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Chapter 4
Steady State HeatTransfer
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ANSYS MechanicalHeat Transfer
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Steady State Heat Transfer
Training ManualChapter ContentsSteady State Heat Transfer:
A. Steady State Theory
B. Geometry Types
C. Thermal Elements
D. Model Setup
E. Steady State Example
F. Multi le Ste Solutions
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G. Workshop
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Steady State Heat Transfer
Training ManualA. Steady State Theory
When the flow of heat does not vary with time, heat transfer isreferred 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 varywith time
From the First Law of Thermodynamics, the steady-state heatbalance can be expressed simply as:
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Energy in - Energy out = 0
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Steady State Heat Transfer
Training Manual
0...=+
+
+
q
z
Tk
zy
Tk
yx
Tk
xzzyyxx
. . . Steady State Theory For steady-state heat transfer, the differential equation expressing thermal
equilibrium is:
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[ ]{ } { }QTK =
The corresponding finite element equation expressing equilibrium is:
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Steady State Heat Transfer
Training ManualB. Geometry Types All geometry types (solid, surface and line
bodies), are supported in Mechanical. Theelements contain temperature degrees of
freedom (DOF).
Solid Geometry (2D and 3D):
Models may be full 3D or symmetry sections
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.
2D geometry can be planar or axisymmetric.
For 2D:
Planar models assume a unit thickness.
Axisymmetric models assume all loads andconstraints are applied to the full 360 degree
model.
Solids
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Steady State Heat Transfer
Training Manual. . . Geometry Types Surface Geometry:
Models representing thin sheet like members (e.g. sheet metal) whereno thickness is modeled
Assumes no temperature variation through the thickness, only across thesurface
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Exterior Surface Interior Surface
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Steady State Heat Transfer
Training Manual. . . Geometry Types Line Geometry:
Simplified geometry typical of beams, pipes, etc. where the cross sectionis not modeled, but assigned to each line section
Assumes no temperature variation through the cross section, only alongthe length
Note: line body geometry may be available from several CAD sourceshowever beam cross section definitions and orientations can only be set inDesignModeler
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Lines
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Steady State Heat Transfer
Training ManualC. Thermal Elements
Thermal solid elements use high order node configuration
Element degree of freedom (DOF) is temperature
Temperature distribution within elements is calculated from the
element shape functions
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3D Solids (SOLID90) 2D Solids (PLANE77)
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Steady State Heat Transfer
Training Manual. . . Thermal Elements Thermal shell elements (surface geometry) use corner node
configuration
Element degree of freedom (DOF) is temperature
Thickness for surface models must be provided in the details foreach surface part
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3D Shells (SHELL57)
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Steady State Heat Transfer
Training Manual. . . Thermal Elements Thermal line elements are uniaxial 2 node elements
Element degree of freedom (DOF) is temperature
The cross section is defined and assigned to line sections in ANSYS
DesignModeler
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Line Element (LINK33)
DesignModeler Cross
Section Library.
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Steady State Heat Transfer
Training ManualD. Model SetupGeneral Notes on Thermal Loads and Boundary Conditions
In Mechanical, model boundaries that have no applied loads aretreated as adiabatic (perfectly insulated)
Symmetry boundary conditions are imposed by letting theboundaries be adiabatic
Reaction heat flow rates are available at fixed temperature DOFs,
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Steady State Heat Transfer
Training Manual. . . Model SetupAnalysis Settings:
Step Controls: control multiple stepsas wells as auto time stepping
Nonlinear Controls: specifyconvergence criteria and control linesearch solver option
Output Control: controls content and
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saved
Analysis Data Management: generaloptions controlling file managementand solver units
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Steady State Heat Transfer
Training ManualE. Steady State Example This example presents a walk through
for a steady state analysis.
The model represents and electrical coil
composed of an iron core surrounded bya copper coil separated by a plasticinsulator. The assembly rests on a steelmounting plate.
