Abstract
Heat sources on rectangular plates with double-sided convective cooling are a common application of heat transfer in electronic packaging. However, it is considerably difficult to obtain analytical solutions for improving thermal performance because of the mixed boundary conditions on a plate’s upper surface. In this study, mixed boundary conditions were adjusted twice. Based on the method of separation of variables, a new analytical model was established and used to calculate the thermal performance of a random application case, including temperature distribution, thermal spreading resistance, and total thermal resistance. The results indicated that accurate analytical solutions can be obtained with few computing resources when more than 30 terms are used in each of single and double summations with a total mesh number of 196 in the heat source region. Subsequently, a series of thermal performances were calculated for random application cases and simulations were also conducted using the commercial software Icepak to offer a reference. The data comparisons revealed that the analytical model is able to calculate the temperature values at arbitrary point coordinates accurately over wide ranges of a plate’s thermal conductivity and heat transfer coefficient.
Highlights
Based on the rapid development of semiconductor technology, electronic devices exhibit a trend towards miniaturisation and their electronic functions are increasing daily
The similar heat transfer structure, in which hot devices are clearly smaller than cooling plates, is applied widely in chips or devices mounted on heat spreader6,7 or broad printed circuit board (PCB)
In this paper, based on two necessary adjustments for the mixed boundary conditions on a plate’s upper surface, a new analytical model of thermal performance was established for the case of eccentric heat source on a rectangular plate with double-sided convective cooling
Summary
Scitation.org/journal/adv thermal spreading resistance. Thermal spreading resistance can cause a nonuniform temperature distribution in the cooling plate, and the maximal temperature increases in according with an increasing ratio of the cooling plate area to that of the heat source. Kabir et al. presented a new solution model for the common heat spreading problem from a uniform circular heat source to a finite cooling plate with convective cooling on both upper and lower surfaces The utility of this model was demonstrated by applying it to a compact thermal model of a BGA package. The data comparisons between COMSOL software simulations and analytical solutions indicate the validity of the proposed analytical model These studies are all based on the thermal resistances network method, and the calculated results are only the mean values of temperature distribution and thermal spreading resistance; the maximal temperature might have been underestimated. In this paper, based on two necessary adjustments for the mixed boundary conditions on a plate’s upper surface, a new analytical model of thermal performance was established for the case of eccentric heat source on a rectangular plate with double-sided convective cooling. The data comparisons demonstrated that the mean relative errors were all considerably low over wide ranges of a plate’s thermal conductivity and heat transfer coefficient, and the proposed analytical model provides accurate results
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