per unit time through a node.

• A positive heat flow indicates heat is being supplied to the model.

• Heat flow rates are mainly used on line elements (conducting bars, convection links, etc.) in thermal network models where convection and heat fluxes cannot be specified.

• If both temperature and heat flow rate are defined on the same node, the temperature constraint will take precedence.

• Heat flow may also be specified on keypoints.

• Heat flow is considered a concentrated or “force” type of load.

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Nodal Heat Flow Rates

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Heat Flux

• Heat flux is a surface load representing heat flow distributed across a surface (heat per unit area).

• Positive heat flux indicates energy is being supplied to the model.

• Heat flux loading is only available for solid, shell, and surface effect elements.

• If a heat flux and a convection load are applied to the same entity, only the last load specified will be used.

NOTE: To enable both convection and heat flux on the same region, surface effect elements may be used. (See notes on surface effect elements).

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Heat flux will be specified of the tip of the fin for the example problem; applied as a solid model load on lines.

Heat flux will be specified of the tip of the fin for the example problem; applied as a solid model load on lines.


Heat Flux

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Heat flux specified of the tip of the fin.Heat flux specified of the tip of the fin.

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A negative value indicates heat is being extracted from the model.

A negative value indicates heat is being extracted from the model.

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General Notes on Plotting Loads and Boundary Conditions:

• In the Utility Menu>>Plot Controls>>Symbols, graphical symbols can be turned on/off for applied boundary conditions, reactions, and many other items. This is useful for checking the model both before and/or after solution. In particular:

– nodal load symbols can be displayed

– various surface loads may be displayed using arrows or face outlines.

– body loads can be displayed graphically.

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Turn on surface load symbols. Choose heat flux, represented as arrows on the region to which it is applied.

Turn on surface load symbols. Choose heat flux, represented as arrows on the region to which it is applied.

Controls plotting of pointboundary conditions

Controls plotting of pointboundary conditions

Controls plotting ofsurfaceboundary conditions

Controls plotting ofsurfaceboundary conditions

Controls plotting ofbody loads.

Controls plotting ofbody loads.

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The resulting plot shows the label, value, and location of load.The resulting plot shows the label, value, and location of load.

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Convection

• Convection is a surface load which accounts for heat transfer to or from a surrounding fluid medium.

• Both a film coefficient and a bulk temperature must be specified when defining convection.

• Convection loading is only available for solid, shell, and surface effect elements.

• If convection is applied to the same solid model entity (or element) as heat flux, only the last load specified will be used. – NOTE: To enable both convection and heat flux on the same region,

surface effect elements may be used. (Refer to Chapters 2 & 7 for discussion of surface effect elements)

• Convection loads may be applied using tables.

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Temperature-Dependent Film Coefficients

• Film coefficients (HF) may be temperature-dependent.

• They are treated as temperature-dependent material properties in ANSYS.

• To use, assign a material number n, and define a temperature table. Then define a film coefficient corresponding to each temperature.

• When applying the convection load, use a value of -n in the HF value field of the loading command, where n is the assigned material number of the temperature-dependent convection curve.

• A temperature-dependent film coefficient makes a thermal analysis non-linear.

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The example problem requires convection be applied at the external surfaces of the tube and fin. Here, the convection load is applied to the solid model entities.

The example problem requires convection be applied at the external surfaces of the tube and fin. Here, the convection load is applied to the solid model entities.

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Pick the two lines for convection loading, and then “Apply”.Pick the two lines for convection loading, and then “Apply”.

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Film coefficient and bulk temperature are constant for this example. Input values as shown, then “OK” to close the dialog box.

Film coefficient and bulk temperature are constant for this example. Input values as shown, then “OK” to close the dialog box.

If using a temperature-dependent convection load, enter the -n here

If using a temperature-dependent convection load, enter the -n here

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With the legend on, we can clearly see the load label, value and location. Note, convection or flux (but not both) can be shown on a given plot since ANSYS uses the same graphical representation for both surface loads.

With the legend on, we can clearly see the load label, value and location. Note, convection or flux (but not both) can be shown on a given plot since ANSYS uses the same graphical representation for both surface loads.

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Apply the convection load to the surface effect elements on the inner diameter.

NOTE: Since these elements lie on top of the PLANE55 elements, load application will be easier if we isolate surface effect elements from the rest of the model. Use Select Logic to select all Type 2 elements, and click “OK”.

Apply the convection load to the surface effect elements on the inner diameter.

NOTE: Since these elements lie on top of the PLANE55 elements, load application will be easier if we isolate surface effect elements from the rest of the model. Use Select Logic to select all Type 2 elements, and click “OK”.

