Mech-HT 120 Lect-04 SteadyState

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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


G. Workshop


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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:


Energy in - Energy out = 0


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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:


[ ]{ } { }QTK =

The corresponding finite element equation expressing equilibrium is:


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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


.

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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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


Exterior Surface Interior Surface


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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


Lines


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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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Training Manual. . . Thermal Elements Thermal shell elements (surface geometry) use corner node

configuration


Thickness for surface models must be provided in the details foreach surface part


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3D Shells (SHELL57)


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Training Manual. . . Thermal Elements Thermal line elements are uniaxial 2 node elements


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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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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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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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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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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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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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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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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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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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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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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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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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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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

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Mech-HT 120 Lect-04 SteadyState