A unique nondimensional scheme that employs a source-to-substrate “area ratio” (e.g., footprint), has been utilized for analytically determining the steady-state temperature field within a centrally-heated, cuboidal heat spreader with square cross-section. A modified Laplace equation was solved using a Fourier expansion method providing for an infinite cosine series solution. This solution can be used to analyze the effects of Biot number, heat spreader thickness, and area ratio on the heat spreader's nondimensional maximum temperature and nondimensional thermal spreading resistance. The solution is accurate only for low Biot numbers (Bi < 0.001); representative of highly-conductive, two-phase heat spreaders. Based on the solution, a unique method for estimating the effective thermal conductivity of a two-phase heat spreader is also presented.

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