Temperature-Dependent Heat Source (Transient Analysis)examples|products|Murata Software Co., Ltd.

Example17 Temperature-Dependent Heat Source (Transient Analysis)

General

  • The model is the same as Exercise 8: A heat source is placed on a substrate, and there is a forced air flow for cooling in parallel to the substrate. The heat radiation is analyzed under the transient condition.
    The heat source is temperature-dependent.
     

  • The heat transfer coefficient is acquired manually.
    To acquire it automatically, see “Ex.1 of Simple Fluid-Thermal Analysis”.
     

  • The temperature distribution and the heat flux vectors are solved.
     

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

 

Analysis Space

Item

Settings

Analysis Space

3D

Model unit

mm

 

Analysis Conditions

Item

Settings

Solvers

Thermal Analysis [Watt]

Analysis Type

Transient analysis

Options

N/A

 

The transient analysis is set up in transient tab as follows. The total number of steps is 20. The time step is 30 second.

Therefore, the temperature distributions for 600 seconds are solved.

Tab

Setting Item

Settings

Transient analysis

Table

Number

Calculation steps

Output steps

Time step [s]

1

20

1

30

 

Initial Temperature

25[deg]

Model

The same as Exercise 7. The material properties and the boundary conditions are the same as well.

The substrate (VOL1) and the heat source (VOL2) are created as solid body box, and the heat source is defined in the body attribute of VOL2.

The heat transfer coefficients for the top and bottom faces of the substrate and the top face of the heat source are calculated based on the simplified equation.

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

 

The heat source of VOL2 is set up as follows.

Body Attribute Name

Tab

Settings

VOL2

Heat Source

Heat density

Temperature Dependency: Yes

 

Heat source is specified by heat density in the analyses where temperature-dependent heating materials are involved.

On Exercise 8, we set 1[w] for the heat source of VOL2. As the volume of VOL2 is 800*10^-9[m^3], the heat density is equal to

1.25 x 10^6 [W/m^3].

This is the value for 25[deg], so

P(25) = 1.25 x 10^6 [W/m^3]

in the Arrhenius equation which is given by the following:

 

P(T) = 1.25 x 10^6 * exp(-0.15/(k*(T+273))) / exp (-0.15/(k*(25+273)))

 

where 0.15[eV] is the activation energy and k is the Boltzmann constant.

Body Attribute Name

Item

Settings

VOL2

Nonlinearity Table

Select “Smooth interpolation”

 

Temperature
[degC]

Heat Source
x10^6[W/m^3]

Temperature
[degC]

Heat Source
x10^6[W/m^3]

Temperature
[degC]

Heat Source
x10^6[W/m^3]

25

1.25

155

7.365383041

605

59.18105993

35

1.51094343

205

11.26925562

655

65.85048973

45

1.804711948

255

15.90794507

705

72.47585198

55

2.132370783

305

21.15582761

755

79.02738627

65

2.494768691

355

26.88623825

805

85.48214754

75

2.892545312

405

32.98193112

855

91.82276684

85

3.326141169

455

39.339762

905

98.03640656

95

3.795809582

505

45.87196227

955

104.1138907

105

4.301629871

555

52.5055812

1005

110.0489868

 

Heat density’s temperature plot is shown below.

Boundary Conditions

The heat transfer coefficients for the forced convection are calculated as follows. The equation is given in Exercise 8: Heat Radiation by Forced Convection (Transient Analysis).

For the details, please refer to the Heat Transfer Coefficient for Forced Convection

To acquire it automatically, see “Ex.1 of Simple Fluid-Thermal Analysis”.
 

Boundary Condition Name/Topology

Tab

Boundary Condition Type

Settings

BC1/Face

Thermal

Heat Transfer/Ambient Radiation

Heat transfer coefficient: 17.26[W/m2/deg]

Room Temperature : 25[deg]

BC2/Face

Thermal

Heat Transfer/Ambient Radiation

Heat transfer coefficient: 27.3[W/m2/deg]

Room Temperature : 25[deg]

Results

The temperature distributions for Exercise 8 (right figures) and this exercise (left figures) are shown below for the elapsed time of 60, 300 and 600 seconds.

The unit of the color scale is [deg].

At Minimum/Maximum Value on the Contour tab of [Graphics Setup], deselect “Automatic” and set 25 => 150.

There is almost no difference in 60 seconds.

However, it becomes obvious that the temperature increases much higher than Exercise 8 in 300 and 450 seconds.

In 60 seconds

In 300 seconds

 

In 450 seconds

 

 

The temperature vs. time is plotted below.