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Listing the elements verifies that all eight surface effect elements (type 2) are currently selected.Listing the elements verifies that all eight surface effect elements (type 2) are currently selected.

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• Select the SURF151 elements that you want to load.

• Apply - convection - uniform - on elements (see next slide).

• Do NOT apply convection on lines

– SURF151 elements are not related to the solid model (lines)

– you will put the load on the underlying solid elements (I.e. PLANE55)

• Do NOT apply convection on nodes

– both the SURF151 and underlying solid are associated with the nodes on the surface

– you will produce double convection loading!!

In the Solution ProcessorSpecial Considerations for Surface Effect Elements

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• Convection may be applied on lines, areas, nodes, and elements.


Now we will apply the uniform convection load directly to the surface effect elements.Now we will apply the uniform convection load directly to the surface effect elements.

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“Pick All” applies the load to all currently selected elements. “Pick All” applies the load to all currently selected elements.

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Enter the film coefficient for the inside of the tube, and click “OK”to finish.

NOTE: The bulk temperature field should be left blank. The bulk fluid temperature will be specified as a temperature constraint on the extra node .

Enter the film coefficient for the inside of the tube, and click “OK”to finish.

NOTE: The bulk temperature field should be left blank. The bulk fluid temperature will be specified as a temperature constraint on the extra node .

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Now apply temperature constraint to the extra node to be 600 F, the bulk fluid temperature.Now apply temperature constraint to the extra node to be 600 F, the bulk fluid temperature.

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Use node 1000.Use node 1000.

<ENTER> after typing keyboard entry

<ENTER> after typing keyboard entry

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Input 600 degrees.Input 600 degrees.

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Remember to select all entities before executing the solution.

Select everything to include all elements and loads in the solution.Select everything to include all elements and loads in the solution.

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Change surface load symbol plotting to show the convective film coefficient. Verify the loading graphically.

Change surface load symbol plotting to show the convective film coefficient. Verify the loading graphically.

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Create an element plot. An element plot provides a quick check of the applied convection load. It shows all active elements, applied temperature at the extra node, and convection load on surface effect elements on the inner diameter of the tube.

Create an element plot. An element plot provides a quick check of the applied convection load. It shows all active elements, applied temperature at the extra node, and convection load on surface effect elements on the inner diameter of the tube.

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Heat Generation

• Heat generation rates are body loads which represent heat generated within an element (heat flow rate per unit volume).

• Heat generation rates may be applied on solid model entities, and finite element entities. Loads are converted to elemental loads.

• A uniform heat generation rate can be applied to all nodes in a model with one command (BFUNIF).

• Heat generation can also be applied with tables.

NOTE: Loading using the BFA and BFK commands distribute the loads to elements differently. Review these commands before using.NOTE: Loading using the BFA and BFK commands distribute the loads to elements differently. Review these commands before using.

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• Apply heat generation using the appropriate menu picks.

• This shows application of heat generation to areas.

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In the Solution ProcessorTransferring Solid Model Loads to FE model

• Transfer of solid model thermal loads and boundary conditions to the finite element model occurs automatically when a solution is requested (SOLVE command ).

• Solid model thermal loads and boundary conditions may also be transferred manually, either by load category, or all at the same time. For example, you may manually transfer:

– only DOF constraints (temperatures)

– only Force loads (heat flow)

– only Surface loads (convection/heat flux)

– only Body loads ( heat generation)

– all Solid Model loads

• Manual transfer, when used, is typically for model checking.

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In the Solution ProcessorTransferring Solid Model Loads and BC’s

Note options for transferring loads to FE model from solid model. The highlighted option transfers all solid model loads.

Note options for transferring loads to FE model from solid model. The highlighted option transfers all solid model loads.

Loads may also be transferred based on load category.

Loads may also be transferred based on load category.

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In the Solution ProcessorDeleting Thermal Loads and Boundary Conditions

• Loads may be deleted in various ways using the following menu picks:

Used to delete loads by category from the entire model.

Used to delete loads by category from the entire model.

Used to delete loads from specific entities.

Used to delete loads from specific entities.

Delete loads in the same manner as they were applied ( e.g. flux on lines).

Delete loads in the same manner as they were applied ( e.g. flux on lines).

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In the Solution ProcessorListing Thermal Loads and Boundary Conditions

• Loads may be listed using the Utility Menu picks.

Here, a listing of surface loads on all lines shows the heat flux load and convection load on the exterior surface of the tube and fin example problem.

NOTE: Recall that the second convection load, on the inside of the tube, was applied to the surface effect elements directly and therefore is not included in this list of surface loads on lines.

