微通道内低马赫数气体的流动与换热特性理论研究

Theoretical Study on Flow and Heat Transfer Characteristics of Gas at Low Mach Number in Microchannels

微通道换热器由于换热系数高、质量小等优点,在微电子系统与航空航天等领域具有极大的应用价值,但截至目前人们对微通道内流体的流动与换热特性仍知之甚少。本文针对平行平板式微通道,在连续介质区、低马赫数以及粘性热可忽略的情形下,采用分离变量法导出并简化了均匀热流边界条件下变物性气体的二维层流流动与换热过程的控制方程,进而计算得到了气体速度、压力、温度在通道内的分布规律,上述计算结果与对原始控制方程进行高精度直接数值求解的结果之间具有较好的一致性。研究结果表明:当马赫数小于0.3时,微通道的尺寸效应使得任一横截面上变物性气体的流动和换热参数分布与常物性下的分布存在相似性,气体密度沿通道长度方向的变化不对摩擦系数和努塞尔数的沿程分布造成显著影响;在给定通道结构和进出口参数的情况下,通道内气体密度的减小和流速的增大不能提高对流换热系数,对流换热系数可通过经典理论予以计算;相比常规尺寸通道,微通道内气体的加速过程更加显著,粘性切应力对加速过程起主导作用,并随马赫数的增大而增大;摩擦损失是气体在微通道内损失的主要部分。相关工作可为微通道换热器设计与高马赫数下流动特征的研究提供参考。

Microchannel heat transfer exchangers have great application value in microelectronic systems,aerospace and other fields due to high heat transfer coefficient and small mass. However,little is known about the specific flow and heat transfer characteristics in microchannels. Assuming gas is in continuum zone with low Mach number and viscous heat can be ignored,this paper adopts the method of separation of variables to simplify the governing equations of the two-dimensional gas flow and heat transfer problem with variable properties in parallel plate microchannels within uniform heat flux in the laminar region. The distributions of velocity,pressure and temperature within the channel are figured out,and the above results are in good agreement with the results obtained by direct numerical solution of the original governing equations. The results show that the size-effect of the microchannel leads to the similarity between the distribution of flow and heat transfer parameters of variable properties gas at any cross section and that under normal physical properties,and the change of gas density along the channel does not affect the distribution of friction coefficient and Nusselt number along the channel. If the channel structure and inlet and outlet parameters are given,the convection heat transfer coefficient cannot be increased by the decrease of gas density and the increase of velocity in the channel,which can be calculated by classical theory. Compared with the conventional size channel,the gas acceleration process in the microchannel is more significant,and the viscous shear stress plays a dominant role in the acceleration process and is enhanced with the increase of Mach number;friction loss is the main part of gas loss in microchannels. This work can provide references for the design of microchannel heat exchangers and the study of flow characteristics at high Mach number.