Effect of Evaporation and Condensation at Menisci on Apparent Thermal Slip

We semi-analytically capture the effects of evaporation and condensation at menisci on apparent thermal slip lengths for liquids suspended in the Cassie state on ridge-type structured surfaces using a conformal map and convolution. An isoflux boundary condition is prescribed at solid-liquid interfaces and a constant heat transfer coefficient or isothermal one at menisci. We assume that the gaps between ridges, where the vapor phase resides, are closed systems; therefore, the net rates of heat and mass transfer across menisci are zero. The reduction in apparent thermal slip length due to evaporation and condensation relative to the limiting case of an adiabatic meniscus as a function of solid fraction and interfacial heat transfer coefficient is quantified in a single plot. The semianalytical solution method is verified by numerical simulation. Results suggest that interfacial evaporation and condensation need to be considered in the design of microchannels lined with structured surfaces for direct liquid cooling of electronics applications and a quantitative means to do so is elucidated. The result is a decrease in thermal resistance relative to the predictions of existing analyses which neglect them.

我们使用共形映射和卷积，半解析地捕捉了弯月面上的蒸发和凝结对处于脊状结构化表面卡西状态的悬浮液体表观热滑移长度的影响。在固 - 液界面规定了等通量边界条件，在弯月面规定了恒定的传热系数或等温条件。我们假设气相所在的脊之间的间隙是封闭系统；因此，穿过弯月面的热量和质量净传递速率为零。在单个图中量化了由于蒸发和凝结相对于绝热弯月面极限情况，表观热滑移长度随固体分数和界面传热系数的变化而减少的情况。通过数值模拟验证了半解析求解方法。结果表明，在为电子应用的直接液体冷却设计带有结构化表面的微通道时，需要考虑界面蒸发和凝结，并阐明了一种定量方法。结果是相对于忽略它们的现有分析预测，热阻降低。