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• After defining all of the loads and load options, the final step in the Solution phase is to initiate the solution.

• Save the database just before solving.

• To review ANSYS solution processing and program messages, bring the ANSYS output window forward before executing the solution.

In the Solution ProcessorGetting Ready to Solve

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In the Solution ProcessorSolving a Single Load Step

To solve a single load step:

• Enter the command

Solve>>Current LS

• Review the status window for proper solution option and load step option settings.

• If ready to solve, click “OK” to execute the solution.

Use Solve>>Current LS to begin solution execution.Use Solve>>Current LS to begin solution execution.

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In the Solution ProcessorSolving a Single Load Step

Review the status window, and click “OK” to solve.Review the status window, and click “OK” to solve.

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In the Solution ProcessorLoad Step

• A load step is a set of boundary conditions and load options for which at least one solution is computed.

• A given ANSYS analysis can consist of either:

– A single load step

or

– Multiple load steps.

• We will discuss two ways to define and solve multiple load steps:

– The multiple solve method

– The load step file method

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• Easiest of the three methods to understand.• Disadvantage -- GUI users must wait for each solution to be

completed before defining the next.

In the Solution ProcessorThe Multiple Solve Method

To use the multiple solve method:1. Specify analysis controls, loads and options for the

first load step.2. Solve (see previous slide) and postprocess if

desired.3. Change the title and loading as required for the next

solution.4. If you have left the solution processor (to do

postprocessing for example) since the last solve (e.g., postprocessing), then specify a RESTART to avoid the new analysis overwriting the results file.

5. Solve, and postprocess as desired.6. Repeat steps 3, 4, and 5 until all load steps are

completed.

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In the Solution ProcessorThe Load Step File Method

• Convenient for GUI users solving multiple load steps.

• Writes loads and options to load step files and, with one command, reads in each file and solves.

To use the load step method:1. Specify analysis controls and specify loads and

options for the first load step, change the title.2. Write load step file.3. Change loads and options as required for the

next load step, change the title.4. Write next load step file.5. Repeat steps 3 and 4 for remaining load steps.6. Solve from load step files.7. Postprocess

NOTE: LSWRITE files may require editing if Solution Control is OnNOTE: LSWRITE files may require editing if Solution Control is On

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In the Solution ProcessorFiles Created During the Solution

• For a linear, static single load step analysis, the thermal results file, jobname.rth is written by default when the solution is executed and results are also stored in database memory.

• By default ANSYS stores end of load step results only. Use Output Controls to force other substep results to be stored.

• The jobname.out file (ASCII) can also be written if requested.

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• Once the solution has been obtained, begin postprocessing to check results.

• Results can be viewed with either the General Postprocessor (POST1), and/or the Time-History Postprocessor (POST26).

Postprocessing Reviewing Results

POST1

POST26

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Postprocessing: Reviewing ResultsGeneral Postprocessor (POST1)

• The General Postprocessor, POST1, is used to review results at a particular substep or timestep for the entire model, or for selected entities.

• For single load step , single substep analyses.

• Typical output from POST1 includes:

– contour displays

– vector displays

– tabular listings of results

– error estimation

– load case combinations

– results data calculations

– path operations

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Postprocessing: Reviewing ResultsTime-History Postprocessor (POST26)

• The Time-History Postprocessor, POST26, is used to review results at specified points in the model over many time steps.

• The Time-History Postprocessor can be used to:

– produce graphs of results versus time.

– produce tables of results versus time.

– operate on tables of data

• More information on POST26 is covered in Chapter 5, Transient Analysis.

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Postprocessing: Reviewing ResultsPostprocessing 101 - Fundamentals

What results are stored on the jobname.rth file?

• Primary Data Items

– Nodal temperatures (TEMP)

– Nodal Reaction Heat Flow Rates (HEAT)

• Secondary Data Items

– Thermal Fluxes (TFX, TFY, TFZ)

– Thermal Gradients (TGX, TGY, TGZ)

• Special Data Items

– Element Table Items

– Solution summary items

– etc.

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• When plotting contours of results, you can choose either nodal or element quantities:

– Nodal DOF Results are values of temperature calculated directly at nodes. Temperature contours will be continuous across element boundaries which share nodes.

– Element Gradient/Flux Results are items derived from the temperature solution (e.g., x component of thermal flux). These quantities are initially computed at element integration points and are then extrapolated to the element’s nodes. Since these quantities are computed on an element-by-element basis and are not averaged at common nodes, contour plots of these items often appear to be discontinuous.

– Nodal Gradient/Flux Results are elemental items which are averaged at common nodes. Because there is only one average value at each node (like nodal DOF solution), contours plots of nodal element quantities appear to be continuous.

