周期压力梯度作用下管内上随体Maxwell流体不稳定流动的解析法

A Variational Analytical Approach to Unsteady Flow of Upper Convected Maxwell Fluid in Tube Under Cyclical Pressure

研究了随体Ｍａｘｗｅｌ流体在水平圆管内的不稳定流动．该问题可归结为无量纲速度分量的二阶偏微分方程的初边值问题．采用改进的Ｋａｎｔｏｒｏｖｉｃｈ方法，将该偏微分方程化为各级近似的二阶常微分方程组，通过解常微分方程组获得在周期压力梯度作用下的一阶、二阶近似变分解析解．

In the present investigation the unsteady flow of upper convected Maxwell fluid in a horizontal cylindrical pipe is studied with the variational approach developed.The unsteady problem is mathematically reduced to a partial differential second order equation.With the improved kantorovich variational approach,the partial differential equation can be reduced to a system of ordinary differential equations for different approximations.The ordinary differential equations are solved with two Methods.The results of the first approximation and second approximation are obtained.