A unique non-dimensional scheme has been employed to analytically determine 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. Plots of the heat spreader non-dimensional maximum temperature and non-dimensional thermal spreading resistance are provided for various Biot numbers, heat spreader thicknesses and a newly-defined ‘area ratio’ — the ratio of heater cross-sectional area to heat spreader cross-sectional area (i.e. footprint). The proposed solution is advantageous for determining optimal heat spreading configurations with low Biot numbers — typical of many electronics packaging applications and heat spreaders of very high effective thermal conductivity. The presented results indicate that the non-dimensional, maximum temperature increases as the area ratio decreases and that a limiting, non-dimensional thermal spreading resistance exists for relatively thick heat spreaders regardless of area ratio or Biot number. A critical, non-dimensional thickness was also found in which the non-dimensional, maximum temperature becomes near unity regardless of Biot number or area ratio.
- Heat Transfer Division
Effect of Area Ratio on Thermal Spreading Resistance of a Cubic Heat Spreader
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Thompson, SM, & Ma, H. "Effect of Area Ratio on Thermal Spreading Resistance of a Cubic Heat Spreader." Proceedings of the ASME 2013 Heat Transfer Summer Conference collocated with the ASME 2013 7th International Conference on Energy Sustainability and the ASME 2013 11th International Conference on Fuel Cell Science, Engineering and Technology. Volume 3: Gas Turbine Heat Transfer; Transport Phenomena in Materials Processing and Manufacturing; Heat Transfer in Electronic Equipment; Symposium in Honor of Professor Richard Goldstein; Symposium in Honor of Prof. Spalding; Symposium in Honor of Prof. Arthur E. Bergles. Minneapolis, Minnesota, USA. July 14–19, 2013. V003T10A018. ASME. https://doi.org/10.1115/HT2013-17321
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