Effect of Area Ratio on Thermal Spreading Resistance of a Cubic Heat Spreader
Thompson, S.M., & Ma, H. B. (2013). Effect of Area Ratio on Thermal Spreading Resistance of a Cubic Heat Spreader. ASME 2013 Summer Heat Transfer Conference. Minneapolis, MN: American Society of Mechanical Engineers.
A unique non-dimensional scheme has been employed to analytically find the steady-state temperature field within a cubic heat spreader of unity aspect-ratio undergoing centralized, uniform heat flux with square footprint. This ‘square-on-square’ boundary value problem was solved using method of Fourier expansion. The exact solution is presented and compared with similar published models in order to determine the current range of applicability. Plots of the maximum, excess temperature of the heat spreader for various Biot numbers, spreader thicknesses and a newly-defined ‘area ratio’ – the ratio of heater cross-sectional area to heat spreader cross-sectional area – are provided in detail. Plots providing the non-dimensional thermal spreading resistance are also provided. Based on a data fitting procedure, a simplistic equation is provided to allow for easy approximation for heat spreader thermal resistance for various low Biot number operating configurations (various area ratios/footprints and non-dimensional thicknesses). The proposed solution is advantageous for determining optimal heat spreading configurations with low Biot numbers – typical of many electronics packaging applications and especially heat spreaders of very high effective thermal conductivity (i.e. heat pipes).