fea thermal intro.ppt - rice university · thermal analysis verification 1thermal analysis...

FEA Thermal AnalysisFEA Thermal AnalysisIs based on the temperatures of

parametric solid models

Copyright © 2010 J. E. Akin Rice University, MEMS Dept.

FEA Thermal Analysis, 1

• Heat transfer takes place by internal conduction through objects in contact, by g j , yconvection to a fluid at external surfaces, and by non-linear radiation from one ysurface to another.

• Heat flows from high temperature towardHeat flows from high temperature toward low temperature regions


FEA Thermal Analysis,2

• Objects can have an internal heat generation per unit volume, from chemical reactions, p , ,electrical resistance, etc.

• Surfaces can have a known heat flux perSurfaces can have a known heat flux per unit area, normal to the surface

• An insulated boundary (no heat flux) is a• An insulated boundary (no heat flux) is a natural BC requiring no input data


FEA Data Reliability, 1• Geometry: generally most accurate if not• Geometry: generally most accurate, if not

de-featured (sliver faces cause mesh failure)M t i l if d di d d• Material: accurate if standardized or tested. Thermal conductivity, k, is known only to 3

4 i ifi fior 4 significant figures• Mesh: requires engineering judgment for

element type, sizes, and transition ratios


FEA Data Reliability, 2• Heat sources (Loads): less accurate require• Heat sources (Loads): less accurate, require

assumptions. Are normal heat flux values known? Are heat flux areas reasonablyknown? Are heat flux areas reasonably located? Internal heat generation of power supplied may be requiredsupplied may be required.

• The convection coefficient, h, on faces is id l i bl I d i ll ff hwidely variable. It can drastically effect the

temperature results.


FEA Data Reliability, 3• Prescribed Temperatures (Restraints):• Prescribed Temperatures (Restraints):

are usually assumed, drastically effect results; several reasonable temperatureresults; several reasonable temperature estimates should be studied. D h l d d i l h i• Does the excluded material, at the restraint, have the ability to supply the heat flow to

i i h i ?maintain the given temperature?


FEA Result Reliability, 4FEA Result Reliability, 4

• Equation Solver: generally the computedEquation Solver: generally the computed temperatures are quite accurate (3 or 4 significant figures)significant figures)

• Reactions: the reaction heat flows, obtained from the solver at the given temperaturefrom the solver, at the given temperature points, are similarly accurate. The SW List Selected feature gives those summationsSelected feature gives those summations.



• Post-processing: calculates the gradient vector of the scalar temperature. The gradient of an approximate solution is always less accurate than the approximate solution. The gradient vector components are multiplied by the thermal conductivity to define the heat flux vector (per unit area).



• Post-processing: The integral over a f f th l t f thsurface, of the normal component of the

heat flux vector, gives the total heat flow in t f th t for out of that surface.



P t i Th t d• Post-processing: The computed temperatures found in the thermal study can b t ti ll d t b dbe automatically saved to be used as a loading condition in a thermal-stress study


FEA Result Reliability, 8FEA Result Reliability, 8• Plotting: temperatures are continuous between

l h i ( i lelements, so their contours are accurate (wiggle lines show that the mesh needs to be finer).

• Heat flux values are discontinuous between elements, but are averaged to look smooth. Two or three significant figures might be accurate, depending on mesh fineness.


Approach for Thermal Studies 1Approach for Thermal Studies, 1

• Select verification tools to independently p ycheck the FEA study– Use analytic, experimental, another FEA

method, etc.– Predict the temperatures and heat flows at

important locationsimportant locations– When done, compare with your prediction– If significantly different, re-access the g y

assumptions used for both solutions– Repeat the prediction and/or FEA study


Approach for Thermal Studies, 2

• Understand the primary variables (PV) in the h l ilib i ithermal equilibrium equation.- Temperature is the unknown

U d t d b d diti (BC)• Understand boundary conditions (BC)– Essential, or Dirichlet BC specify a temperature

(often zero) at some boundary points (EBC)(often zero) at some boundary points (EBC)– Natural (insulated), or Neumann (known normal

heat flows) BC apply at other points (NBC)– One or the other acts at a boundary point, never

both conditions


Approach for Thermal Studies, 3

• Understand reactions needed to maintain the prescribed temperature at a boundary:

• Total heat flow through a given t t itemperature region

• Can the omitted material at the reaction supply the necessary heat flow? pp y y


Primary Thermal Assumptions, 1• Model geometry (? De-featured, neglected regions ?)• Material properties for thermal models

– Thermal conductivity, k (? Temperature dependent ?)• Mesh(s)

– Element type and size, size transition rates– Interface contact or bond condition

• Heat source (loading) cases• Heat source (loading) cases– Know flux values, power generation, surface

convection• Boundary conditions (Fixtures)

– Specified temperatures


Primary Thermal Assumptions, 2• Material properties are tabulated for

common materials:– Thermal conductivity, k, defines the

conduction matrix contributions of an element (terms in the square matrix ofelement (terms in the square matrix of the algebraic system).

