用非笛卡儿张量分析建立数学模型 研究影响螺旋状管对流换热的因素

Application of Non-Cartesian Tensor Analysis Constructed Mathematical Model Investigate for the Effect of Parameters on Convective Heat Transfer Characterstics in a Helicoidal Pipe

本文基于带有物理基的非笛卡儿张量分析为基础的广义矩阵法,在非正交的螺旋线坐标系中,推导出螺旋状管中充分发展、层流流动的非线性连续性方程、Navier -Stokes方程组和能量方程。并用 SIMPLE算法解出了上述一系列方程。结果表明:对大普朗特数的流体,桡率将显著改变等温轮廓线的形状。随着普朗特数的增加,挠率将使螺旋状管的等温轮廓线变形加剧。并使努塞尔数大小减小。

Using the generalized matrix method based on nonCartesian tensor analyses with physical base, in a nonorthogonal helical coordinate system , the authors derived the fully developed laminar flow of constant fluid properties nonlinear equations (e. g. continuity equation, Navier-Stokes equations and energy equation) in a helicoidal pipe. And solved these nonlinear partial differential equations by the SMPIE algorithm. As the result shows, When Prandtl number increasing, That the torsion will distort the shape of the isothermal contour, and the Nusselt number may remarkably discreas-ing.