Heat Sink

This example is intended as a first introduction to simulations of fluid flow and conjugate heat transfer. It shows the following important points:

•

How to draw an air box around a device in order to model convective cooling in this box.

•

How to set a total heat flux on a boundary using automatic area computation.

•

How to display results in an efficient way using selections in data sets.

The application is also described in detail in the book Introduction to the Heat Transfer Module. An extension of the application that takes surface-to-surface radiation into account is also available; see Heat Sink with Surface-to-Surface Radiation.

Figure 1: The application setup including channel and heat sink.

Model Definition

The modeled system consists of an aluminum heat sink for cooling of components in electronic circuits mounted inside a channel of rectangular cross section (see Figure 1).

Such a setup is used to measure the cooling capacity of heat sinks. Air enters the channel at the inlet and exits the channel at the outlet. The base surface of the heat sink receives a 1 W heat flux from an external heat source. All other external faces are thermally insulated.

The cooling capacity of the heat sink can be determined by monitoring the temperature of the base surface of the heat sink.

The model solves a thermal balance for the heat sink and the air flowing in the rectangular channel. Thermal energy is transported through conduction in the aluminum heat sink and through conduction and convection in the cooling air. The temperature field is continuous across the internal surfaces between the heat sink and the air in the channel. The temperature is set at the inlet of the channel. The base of the heat sink receives a 1 W heat flux. The transport of thermal energy at the outlet is dominated by convection.

The flow field is obtained by solving one momentum balance for each space coordinate (x, y, and z) and a mass balance. The inlet velocity is defined by a parabolic velocity profile for fully developed laminar flow. At the outlet, the normal stress is equal the outlet pressure and the tangential stress is canceled. At all solid surfaces, the velocity is set to zero in all three spatial directions.

The thermal conductivity of air, the heat capacity of air, and the air density are all temperature-dependent material properties.

You can find all of the settings mentioned above in the predefined multiphysics coupling for Conjugate Heat Transfer in COMSOL Multiphysics. You also find the material properties, including their temperature dependence, in the Material Browser.

Results

In Figure 2, the hot wake behind the heat sink visible in the plot is a sign of the convective cooling effects. The maximum temperature, reached at the heat sink base, is about 380 K.

Figure 2: The surface plot shows the temperature field on the channel walls and the heat sink surface, while the arrow plot shows the flow velocity field around the heat sink.

Heat_Transfer_Module/Tutorials,_Forced_and_Natural_Convection/heat_sink

Modeling Instructions

From the menu, choose .

New

In the window, click .

Model Wizard

In the window, click .

In the tree, select .

Click .

In the tree, select .

Click .

Geometry 1

Note that the must be set to to fit with the numbering of the boundaries used in these instructions.

The model geometry is available as a parameterized geometry sequence in a separate MPH-file. If you want to create it from scratch yourself, you can follow the instructions in the Geometry Modeling Instructions section. Otherwise, insert the geometry sequence as follows:

On the toolbar, click .

Browse to the model’s Application Libraries folder and double-click the file heat_sink_geom_sequence.mph.

The application’s Application Library folder is shown in the section immediately before the current section. Note that the path given there is relative to the COMSOL Application Library root, which for a standard installation on Windows is C:\Program Files\COMSOL\COMSOL53\Multiphysics\applications.

Rotate 1 (rot1)

In the window, under click .

In the window for , click .

Work Plane 2 (wp2)

In the window, expand the node.

Convert to Solid 1 (csol1)

In the window, expand the node, then click .

In the window for , click .

Delete Entities 1 (del1)

In the window, under click .

In the window for , locate the section.

In the tree, select .

On the object , select Domains 1–5 and 7–9 only.

In the window, click .

On the toolbar, click .

Click the button on the toolbar.

To facilitate face selection in the next steps, use the option (skip this step if you followed the instructions in the appendix):

Click the button on the toolbar.

Laminar Flow (spf)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Heat Transfer (ht)

On the toolbar, click and choose .

Fluid 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Materials

Next, add materials.

Add Material

On the toolbar, click to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

Materials

Air (mat1)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Add Material

Go to the window.

In the tree, select .

Click in the window toolbar.

Materials

Aluminum 3003-H18 (mat2)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Add Material

Go to the window.

In the tree, select .

Click in the window toolbar.

Materials

Silica glass (mat3)

In the window, under click .

In the window for , locate the section.

From the list, choose .

On the toolbar, click to close the window.

Global Definitions

Parameters

In the window, expand the node, then click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
U0	5[cm/s]	0.05 m/s	Mean inlet velocity
P0	1[W]	1 W	Total power dissipated by the electronics package

Now define the physical properties of the model. Start with the fluid domain.

Laminar Flow (spf)

On the toolbar, click and choose .

The no-slip condition is the default boundary condition for the fluid. Define the inlet and outlet conditions as described below.

In the window, under click .

Inlet 1

On the toolbar, click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Locate the section. In the Uav text field, type U0.

Outlet 1

On the toolbar, click and choose .

Click the button on the toolbar.

In the window for , locate the section.

From the list, choose .

Heat Transfer (ht)

Thermal insulation is the default boundary condition for the temperature. Define the inlet temperature and the outlet condition as described below.

In the window, under click .

Temperature 1

On the toolbar, click and choose .

In the window for , locate the section.

From the list, choose .

The ambient temperature is defined in the main node of the Heat Transfer interface. Its default value is 293.15 K which corresponds to the inlet temperature used in this model. It is possible to edit the ambient temperature value or to define it using the meteorological data which gives access to climate data from more than 6000 stations in the world.

Locate the section. From the T0 list, choose .

Outflow 1

On the toolbar, click and choose .

In the window for , locate the section.

From the list, choose .

Next, use the P0 parameter to define the total heat source in the electronics package.

Heat Source 1

On the toolbar, click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. Click the button.

In the P0 text field, type P0.

Mesh 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Click .

To get a better view of the mesh, hide some of the boundaries.

Click the button on the toolbar.

Select Boundaries 1, 2, and 4 only.

The finished mesh should look like that in the figure below.

To achieve more accurate numerical results, this mesh can be refined by choosing another predefined element size. However, doing so requires more computational time and memory.

Study 1

On the toolbar, click .

Results

Temperature (ht)

Four default plots are generated automatically. The first one shows the temperature on the wall boundaries, the third one shows the velocity magnitude on five parallel slices, and the last one shows the pressure field. Add an arrow plot to visualize the velocity field with temperature field.

In the window, under click .

On the toolbar, click .

Arrow Volume 1

In the window, under click .

In the window for , click in the upper-right corner of the section. From the menu, choose .

Locate the section. Find the subsection. In the text field, type 40.

Find the subsection. In the text field, type 20.

Find the subsection. From the list, choose .

In the text field, type 5[mm].

Color Expression 1

On the toolbar, click .

In the window for , click in the upper-right corner of the section. From the menu, choose .

On the toolbar, click .

Global Evaluation 1

On the toolbar, click .

In the window for , type Energy Balance in the text field.

Click in the upper-right corner of the section. From the menu, choose .

Click .

Table

Go to the window.

You can verify that the two values match and are close to 1 W in the tab.

Geometry Modeling Instructions

If you wish to create the geometry yourself, follow these steps.

Root

Parameters

On the toolbar, click .

Global Definitions

Parameters

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
L_channel	7[cm]	0.07 m	Channel length
W_channel	3[cm]	0.03 m	Channel width
H_channel	1.5[cm]	0.015 m	Channel height
L_chip	1.5[cm]	0.015 m	Chip size
H_chip	2[mm]	0.002 m	Chip height