非均匀产热“盘-点”导热构形设计

Constructal Design for Nonuniform Heat Generating "Disc-point" Heat Conduction

建立非均匀产热“盘-点”导热模型,以[火积]耗散率最小为目标,分别对辐射状圆盘、恒截面高导热通道树状圆盘和变截面高导热通道树状圆盘进行构形优化,在不同产热分布条件下得到圆盘产热体的最优构形,分析非均匀产热系数和宽度系数等参数对构形优化结果的影响。结果表明:对于恒截面高导热通道树状圆盘,在总产热量恒定的情况下,靠近冷源位置处产热量越大,茎趋向于粗长,而分支趋向于细短,即产热量相对较大的区域布置较多的高导热材料可降低产热体[火积]耗散率,降低传热的等效温差,并提高树状圆盘导热性能。当树状圆盘内包含的单元体数目小于9时,树状圆盘有简化为辐射状圆盘的趋势;当圆盘产热体包含20个单元体时,辐射状圆盘单元体内无量纲[火积]耗散率为0.00369;恒截面高导热通道树状圆盘单元体内二次最小无量纲[火积]耗散率为0.00329;而变截面高导热通道树状圆盘单元体内三次最小无量纲[火积]耗散率为0.00328,因此采用变截面高导热通道树状结构可进一步降低产热体内的[火积]耗散,提升其导热性能。所得优化结果可为电子器件的散热优化设计提供理论指导。

This paper reports a "disc-point" heat conduction model which featuring the nonuniform heat generating characteristic.With the index of minimizing the entransy dissipation rate,constructal optimizations are performed for radial-pattern disc and tree-shaped discs with constant and variable cross-sectional high conductivity channels,respectively.For a variety of heat generation distributions,the optimal constructs of discal heat generating area are obtained,and then the impacts of nonuniform heat generating coefficient and width coefficient over the optimized results are analyzed in detail.The results obtained show that for the tree-shaped disc with constant cross-sectional highly conductive channels and with the fixed total heat generation,the highly conductive stems tend to be thicker and longer while the branches grow thinner and shorter when it comes to that more heat is generated near the heat sink.In other words,the high conductivity material can be distributed in the region where the heat is comparably concentrated as part efforts to decrease the entransy dissipation rate,lower the equivalent average temperature difference and enhance the heat transfer performance.Meanwhile,the tree-shaped disc has a tendency to be degraded into radial-pattern disc when the entire fundamental elements involved in the disc count less than 9.As the disc area is composed of 20 fundamental elements,the relative dimensionless entransy dissipation rates of a singular element divested from radial-pattern disc,tree-shaped disc with constant cross-sectional highly conductive channels and tree-shaped disc with variable cross-sectional highly conductive channels are respectively 0.00369,0.00329 and 0.00328.Apparently,applying the tree-shaped stratagem with variable cross-sectional highly conductive channels can further decline the entransy dissipation rate and improve the thermal performance.The results obtained herein can offer theoretical indications in the thermal design for electronics.