外掠平板层流流动边界层微分方程积分解的实现

Implementation of Integration Solution to Boundary Layer Equation of Laminar Flow over Plane

边界层理论及其在典型流动问题中的应用是流体力学和传热学的重要内容,通过对外掠平板层流流动和换热等问题的分析,可以揭示流体流动和传热的基本规律,是认识更为复杂流体流动和传热现象的基础。在分析和介绍边界层微分方程建立方法、相似变量表达式以及边界层方程典型解法的基础上,重点探讨了外掠平板边界层相似变换微分方程的积分解解法,并给出了相应的MATLAB计算程序。计算结果表明,边界层相似变换微分方程的积分解法简单、易行,该方法对于教师讲解和学生理解边界层流动和传热特性有积极作用。

Boundary layer theory and its application in typical flow problems are important contents of fluid mechanics and heat transfer courses. Through the analysis of laminar flow and heat transfer over a flat plate, the basic laws of fluid flow and heat transfer can be revealed, which is the basis of understanding more complex fluid flow and heat transfer phenomena. Based on the analysis and introduction of the establishment method of the boundary layer differential equation, the expression of similar variables and the typical solution of the boundary layer equation, the integral solution of the similar transformation differential equation of the boundary layer formed by fluid flowing over the flat plate was introduced, and the corresponding MATLAB program was given. The results showed that the integral method for solving boundary layer similarity transformation differential equation was simple and easy to use. This method has a positive effect on teachers’ explanation and students’ understanding of the characteristics of boundary layer flow and heat transfer.