Isoflux Nusselt Number and Slip Length Formulae for Superhydrophobic Microchannels

We analytically and numerically consider the hydrodynamic and thermal transport behavior of fully developed laminar flow through a superhydrophobic (SH) parallel-plate channel. Hydrodynamic slip length, thermal slip length and heat flux are prescribed at each surface. We first develop a general expression for the Nusselt number valid for asymmetric velocity profiles. Next, we demonstrate that, in the limit of Stokes flow near the surface and an adiabatic and shear-free liquid-gas interface, both thermal and hydrodynamic slip lengths can be found by redefining existing solutions for conduction spreading resistances. Expressions for the thermal slip length for pillar and ridge surface topographies are determined. Comparison of fundamental half-space solutions for the Laplace and Stokes equations facilitate the development of expressions for hydrodynamic slip length over pillar-structured surfaces based on existing solutions for the conduction spreading resistance from an isothermal source. Numerical validation is performed and an analysis of the idealized thermal transport behavior suggests conditions under which superhydrophobic microchannels may enhance heat transfer.

我们从解析和数值两方面考虑了通过超疏水（SH）平行板通道的充分发展层流的流体动力学和热传输行为。在每个表面规定了流体动力滑移长度、热滑移长度和热通量。我们首先推导出了一个适用于非对称速度分布的努塞尔数的通用表达式。接下来，我们证明，在表面附近的斯托克斯流以及绝热且无剪切的液 - 气界面的极限情况下，通过重新定义现有的传导扩展热阻的解，可以得到热滑移长度和流体动力滑移长度。确定了柱体和脊状表面形貌的热滑移长度表达式。拉普拉斯方程和斯托克斯方程的基本半空间解的比较有助于基于等温源传导扩展热阻的现有解，推导出柱体结构表面的流体动力滑移长度表达式。进行了数值验证，并且对理想化热传输行为的分析表明了超疏水微通道可能增强热传递的条件。