Compact Thermal Model And Its Verification Of A Fractal Tree-like Microchannel Cooler With High Temperature Uniformity

Multiple chips arrays are the main-steam developmental tendency for microelectronicspackaging and devices. For microelectronics with multiple chip arrays, it is important toachieve temperature uniformity among the chips to guarantee consistency and stability oftheir performances, and their reliability. This paper investigated a fractal tree-likemicrochannel cooler for cooling multiple chips array. The fractal tree-like microchannelincreases convective heat transfer area at downstream gradually. The increasing heattransfer area could act as a compensation for worse heat transfer caused by heating fluid forthe downstream heat sources. Thus, the fractal tree-like microchannels are able to minimizetemperature gap among the heat sources located at upstream and downstream, even helpachieve temperature uniformity among those heat sources.A thermal analysis was done to find thermal paths of a fractal tree-like microchannelcooler unit subjected to three heat sources. Three thermal resistances networks were set upto model thermal performance of the separated three parts of the cooler. Thermalresistances in the networks were simplified and analyzed. Analytical expressions tocalculate the thermal resistances were obtained as well.Convective heat transfer in the fractal tree-like microchannel was analyzed bynumerical simulation. It is found that “entrance effect” exists at the inlet of each level offractal tree-like microchannel, and the flow in the microchannel was thermally developingflow. Based on the numerical simulation, proposed expressions, which could be used tocalculate local and average Nusselt number in rectangular straight microchannel, areapplied to model convective heat transfer in the fractal tree-like microchannel. According tothe analysis and verification of the expressions, a new fitted expression for calculatingaverage Nusselt number in rectangular straight microchannel was given.A micro-scale and a mini-scale fractal tree-like microchanenl cooler with hightemperature uniformity were designed based on the established thermal model. Numericalsimulation was conducted to verify the micro-scale fractal tree-like microchannel cooler.The average temperatures of the three heat sources, obtained by the simulation, were 45.51℃,45.74℃, and45.71℃, respectively. The results predicted by the thermal modelwere44.61℃,44.61℃, and45.37℃, respectively, which were close to the results obtainedby simulation. Moreover, both the results from the simulation and the thermal modelshowed good temperature uniformity among the heat sources. The temperature gap amongthe heat sources was less than1℃.An experiment was done to verify the design of millimeter scale fractal tree-likemicrochannel cooler. The cooler was tested under three groups of conditions, and it showedgood temperature uniformity at all the conditions. The maximum temperature gap amongthe three heat sources was1.7℃, but it was only0.7℃at the design condition. A parallelstraight microchannel cooler was also tested under the same three groups of conditions.There were high temperature gap among the heat sources on the parallel straightmicrochannel cooler. The minimum temperature gap was3℃while the maximum one was7.8℃.