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Three-Dimensional Analysis of a Thermal Dissipation System with a Rectangular Diamond Heat Spreader on a Semi-infinite Copper Heat Sink

We consider the 3-D problem of conductive heat dissipation from a rectangular patch source of constant heat flux, through a finite rectangular parallelepiped heat spreader into a semi-infinite heat sink. Using the Fourier analysis, we have developed a rigorous series solution to this 3-D boundary value problem. Considering the case of a diamond heat spreader with a copper heat sink, we have investigated the effects of the geometrical dimensions of the spreader and the shape of the rectangular heat patch source on the thermal behavior of the system. The main results we have obtained are: (1) the commonly-used assumption of isothermal spreader-sink interface is valid provided that the spreader thickness is relatively large compared with the heating-patch's length and width; (2) for a square heat spreader with a fixed area ratio of rectangular heat patch to the spreader's cross section, the maximum temperature occurs for square heat patches as a result of the minimum perimeter; (3) for the same thickness and cross-section area of the spreaders, circular systems can be used to predict an upper bound of thermal behaviors for the rectangular heat dissipation systems.