3-DIMENSIONAL ANALYSIS OF A THERMAL DISSIPATION-SYSTEM WITH A RECTANGULAR DIAMOND HEAT SPREADER ON A SEMIINFINITE COPPER HEAT SINK

We consider the 3-D problem of conductive heat dissipation from a rect angular patch source of constant heat flux, through a finite rectangul ar parallelpiped heat spreader into a semi-infinite heat sink. Using t he Fourier analysis, we have developed a rigorous series solution to t his 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 recta ngular heat patch source on the thermal behavior of the system. The ma in results we have obtained ate: (1) the commonly-used assumption of i sothermal 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 te mperature occurs for square heat patches as a result of the minimum pe rimeter; (3) for the same thickness and cross-section area of the spre aders, circular systems can be used to predict an upper bound of therm al behaviors for the rectangular heat dissipation systems.