Constructal Equivalent Thermal Resistance Minimization for Tau-Shaped Fin

With the aid of constructal theory and entransy theory, a Tau-shaped fin (TAUSF) is investigated in this paper, and the widths of the bend end and elemental fins are assumed to be different. The construct of the TAUSF is optimized by the minimum equivalent thermal resistance (ETR) obtained by entransy dissipation rate. The constraints of total enveloping volume and fin material volume are considered. The results show that in the specified range of width ratio, the twice minimum ETR of the TAUSF can be yielded by an optimal width ratio and an optimal length ratio. In addition, comparing the optimal performance of the TAUSF with the counterpart of a T-shaped fin, the former sacrifices a small amount of heat transfer performance and its stiffness increases due to its structure with the bend end. The optimal structure of the TAUSF yielded from ETR minimization is conspicuously different with the counterpart yielded from maximum thermal resistance minimization. Comparing the thermal performances of the two optimal constructs, the ETR of the former optimal construct is declined by 10.58%, whereas the maximum thermal resistance is augmented by 5.22%. The former optimal construct can lead to the uniformity of temperature gradient and the reduction in thermal stress, and can guide the engineering designs of practical fins.

Thermal Behavior of Nominally Flat Silicon-Based Heat Spreaders

Thermal characteristics for a horizontal heated chip mounted with three types of nominally flat silicon-based heat spreaders have been systematically investigated. They include the natural convective and radiative heat transfer from the top surface of the heat spreaders to the external ambient, external thermal resistance, and maximum overall thermal resistance. In the aspect of natural convection, an axisymmetric bowl-shaped profile of local Nusselt number is achieved, and the highest convective heat transfer performance occurs at the location near the rim of the heat spreader. The effect of surface roughness on both local and average natural convective heat transfer behaviors from nominally flat silicon-based spreader surfaces to the external ambient is not significant. Two new generalized correlations of local and average Nusselt numbers for various heat spreader surfaces are presented. The contributions of convection and radiation on the total heat dissipated from the top surface of the heat spreader to the ambient are about 72% and 28%, respectively. The effect of surface roughness on external thermal resistance for nominally flat silicon-based surfaces is not significant. The influence of the conductive thermal resistance within the silicon-based heat spreader on the maximum thermal resistance is not significant. The maximum thermal resistance is mainly dominated by external thermal resistance for flat nominally silicon-based heat spreaders.

Thermal Insulation Provided by Vertical, Annular, Air-Filled Cavities

Steady-state rates of heat transfer outwards across vertical air-filled annular cavities, with aspect ratios (i.e. height divided by annular gap) which ranged from 16·0 to 70·3, were measured for several pressures of the contained air between 10-3and 760 torr. The chosen temperature difference between the isothermal cylindrical walls ranged from 20 to 180 K. For constant values of the temperature difference the gaseous conductive, convective and radiative components of the heat leaks across the air gap to the outer cylindrical wall were distinguished and evaluated using a technique which employed the air pressure as the variable. Convection of the air ensued throughout the whole height of the cavity when the Rayleigh number attained a value of 1·6 × 104. The optimal separation for maximum thermal resistance greatly exceeded the 6 mm annular gap recommended for chimneys in British Standard 4076:1966 (1)‡.