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A novel solution for pressure drop in singly connected microchannels of arbitrary cross-section

机译：任意横截面的单连接微通道中压降的新解决方案

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摘要

This paper outlines a novel approximate solution for determining the pressure drop of fully developed, laminar, single-phase flow in singly connected microchannels of arbitrary cross-section. Using a "bottom-up" approach, it is shown that for constant fluid properties and flow rate in fixed cross-section channels, the Poiseuille number is only a function of geometrical parameters of the cross-section, i.e., perimeter, area, and polar moment of inertia. The proposed model is validated with experimental data for rectangular, trapezoidal, and triangular microchannels. The model is also compared against numerical results for a wide variety of channel cross-sections including: hyperellipse, trapezoid, sine, square duct with two adjacent round corners, rhombic, circular sector, circular segment, annular sector, rectangular with semi-circular ends, and moon-shaped channels. The model predicts the pressure drop for the cross-sections listed within 8% of the values published.
机译：本文概述了一种新颖的近似解决方案，用于确定任意横截面的单连接微通道中完全展开的层流单相流的压降。使用“自下而上”的方法表明，对于固定横截面通道中恒定的流体特性和流速，泊松叶数仅是横截面几何参数的函数，即周长，面积和极惯性矩。利用矩形，梯形和三角形微通道的实验数据验证了所提出的模型。还将模型与各种通道横截面的数值结果进行比较，包括：超椭圆形，梯形，正弦，带有两个相邻圆角的方管，菱形，圆形扇形，圆形扇形，环形扇形，带有半圆形端部的矩形和月亮形的通道。该模型预测列出的横截面的压降在已发布值的8％内。

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