Home / Examples / Coupled Analysis / Thermal-Stress Analysis [Watt/Galileo] / Example 2: Deformation due to the Temperature Gradient #2 - Multiple Materials

Example 2: Deformation due to the Temperature Gradient #2 - Multiple Materials

General

• A heat source is placed on a substrate to cause a temperature gradient. The temperature distribution is calculated using the thermal analysis with
  forced air flow cooling taken into account. The resulting thermal expansion is analyzed by the stress analysis.
   

• The temperature distribution is calculated using the thermal analysis [Watt].
  The result is forwarded to the stress analysis [Galileo] as a thermal load corresponding to the reached temperature.
   

• The deformation, the displacement and the stress are solved.
   

• Unless specified in the list below, the default conditions will be applied.
   

• Obtain this session's project file. (Right-click and choose 'Save link as')




• Results will vary depending on Femtet version and the PC environment.

 

Analysis Space

Item	Settings
Analysis Space	3D
Model Unit	mm

 

Analysis Conditions

The coupled analysis of the thermal analysis [Watt] and the stress analysis [Galileo] is performed.

Item	Settings
Solver	Thermal Analysis [Watt] Stress Analysis [Galileo]
Thermal-Analysis Type	Steady-State Analysis
Options	N/A *

* [Thermal Load] is selected by default for the thermal-stress coupled analysis.

 

The Step/Thermal Load tab is set as follows.

Tab	Setting Item	Settings
Step/Thermal Load *	Reference Temperature	25 [deg]

* The reached temperatures come from the thermal analysis.

Model

The same as example 7 of thermal analysis.

 

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
0/Solid	VOL1	006_Glass_epoxy *
1/Solid	VOL2	001_Alumina *

* Available from the material DB

Boundary Conditions

The coefficient of heat transfer for the forced convection is calculated as follows.

 

h = 3.86 x (V/L)0.5xC [W/m2/deg]

 

where

Air flow V=1 [m/s]

Top and Bottom Faces of VOL1: Typical Length L =0.05, C=1 -> h=17.26
Top Face of VOL2: Typical Length L=0.02, L'=0.015, C=1 * -> h=27.3

 

*

The thickness (d) of the speed boundary layer at the edges of the heat source is calculated as follows

 

δ = 0.0182 x (L’/V)0.5= 2.3 [mm]

 

This is close enough to the thickness of heat source, so we set C=1.

 

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Settings
BC1/Face	Thermal	Heat Transfer/Convection	Coefficient of Heat Transfer: 17.26 [W/m2/deg] Ambient Temperature: 25 [deg]
BC2/Face	Thermal	Heat Transfer/Convection	Coefficient of Heat Transfer: 27.3 [W/m2/deg] Ambient Temperature: 25 [deg]

 

Thermal analysis is performed based on the boundary conditions below. The resulting temperature distribution is forwarded to stress analysis.

Results

The temperature distribution as a result of Watt is shown below.

 

The next figure shows the vectors of displacement as a result of Galileo following Watt.

The temperature gradient results in deformation, warping at the four corners of the substrate.