Natural Convection with Correction Coefficient Manually Calculatedexamples|products|Murata Software Co., Ltd.

Example10 Natural Convection with Correction Coefficient Manually Calculated

General

  • Two heat sources are placed on a substrate. Some heat is conducted to the bottom of the substrate through via holes.
    The heat is released to the ambient by natural convection. The steady-state analysis is performed.
     

  • 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

Steady-state analysis

Options

N/A

Model

Body Attributes and Materials

The finer mesh size is set for via holes (HOLE), where the heat flux is expected to change drastically.

Body Number/Type

Body Attribute Name

Material Name

Mesh Size

0/Solid

SUB

006_Glass_epoxy *

 

1/Solid

GND

008_Cu *

 

2/Solid

MAINCHIP

001_Alumina *

 

3/Solid

SUBCHIP

001_Alumina *

 

4/Solid

HOLE

008_Cu *

0.5

5/Solid

HOLE

008_Cu *

0.5

6/Solid

HOLE

008_Cu *

0.5

7/Solid

HOLE

008_Cu *

0.5

8/Solid

HOLE

008_Cu *

0.5

9/Solid

HOLE

008_Cu *

0.5

10/Solid

HOLE

008_Cu *

0.5

11/Solid

HOLE

008_Cu *

0.5

* Available from the Material DB

 

The heat sources of MAINCHIP and SUBCHIP are set up as follows.

Body Attribute Name

Tab

Settings

MAINCHIP

Heat Source

0.2[W]

SUBCHIP

Heat Source

0.1[W]

Boundary Condition

It is assumed that the heat is released to the ambient only from the top and bottom faces of the model. The heat released from the side faces is ignored because the total area of the side faces is much smaller than that of the top and bottom faces.

Boundary Condition Name/Topology

Tab

Boundary Condition Type

Settings

Bottom/Face

Thermal

Heat Transfer/Ambient Radiation

Coefficient for natural convection (*1) : 1.39[W/m2/deg5/4]

Room Temperature : 25[deg]

TOP/Face

Thermal

Heat Transfer/Ambient Radiation

Coefficient for natural convection (*2) : 2.78[W/m2/deg5/4]

Room Temperature : 25[deg]

MAINCHIPUPPER/Face

Thermal

Heat Transfer/Ambient Radiation

Coefficient for natural convection (*3) : 6.41[W/m2/deg5/4]

Room Temperature : 25[deg]

SUBCHIPUPPER/Face

Thermal

Heat Transfer/Ambient Radiation

Coefficient for natural convection (*4) : 7.62[W/m2/deg5/4]

Room Temperature : 25[deg]

 

The formulas to calculate the coefficients(*1-4) for natural convection are shown below. See [Heat Transfer/Ambient Radiation] for more information.

 

(*1) BOTTOM

2.51×C×(1/L)^(1/4) = 1.39 [W/m2/deg5/4]

where

C = 0.26

Size of the substrate : 0.06×0.04

L (Typical Length) = (0.06 x 0.04 x 2) / (0.06 + 0.04) = 0.048

 

(*2) TOP

2.51×C×(1/L)^(1/4) = 2.78 [W/m2/deg5/4]

where

C = 0.52

Size of the substrate : 0.06×0.04

L (Typical Length) = (0.06 x 0.04 x 2) / (0.06 + 0.04) = 0.048

 

(*3) MAINCHIPUPPER

2.51×C×(1/L)^(1/4) = 6.41 [W/m2/deg5/4]

where

C = 0.96

Size of the chip : 0.02×0.02

L (Typical Length) = (0.02 x 0.02 x 2) / (0.02 + 0.02) = 0.02

 

(*4) SUBCHIPUPPER

2.51×C×(1/L)^(1/4) = 7.62 [W/m2/deg5/4]

where

C = 0.96

Size of the chip : 0.01×0.01

L (Typical Length) = (0.01 x 0.01 x 2) / (0.01 + 0.01) = 0.01

 

Results

The temperature distribution is shown below.


MAINCHIP has the highest temperature in this model.

 

The vectors of the heat flux are shown below.

The heat is well transfered through the via holes.