Thermal properties of five-layer infinite plate structures with embedded heat sources

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Abstract
The analytical three-dimensional temperature solution of a five-layer anisotropic plate structure with infinite lateral boundaries and with embedded heat sources has been derived. By incorporating the method of images, this solution can be utilized to obtain the exact solution of a five-layer structure with rectangular lateral boundaries and with embedded heat sources. Consequently, this solution constitutes the most general analytical expression reported so far. The solution is in the form of a double Fourier integration. To carry out the integration effectively, the characteristics of the transformed temperature in the Fourier domain have been studied. Subsequently, an integration algorithm has been developed for the efficient numerical integration of the double Fourier inverse transform for temperature calculation. In comparison with the double Fourier series solution of rectangular structure, the solution reported here is not only much more computationally effective but also more general. Besides thermal problems, the solution also has important applications in electrostatics since the thermostatics share the same equations with electrostatics. Examples of electrostatic problems are multilayer stripline, and microstrip, multilevel interconnection of integrated circuits, and multilayer printed circuit boards.

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