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Heat Transfer Handbook part 98

Heat Transfer Handbook part 98. The Heat Transfer Handbook provides succinct hard data, formulas, and specifications for the critical aspects of heat transfer, offering a reliable, hands-on resource for solving day-to-day issues across a variety of applications. | 966 HEAT TRANSFER IN ELECTRONIC EQUIPMENT suggested that when the grouping NT fy where N is the number of atomic layers in the thin film T the temperature and the Debye temperature is less than unity the heat capacity can be expected to display sensitivity to the characteristic dimension. Their results show that such size effects on the thermodynamic properties are more important at cryogenic temperatures. 13.3.1 Spreading Resistance In chip packages that provide for lateral spreading of the heat generated in the chip the increasing cross-sectional area for heat flow in the layers adjacent to the chip reduces the heat flux in successive layers and hence the internal thermal resistance. Unfortunately however there is an additional resistance associated with this lateral flow of heat which must be taken into account in determination of the overall chip package temperature difference. The temperature difference across each layer of such a structure can be expressed as AT qR-T where RT R1D Rsp or Rt kA R 13.19 13.20 13.21 For the circular and square geometries common in microelectronic applications Negus et al. 1989 provide an engineering approximation for the spreading resistance Rsp of a small heat source on a thick substrate or heat spreader insulated on the sides and held at a fixed temperature along the base as _ 0.475 - 0.626 0.13 3 Rsp J 13.22 fcs a where Z is the square root of the heat source area divided by the substrate area k the thermal conductivity of the substrate and a the area of the heat source. The spreading resistance Rsp from eq. 13.22 can now be added to the onedimensional conduction resistance to yield the overall thermal resistance of that layer. It is to be noted that the use of eq. 13.22 requires that the substrate be three to five times thicker than the square root of the heat source area. Consequently for relatively thin layers on thicker substrates such as thin lead frames or heat spreaders interposed between the chip and the substrate eq.