– Properties are known only to 3 no 4 i ifi fisignificant figures.

– Conductivity can be tabulated as a function of temperature, requiring anfunction of temperature, requiring an iterative non-linear solution


Primary Thermal Assumptions, 3

• Boundary conditions (Fixtures) are idealizations– Specified temperatures are often just guesses– Contacting faces may be fully bonded (default),

h diffi lt t ti t th l i t for have a difficult to estimate thermal interface resistance.


Primary FEA Solution Costsy

• Assume a sparse, banded, linear algebra system of Eequations, with a half-bandwidth of B. Full system if B = E.– Storage required, S = B * E (Mb)

S l ti C t C B * E2 (ti )– Solution Cost, C α B * E2 (time)– Half symmetry: B’ ← B/2, E’ ← E/2, S’ ← S/4, C’ ← C/8

, answers obtained eight times faster, g f– Quarter symmetry: B’ ← B/4, E’ ← E/4, S’ ← S/16,

C’ ← C/64 , answers 64 times faster– Eighth symmetry, Cyclic symmetry, ...


Thermal Result AccuracyThermal Result Accuracy• Temperatures are most accurate at the p

mesh nodes.• Heat flux vectors are least accurate at theHeat flux vectors are least accurate at the

mesh nodes, most accurate at element center.center.– Heat flux is discontinuous at element

interfaces, but can be post-processed for , p paccurate averaged nodal values


Local Heat Flux Singularitiesg• All thermal analysis problems have local radial

gradient singularities near re-entrant corners in the g gdomain. The radial heat flux there is theoretically infinite, but not in practice. Mesh refinement never helps therehelps there.

Radius, ru = r p f(θ)

∂u/∂r = r (p-1) f(θ)

Strength, p = π/C Corner: p = 2/3, weak

Crack: p = 1/2 strongRe-entrant, C

Crack: p 1/2, strong

∂u/∂r ⇒∞ as r ⇒ 0


Local Heat Flux ErrorLocal Heat Flux Error• The thermal error at a (non-singular)

i i h d f h l ipoint is the product of the element size, h, the heat flux gradient, and a constant d d h d i h ddependent on the domain shape and boundary conditions.– Large heat flux gradient points need small

element sizes– Small heat flux gradient regions can have

large element sizes


Thermal Mesh Considerations, 1• Crude meshes that “look like” a part are ok

for images and mass properties but not for FEA thermal analysis.

• Temperature values are piecewise continuous l i l f d hil h h flpolynomials of degree p, while the heat flux

vectors are piecewise discontinuous polynomials of degree (p 1) In SW p=2polynomials of degree (p-1). In SW p=2.


Thermal Mesh Considerations, 2Thermal Mesh Considerations, 2• Plan local mesh size with engineering

j d b d i d h fljudgment based on estimated heat flux gradients (heat flow concentrations).

• Always utilize the SolidWorks Mesh Control Option

• Revise the mesh where you see (non-singular) high heat flux values.g ) g


Symmetry & Anti-symmetry Planesy y y y

• Use symmetry planes for the maximumUse symmetry planes for the maximum accuracy at the least cost in thermal problems.p ob e s.

• Cut the object with symmetry planes and apply new boundary conditionsand apply new boundary conditions (EBC or NBC) to account for the removed materialremoved material.


Symmetry (Anti-symmetry) Planes

• Requires symmetry of the geometry and material properties.p p

• Requires symmetry (anti-symmetry) of the heat source termsthe heat source terms.

• Requires symmetry (anti-symmetry) of the imposed temperaturesthe imposed temperatures.


Symmetry, Anti-symmetryTh l C ditiThermal Conditions

• Symmetry• Symmetry– Zero heat flux normal to surface (the

natural BC no input data required)natural BC, no input data required)• Anti-symmetry

– Specify the mean temperature on the surface


Thermal Analysis Verification 1Thermal Analysis Verification, 1

• Prepare initial estimates of thePrepare initial estimates of the temperatures, reaction flux, and heat flux vectorsflux vectors.

• Eyeball check the temperature contours and the heat flux vectorsand the heat flux vectors.

• Temperature contours should be di l i l d b dperpendicular to an insulated boundary.


Th l A l i V ifi ti 2Thermal Analysis Verification, 2

• The temperatures often depend only on the shape of the part for homogeneous material properties.

• The heat flux, and reaction heat flows, , ,will always depend on the material properties.p p


Thermal Analysis Verification, 3

• The resultant heat flow can be obtained from the normal component pof the heat flux by integration over a surface via the List Selected feature in SW


fea thermal intro.ppt - rice university · thermal analysis verification 1thermal analysis...

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