恒热流边界条件下流体横掠多孔介质中平板的边界层分析

Boundary analysis of fluid′s forced flow over a plate in a porous medium under the condition of constant heat flux

基于Brinkman-Forchheimer-extended Darcy流动模型,对恒热流条件下流体横掠多孔介质中平板的强制对流进行了边界层分析。通过建立二维流动的连续方程、动量方程和考虑流体与多孔介质局部非热平衡时的能量方程,应用数量级分析和积分的方法对方程组进行简化和求解,得出了流体的速度分布、温度分布、速度边界层和温度边界层的厚度、对流传热的理论关联式。研究结果表明:恒热流条件下流体横掠多孔介质中平板的速度边界层与光板时完全不同,其在平板前端迅速增长,随后沿着流动方向变得非常平坦并趋于一定值;而温度边界层的厚度发展则与光板时类似,沿着流动方向不断增长,且与壁面处热流密度的大小无关。

In this paper, the boundary of forced convection of fluid laminar flow over a plate in a porous medium under the condition of eoustant heat flux was analyzed on the basis of Brinkman - Forehheimer - extended Darey model. The mass equation, momentum equations and the energy equations were established considering the local non -equilibrium between the fluid and the porous medium. The equations were simplified by analyzing the order of magnitude of each item and then were solved. The formulas of velocity distribution, temperature distribution, boundary layer thickness, thermal boundary layer thickness and the theoretical convection heat transfer correlation have been obtained approximately by the integration method. It was shown that the boundary layer thickness was completely different from that of the plain plate. It increased rapidly at the frontier of the plate then was much more fiat almost to be a constant. But the development of the thermal boundary layer thickness along the flow direction was much more similar to that of the plain plate, and it was independent of the heat flux.