FEA_Thermal_Intro.pdf

FEA Thermal Analysis
FEA Thermal Analysis
Is 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 , y
convection to a fluid at external surfaces,
and by non-linear radiation from one
y
surface to another.
• Heat flows from high temperature toward
Heat 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 per
Surfaces 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 fi
or 4 significant figures
• Mesh: requires engineering judgment for
element type, sizes, and transition ratios

• Heat sources (Loads): less accurate require
• Heat sources (Loads): less accurate, require
assumptions. Are normal heat flux values
known? Are heat flux areas reasonably
known? Are heat flux areas reasonably
located? Internal heat generation of power
supplied may be required
supplied may be required.
• The convection coefficient, h, on faces is
id l i bl I d i ll ff h
widely variable. It can drastically effect the
temperature results.

• Prescribed Temperatures (Restraints):
• Prescribed Temperatures (Restraints):
are usually assumed, drastically effect
results; several reasonable temperature
results; 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, 4
• Equation Solver: generally the computed
Equation 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 temperature
from the solver, at the given temperature
points, are similarly accurate. The SW List
Selected feature gives those summations
Selected 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 th
surface, of the normal component of the
heat flux vector, gives the total heat flow in
t f th t f
or 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 d
be automatically saved to be used as a
loading condition in a thermal-stress study

• Plotting: temperatures are continuous between
l h i ( i l
elements, 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 1
Approach for Thermal Studies, 1
• Select verification tools to independently
p y
check the FEA study
– Use analytic, experimental, another FEA
method, etc.
– Predict the temperatures and heat flows at
important locations
important 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

• Understand the primary variables (PV) in the
h l ilib i i
thermal 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

• Understand reactions needed to
maintain the prescribed temperature
at a boundary:
• Total heat flow through a given
t t i
temperature 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

• Material properties are tabulated for
common materials:
– Thermal conductivity, k, defines the
conduction matrix contributions of an
element (terms in the square matrix of
element (terms in the square matrix of
the algebraic system).
– Properties are known only to 3 no 4
i ifi fi
significant figures.
– Conductivity can be tabulated as a
function of temperature, requiring an
function of temperature, requiring an
iterative non-linear solution

• 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 f
or have a difficult to estimate thermal interface
resistance.

Primary FEA Solution Costs
y
• Assume a sparse, banded, linear algebra system of E
equations, 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 Accuracy
Thermal Result Accuracy
• Temperatures are most accurate at the
p
mesh nodes.
• Heat flux vectors are least accurate at the
Heat 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 p
accurate averaged nodal values

Local Heat Flux Singularities
g
• All thermal analysis problems have local radial
gradient singularities near re-entrant corners in the
g g
domain. The radial heat flux there is theoretically
infinite, but not in practice. Mesh refinement never
helps there
helps there.
Radius, r
u = r
p
f(θ)
∂u/∂r = r
(p-1)
f(θ)
Strength, p = π/C Corner: p = 2/3, weak
Crack: p = 1/2 strong
Re-entrant, C
Crack: p 1/2, strong
∂u/∂r ⇒ ∞ as r ⇒ 0

Local Heat Flux Error
Local Heat Flux Error
• The thermal error at a (non-singular)
i i h d f h l i
point is the product of the element size,
h, the heat flux gradient, and a constant
d d h d i h d
dependent 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 fl
polynomials of degree p, while the heat flux
vectors are piecewise discontinuous
polynomials of degree (p 1) In SW p=2
polynomials of degree (p-1). In SW p=2.

• Plan local mesh size with engineering
j d b d i d h fl
judgment 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 Planes
y y y y
• Use symmetry planes for the maximum
Use 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 conditions
and apply new boundary conditions
(EBC or NBC) to account for the
removed material
removed material.

Symmetry (Anti-symmetry) Planes
• Requires symmetry of the geometry and
material properties.
p p
• Requires symmetry (anti-symmetry) of
the heat source terms
the heat source terms.
• Requires symmetry (anti-symmetry) of
the imposed temperatures
the imposed temperatures.

Symmetry, Anti-symmetry
Th l C diti
Thermal 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 1
Thermal Analysis Verification, 1
• Prepare initial estimates of the
Prepare initial estimates of the
temperatures, reaction flux, and heat
flux vectors
flux vectors.
• Eyeball check the temperature contours
and the heat flux vectors
and the heat flux vectors.
• Temperature contours should be
di l i l d b d
perpendicular to an insulated boundary.

Th l A l i V ifi ti 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

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

FEA_Thermal_Intro.pdf

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