Home / Examples / Thermal Analysis [Watt] / Example 29: Water Cooling (Temperature-Dependent Coefficient of Heat transfer)

Example 29: Water Cooling (Temperature-Dependent Coefficient of Heat transfer)

General

• A heat source is placed on a substrate, and there is a forced convection flow for water cooling in parallel to the substrate. The heat dissipation is analyzed under the steady-state condition.
   

• The coefficient of heat transfer for forced convection 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 are 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

Item	Settings
Solver	Thermal Analysis [Watt]
Analysis Type	Steady-state Analysis
Analysis Options	None

Model

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

The coefficients of heat transfer for forced convection on 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	008_Cu *
1/Solid	VOL2	001_Alumina *

* Available from the material DB

 

The heat quantity of VOL2 is set up as follows.

Body Attribute Name	Tab	Settings
VOL2	Heat Quantity	10 [W]

Boundary Condition

The coefficient of heat transfer for the forced convection by water is calculated as follows. For the details, please refer to the Coefficient of Heat Transfer for Forced Convection

To acquire it automatically, see [Ex.1: Air Cooling of Chips on Substrate (Forced Convection)].
 

h = 3.86 × (V/L)0.5 × C × Ctype [W/m2/deg]

 

where

Flow velocity of water V=1 [m/s]

Top and Bottom Faces of Substrate (VOL1): Typical Length L = 0.05, C = 1, See [Coefficient of Heat Transfer for Forced Convection] for the value of Ctype.
Top Face of Heat Source (VOL2): Typical Length L = 0.02, L' = 0.015, C = 1 *, See above for the value of Ctype.

 

Calculating coefficients of heat transfer with values above gives the table below.

If [Smooth Interpolation] is selected in the [Edit Nonlinear Table] dialog box, the values interpolated by spline are used in calculation.

 

 

* Note

The thickness (δ) of the speed boundary layer at the edges of the heat source is given by

 

δ=0.0182 x (L’/V)0.5 = 2.3 [mm]

 

This is close enough to the thickness of the heat source, 2 [mm], so we set C=1.

 

・ Coefficient of Heat Transfer, h1, of Substrate (VOL1)

Temperature [deg]	h1 [W/m2/deg]
0	2955.4
10	3178.2
20	3385.1
30	3573.5
40	3739.6
50	3895.9
60	4029.8
70	4156.5
80	4270.6
90	4366.7
100	4463.5

 

・ Coefficient of Heat Transfer, h2, of Substrate (VOL2)

Temperature [deg]	h2 [W/m2/deg]
0	4672.9
10	5025.2
20	5352.3
30	5650.2
40	5912.9
50	6159.9
60	6371.7
70	6372.1
80	6752.4
90	6904.3
100	7057.5

 

 

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Settings
BC1/Face	Thermal	Heat Transfer/Convection	Coefficient of Heat Transfer: Enter the values from the h2 column of the table above Select [Temperature-Dependent] > [Smooth Interpolation] Room Temperature: 25 [deg]
BC2/Face	Thermal	Heat Transfer/Convection	Coefficient of Heat Transfer: Enter the values from the h1 column of the table above Select [Temperature-Dependent] > [Smooth Interpolation] Room Temperature: 25 [deg]

Results

The temperature distribution is shown below.

 

A cross section's temperature distribution is shown below.