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首页> 外文期刊>International Journal of Heat and Mass Transfer >Heat and mass transfer in polygonal micro heat pipes under small imposed temperature differences
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Heat and mass transfer in polygonal micro heat pipes under small imposed temperature differences

机译：在很小的温差下，多边形微型热管中的传热和传质

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Micro heat pipes have been used to cool microelectronic devices, but their heat transfer coefficients are low compared with those of conventional heat pipes. We model heat and mass transfer in triangular, square, hexagonal, and rectangular micro heat pipes under small imposed temperature differences. A micro heat pipe is a closed microchannel filled with a wetting liquid and a long vapor bubble. When a temperature difference is applied across a micro heat pipe, the equilibrium vapor pressure at the hot end is higher than that at the cold end, and the difference drives a vapor flow. As the vapor moves, the vapor pressure at the hot end drops below the saturation pressure. This pressure drop induces continuous evaporation from the interface. We solve for the evaporation rate in the limit the evaporation number E → ∞, and find that the liquid evaporates mainly in a boundary layer at the contact line. An analytic solution is obtained for the leading-order evaporation rate. Since the pipe is slender and the imposed temperature difference small, the heat and mass transfer along the pipe is skew-symmetric about the mid point of the pipe. Hence, we only need to focus on the heated half of the pipe. Furthermore, because the pipe and bubble are long, the coupled vapor and liquid flows along the pipe are predominantly uni-directional, and the heat transfer by vapor flow and by conduction in the liquid and wall are essentially one-dimensional. Thus, we find analytic solutions for the temperature profile and vapor and liquid pressure distributions along the pipe. Two dimensionless numbers emerge from the momentum and energy equations: the heat-pipe number, H, which is the ratio of heat transfer by vapor flow to conductive heat transfer in the liquid and pipe wall, and the evaporation exponent S, which controls the evaporation gradient along the pipe. In the limit H → 0 or S → 0, conduction in the liquid and wall dominates. When H → ∞ and S → ∞, vapor-flow heat transfer dominates and a thermal boundary layer appears at the hot end, the thickness of which scales as S~(-1)L, where L is the half-length of the pipe. A similar boundary layer exists at the cold end. Outside the boundary layers, the temperature is uniform. These regions correspond to the evaporating, adiabatic, and condensing regions commonly observed in conventional heat pipes and are absent in most micro heat pipes leading to their low heat transfer coefficients. We also find a dimensionless optimal pipe length S_m=S_m(H) for maximum evaporative heat transfer. Thus, our model suggests that micro heat pipes should be designed with H ＞＞1 and S = S_m. We calculate H and S for four published micro-heat-pipe experiments, and find encouraging support for our design criterion.
机译：微型热管已经用于冷却微电子器件，但是与传统的热管相比，它们的传热系数较低。我们在施加小的温差的情况下，对三角形，正方形，六角形和矩形微型热管中的传热和传质建模。微型热管是一个封闭的微通道，里面充满了润湿液和长气泡。当在微型热管上施加温差时，热端的平衡蒸气压高于冷端的平衡蒸气压，并且该差驱动蒸汽流动。随着蒸气的移动，热端的蒸气压下降到饱和压力以下。该压降引起从界面的连续蒸发。我们在极限蒸发量E→∞的条件下求解蒸发速率，发现液体主要在接触线的边界层蒸发。获得了前导蒸发速率的解析解。由于管道细长且施加的温度差较小，因此沿管道的热量和质量传递围绕管道的中点倾斜对称。因此，我们只需要关注管道的加热部分。此外，由于管道和气泡较长，因此沿着管道的耦合的蒸气和液体流动主要是单向的，并且由蒸气流动以及在液体和壁中的传导引起的热传递基本上是一维的。因此，我们找到了沿管道温度分布以及蒸汽和液体压力分布的解析解。动量和能量方程式产生了两个无量纲数：热管数H，即通过蒸汽流动的热传递与液体和管壁中的传导性热传递的比率，以及蒸发指数S，其控制蒸发沿管道渐变。在极限H→0或S→0中，液体和壁中的传导占主导。当H→∞和S→∞时，蒸汽流传热占主导，热边界出现热边界层，其厚度缩放为S〜（-1）L，其中L是管道的半长。在冷端存在类似的边界层。在边界层之外，温度是均匀的。这些区域对应于常规热管中通常观察到的蒸发，绝热和冷凝区域，并且在大多数微型热管中不存在，导致它们的传热系数低。我们还找到了无量纲的最佳管道长度S_m = S_m（H），以实现最大的蒸发热传递。因此，我们的模型建议将微型热管设计为H ＞＞ 1且S = S_m。我们为四个已发布的微型热管实验计算了H和S，并为我们的设计标准提供了令人鼓舞的支持。

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