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• Getting a summary of load steps/titles on the jobname.rth file:

Enter the General Postprocessor to review results for the example problem. Use Results Summary to list and read load steps and titles from the results file.

Enter the General Postprocessor to review results for the example problem. Use Results Summary to list and read load steps and titles from the results file.

For a nonlinear or transient analysis, there may be several solutions available for review.

For a nonlinear or transient analysis, there may be several solutions available for review.

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Postprocessing: Reviewing ResultsPostprocessing 101 - Basic Operations

• Contour plots can be produced for component or resultant quantities based on either the nodal solution or element solution.

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• Plot Temperatures


Plot nodal solution, temperatures

Plot nodal solution, temperatures

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• Temperature Plot

NOTE: This plot has all model entities selected, including the extra node.NOTE: This plot has all model entities selected, including the extra node.


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• Plotting Temperature Contours

• Produce a contour plot of temperatures

• Select all Type 1 (PLANE55) elements for postprocessing

• Select everything below the selected elements

• Produce a contour plot of temperatures

• Select all Type 1 (PLANE55) elements for postprocessing

• Select everything below the selected elements


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Notice the temperature scale is reset.Notice the temperature scale is reset.

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Plot TFSUM, thermal flux magnitude for the example problem.

Plot TFSUM, thermal flux magnitude for the example problem.


• Plot Thermal Flux

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NOTE: Due to the geometric discontinuity in this model (re-entrant corner) flux and gradient results in the corner region are not accurate (singularity exists).


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Plot TGSUM, thermal gradient magnitude for the example problem. Note that component options are available as well.

Plot TGSUM, thermal gradient magnitude for the example problem. Note that component options are available as well.


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Element solution data (unaveraged) is also available for plotting. Plot TFSUM - unaveraged for the example problem.Element solution data (unaveraged) is also available for plotting. Plot TFSUM - unaveraged for the example problem.


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Note the difference in the element solution plot compared to the smooth contours in the nodal solution plot. This is one way to help gauge mesh error. (See Chapter 2).



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Plot TGSUM, unaveraged.Plot TGSUM, unaveraged.


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Predefined vector plots include thermal flux vectors and thermal gradient vectors.

Predefined vector plots include thermal flux vectors and thermal gradient vectors.

Vector Plot of Thermal Gradient


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thermal fluxthermal flux


• Produce Vector Plot of Thermal Flux

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• For the exterior surfaces, use of the element table is required, since we did not use surface effect elements.

• There are a few steps involved:

– select the elements (PLANE55 solid elements)

– create an element table item to store heat flow rate due to convection for each element face for each of these elements. (PLANE55 has four faces so this must be done a total of four times).

– sum the element table item to get the total.

Next, we’ll use two different methods to check results. First, we’ll obtain the heat lost through the exterior tube/fin surfaces to the surrounding fluid. Then we’ll check and the heat input from the hot fluid at the inner tube surface. These values should be equal.

Next, we’ll use two different methods to check results. First, we’ll obtain the heat lost through the exterior tube/fin surfaces to the surrounding fluid. Then we’ll check and the heat input from the hot fluid at the inner tube surface. These values should be equal.


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• To get similar results data on the interior surface where surface effect elements were applied, there is only one step required:

– list the reaction solution at the extra node.


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The Element Table - A Quick Review

• In ANSYS, the element table serves two main functions.– First, it is a tool for performing arithmetic operations on results data.

– Secondly, it allows access to certain element results data that are not otherwise directly accessible.

• The element table can be thought of as a spreadsheet, where each row represents a particular element, and each column contains a specific data item for the elements.

• For some elements, the ETABLE is the only way to access certain results data (COMBIN, LINK, etc…).


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Request help on PLANE55 elements to get a listing of ETABLE items available. Remember the Heat Rate item applies to convection only.

NOTE: FC1 refers to element face 1, FC2 to face 2 etc. Data must be collected for all faces of all PLANE55 elements to be complete.

Request help on PLANE55 elements to get a listing of ETABLE items available. Remember the Heat Rate item applies to convection only.

NOTE: FC1 refers to element face 1, FC2 to face 2 etc. Data must be collected for all faces of all PLANE55 elements to be complete.


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Begin Element Table definition to collect the required data.

Begin Element Table definition to collect the required data.


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Define ETABLE items using sequence number. Data is collected from each element face for all PLANE55 elements.Define ETABLE items using sequence number. Data is collected from each element face for all PLANE55 elements.


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Continue to define ETABLE items heat2, heat3, and heat4 using NMISC 11, 17 and 23.

