Iterative direct solution method for thermal analysis of electronic equipment

The numerical procedure described in this work performs analysis of 3-dimensional structures by partitioning the geometry in basic blocks, which can be described as multi-layer-structures with rectangular base area. Combining such basic regions, complex geometries like stacked structures can be treated. The Laplacian equation describing the steady state heat flux is solved efficiently in three dimensions using a Fast Fourier Transform (FFT) algorithm. By the use of an iterative procedure handling of inhomogeneous, nonlinear boundary conditions on the top and bottom side of the geometry and modeling complex geometries by matching the solution at the interface of two or more basic blocks is possible. This allows to take into account boundary conditions calculated by the analytical solution of the Navier-Stokes equations describing convection and the Stefan Boltzmann law describing radiation. Experimental studies using infrared thermography, thermal sensors and laser doppler velocimetry were carried out. By measurement of the temperature distribution and the flow field it is shown, that the simultaneous solution of the heat flux in the solid structure and the heat-transfer by boundary approximation improves the accuracy of temperature computation and expands the application range of the Fourier method. It is shown, that parallel placed substrates with bare chips can be handled with high accuracy by the proposed model for laminar flow. The model gives good results for mountings up to 0.6 mm height. For low fluid velocities up to 1 m/s and natural convection the model works also for higher mountings (e.g. SMD). Further applications demonstrate the accuracy and applicability of the presented program. The simple model-creation and the numerical efficiency enables the handling of problems with a high number of components and high aspect ratios between the components and the board. Analytical models describing heat dissipation in special applications can be easily incorporated for simultaneous solution.<
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