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sufficient time to reach a steady state. Boundary Conditions:
The iron core generates heat at 0.001W/mm^3.
The copper coil is experiencing forced
convective heat loss at a rate of 0.1W/mm^2 in a 30 C ambient environment.
The mounting plate is attached on one sideand assumed to be at a fixed 25 C.
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Steady State Heat Transfer
Training Manual. . . Steady State Example After specifying a Steady State Thermal analysis type, selecting the
desired geometry and adding or creating the necessary materials inWorkbench, we begin the model setup in Mechanical
The materials are assigned in the details of each part as shown here
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Steady State Heat Transfer
Training Manual. . . Steady State Example After evaluating the default mesh, several mesh controls are added to
modify element size and shape
Note, the DesignModeler geometry was assembled as a multi-body part,thus the mesh is continuous across parts which means no contact isnecessary
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Multi-body Part MeshDetail Showing
Shared Nodes
RMB and Generate Meshto Evaluate Any Changes
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Steady State Heat Transfer
Training Manual. . . Steady State Example The boundary conditions detailed earlier are applied to the
appropriate regions of the model
Highlighting the Steady-State Thermal (A5) branch allows all BCs to bedisplayed on a common plot
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Since the model is steady state and linear we will leave the AnalysisSettings in their default configuration and solve the model
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Steady State Heat Transfer
Training Manual. . . Steady State Example When the solution is finished its good practice to
check the validity of the solution before proceeding
By inspecting the core details we can see that thecores volume is 44698 mm^3
Since the heat generation load is 0.001 W/mm^3, wecan calculate the heat generation as 44.698 W
The steady state assumption means that the
temperature and convection boundary conditions must
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equal the heat input
Reaction probes can be quickly configured by draggingand dropping both boundary conditions onto theSolution branch
An RMB to Evaluate All Results will update thereaction probes
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Steady State Heat Transfer
Training Manual. . . Steady State Example By summing the probe results we find good
agreement
Hgen - Rtemp - Rconv = 0
44.698 10.532 34.165 = 0.001
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Having verified an energy balance we canproceed to postprocess other results
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Steady State Heat Transfer
Training Manual. . . Steady State Example
Results Can BeScoped to
Individual Parts toRefine the Solution
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Temperature Plot forAll Bodies Gives a
Good Overview ofthe Distribution
Throughout theAssembly
sp ay or ac
Directional Results, HeatFlux Here, Can Be
Displayed as Vectors to
Enhance theInterpretation of Heat
Flow
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Steady State Heat Transfer
Training Manual. . . Steady State Example In addition to the default results, user defined results can be
requested. These results may be combined in expressions as well.
Worksheet View forSolution Branch
Shows User
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User Defined Result Definitions:
TEMP = temperature.
TF = thermal flux.
ENERGY (Potential) = thermal heat dissipationenergy.
VOLUME = displays the volume of all elementsattached to scoped region.
ENERGY (kinetic) = N/A .
TERR = thermal error energy. HEAT = heat flow.
NDIR = nodal angles (see ANSYSN command).
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Steady State Heat Transfer
Training ManualF. Multiple Step Solutions Multiple steady state solutions can be setup and solved sequentially
from the Analysis Settings
The graph and table display solution points
By changing the Current Step Number each step is configuredindependently
Note this is not a transient analysis
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Steady State Heat Transfer
Training Manual. . . Multiple Step Solutions Loads can be varied for each solution by
choosing the Current Step Number
Example, temperature load
Again the graph and table display the input
variation Loads will ramp from the previous step
Note: for linear analyses (single solution) there is nodifference between ramped or step applied loads
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Steady State Heat Transfer
Training Manual. . . Multiple Step Solutions The Analysis Settings
can be set up for multiplesteps rather than one at atime
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The Analysis SettingsWorksheet view allowsreview of all settings in asingle page
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Workshop 4
Solenoid
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ANSYS MechanicalHeat Transfer