Air cooling of IC substrate
===================================

.. |SAMPLE_NAME| replace:: paswat_ex1

Using Femtet's simple fluid-thermal analysis solver,
we explain an example of searching for the substrate dimensions and its angle
that minimize the size of the substrate while keeping the maximum temperature of an IC chip on the substrate to a minimum.

.. note::

   Related example: :doc:`../wat_ex14/wat_ex14`


Sample File
--------------------
.. note::

   Keep the :download:`sample project<../_temporary_sample_files/paswat_ex1_parametric.femprj>`
   open in Femtet, and double-click on the :download:`sample code<../_temporary_sample_files/paswat_ex1_parametric.py>`
   to execute it.

.. note::

   For details on the FEM problem, please refer to FemtetHelp / Examples / Simple Fluid-Thermal Analysis / Example 1.


Analysis Model and Design Variables
------------------------------------

.. figure:: paswat_ex1_model.png
   :width: 450

   Appearance of the Model

============== ==================================
Variable Name  Description
============== ==================================
substrate_w    Width of the substrate
substrate_d    Depth of the substrate
rot            Rotation angle of the substrate
============== ==================================


Objective Function
-----------------------------

- Maximum temperature of the main chip (to minimize)
- Maximum temperature of the sub chip (to minimize)
- Occupied area on the substrate plane (to minimize)


Sample Code
---------------

.. literalinclude:: ../_temporary_sample_files/paswat_ex1_parametric.py
   :language: python
   :linenos:
   :caption: |SAMPLE_NAME| _parametric.py


Execution Result of the Sample Code
--------------------------------------------------

.. figure:: paswat_ex1_result.png
   :width: 450

   Execution result of |SAMPLE_NAME| _parametric.py. This is a pair plot with the combination of each objective function on the vertical axis and horizontal axis.


From this result, we can see the following:
   - MAINCHIP temperature and SUBCHIP temperature have a positive correlation.
   - Substrate size and CHIP temperature have a negative correlation and cannot be reduced at the same time.
   - Depending on the combination of design variables, there are conditions under which MAINCHIP and SUBCHIP temperatures can be further reduced even with the same substrate size.

In multi-objective optimization, a solution for which all objective function
values are far from the goal compared to other solutions (that is, there is
no reason to choose it) is called a **"dominated solution."**

On the other hand, the set of **"non-dominated solutions"** is called the **Pareto set**.

Pareto sets generally have tradeoffs. In parameter optimization for product design,
the Pareto set is determined by the rough design of the product and how variables are set.

Therefore, it is important for the designer to perform a rough design so that the entire
Pareto set approaches the target values of all objective functions.

Finally, select a solution from the Pareto set and reflect it in the design.


.. tip::

   In multi-objective optimization, it is possible that the optimization of objective functions may not be compatible. In such cases, the designer needs to select the appropriate design from among the trade-off solutions.


.. note::

   Since the physical reasons for these trade-offs cannot be derived from optimization algorithms, designers need to interpret the analysis results of Femtet.


.. note::

   Results may vary slightly depending on the versions of Femtet, PyFemtet, and the optimization engine it depends on.