Port-based approach of complex distributed-parameter system models for analysis and simulation (PACDAS, STW-TWI.6012)

Linear, uncoupled heat conduction problem

The stationary temperature distribution does not always say much about the critical parts in the design and processes. However, not all FEM methods allow one to look at other aspects numerically. In the case of bond-graph modelling, the natural variables are the power flow and the energy distribution, or, in thermal language: the heat flow and the heat capacitance.

We analyzed a 3D system with heat generation and constant temperature outflow. The system is modelled as a network of capacitances to ground, connected by resistances. Unlike most electrical networks the input is a current source. There are 441740 nodes in the system and 1355682 links. The large system is also to test the convergence, and the limits to numerical processing.

The inflow is given by a distributed heat, or current, source. The stationary equations are solved with a directional iterative solver, and takes a couple of minutes on a 3.4 GHz pentium4, all the code is written by Norbert Ligterink as part of the STW-PACDAS project.

The temperature distribution in a cross section of the material. The high temperature, red areas, is where the heat is produced. The boundaries and the internal boundaries, at the black areas, is where the heat flows out of the system. The image is square, corresponding to one node per 2x2 pixels, but in the true geometry the width is about three times as large as the height. The small black rectangles are water channels, the large ones are air cavities.

The total heat flow in the system: |Vx| + |Vy| + |Vz|. This heat flow shows where the critical regions are, in particular in between the heat cells.