Exact series solutions for three-dimensional temperature distribution in two-layer bodies subject to various types of boundary conditions are presented. Special consideration is given to the case when one layer is a thin diamond film. The computation emphasizes the temperature effect of an embedded thin heat source of the type used in electronic devices. The mathematical formulation employs the Green’s function solution method. The solution is time partitioned in order to achieve a high degree of accuracy. Time partitioning greatly improves the convergence of three-dimensional heat conduction solutions. Time-partitioned series solutions with a reduced number of terms yield highly accurate temperature data. A two-layer model is chosen for simplicity of presentation; however, the method can be extended to more than two layers.
Thermal Characteristics of Two-Layered Bodies With Embedded Thin-Film Heat Source
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Yan, L., Haji-Sheikh, A., and Beck, J. V. (September 1, 1993). "Thermal Characteristics of Two-Layered Bodies With Embedded Thin-Film Heat Source." ASME. J. Electron. Packag. September 1993; 115(3): 276–283. https://doi.org/10.1115/1.2909329
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