Continue to define ETABLE items heat2, heat3, and heat4 using NMISC 11, 17 and 23.

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• Entries in the current Element Table:

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• Element table data may be listed and plotted.

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Listing the sum of each item produces the desired results quantities.Listing the sum of each item produces the desired results quantities.


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Use the ETABLE data to check results.Use the ETABLE data to check results.

9075.207

856.1750515.32

heat4 and heat3 heat2, heat1, :items ETABLE of Sum

9075.207

856.1750515.32

heat4 and heat3 heat2, heat1, :items ETABLE of Sum

62.8318)3.14159(20 Flux Heat x 14159.3

14159.3125.00.422 area Surface 2

inrh

62.8318)3.14159(20 Flux Heat x 14159.3

14159.3125.00.422 area Surface 2

inrh


• Sum of ETABLE entries represents heat lost by convection through PLANE55 elements. When added to heat flux lost at the fin tip, the result should equal the heat input to the system by the hot fluid at the tube inner diameter.

• To calculate heat lost at fin tip, calculate the surface area and multiply by the heat flux value:

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Continued….Using the ETABLE data to check results.Continued….Using the ETABLE data to check results.

270.74 surfacesexterior from LossHeat Total

62.83 n calculatio lossflux heat From

207.91 loss convection data, ETABLE From

270.74 surfacesexterior from LossHeat Total

62.83 n calculatio lossflux heat From

207.91 loss convection data, ETABLE From

In the example, the total heat lost from exterior surfaces = convection loss + flux loss

Next, we’ll compare this result to the reaction solution data from the extra node of the surface effect elements.Next, we’ll compare this result to the reaction solution data from the extra node of the surface effect elements.


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After completion of the calculation, use Select >>Everything to continue postprocessing the entire model.After completion of the calculation, use Select >>Everything to continue postprocessing the entire model.


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Now, to find the heat flow rate into the tube, simply display the reaction solution.Now, to find the heat flow rate into the tube, simply display the reaction solution.


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Here, the reaction solution is shown for node 1000, (the “extra node” used in the surface effect element definition). Here, the reaction solution is shown for node 1000, (the “extra node” used in the surface effect element definition).

Now, compare results from the two methods:

1.) ETABLE (for convection) + Heat Flux calculation = 270.742.) Reaction Solution for extra node = 270.74

The answers match as expected.

Now, compare results from the two methods:

1.) ETABLE (for convection) + Heat Flux calculation = 270.742.) Reaction Solution for extra node = 270.74

The answers match as expected.


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• Listing Results

Instead of plotting, list the nodal temperatures.Instead of plotting, list the nodal temperatures.


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This is an “unsorted” results listing. It lists the nodes in numerical order by default.

This is an “unsorted” results listing. It lists the nodes in numerical order by default.


• Listing Results (continued)

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Now sort the nodal data based on the nodal temperatures in descending order, and list.Now sort the nodal data based on the nodal temperatures in descending order, and list.


• Lists may be sorted based on chosen data items.

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Review the list, which now shows descending temperatures.

NOTE: Since the entire model is selected, we can also see the applied temperature at node 1000.

Review the list, which now shows descending temperatures.

NOTE: Since the entire model is selected, we can also see the applied temperature at node 1000.


• Sorted Listings (continued)

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Restore the list to the original order.Restore the list to the original order.


• Un-sorting restores data to the original order.

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• Element data may be sorted also.


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Query Results

• Querying results enables you to request numerical results by graphical picking.

• Values are shown right on top of an existing plot.

• The plot does not have to match the data type being queried.


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Use this button to automatically generate 3-D annotation.

Use this button to automatically generate 3-D annotation.

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• Basic Path Operations

Produce a plot of temperature as a function of distance along the exterior surfaces of the model.

Produce a plot of temperature as a function of distance along the exterior surfaces of the model.


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Pick 3 corner nodes to define the path.Pick 3 corner nodes to define the path.

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• The path can be given a unique name.

Name the path “top”Name the path “top”


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• Label the data and map the desired data onto the path.

Select Temperature to map onto path. Note the option to average results across element for quantities that are discontinuous; call the data “toptemp”

Select Temperature to map onto path. Note the option to average results across element for quantities that are discontinuous; call the data “toptemp”


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• Create the plot.

Produce a plot of “toptemp” data by selecting it from the list of items to be graphed.Produce a plot of “toptemp” data by selecting it from the list of items to be graphed.


XG, YG, ZG and S are predefined variablesXG, YG, ZG and S are predefined variables

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Note the path is 1.75 inches long.Note the path is 1.75 inches long.


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• Clearing Path Data


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Steady State Heat Transfer (no mass transport) Chapter 3.

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