Oldroyd B流体依时性管内流动的变分解析方法<sup>*</sup>

Oldroyd B流体依时性管内流动的变分解析方法^*

基金项目: * 第三世界科学院;中国国家自然科学基金

1.
Res. Lab. Non-Newtonian Fluid Mech., Chengdu Branch, Academia Sinica, Chengdu;
2.
Department of Mathematics, The University of West Indles, St. Augustine Trinidad W. I.

摘要: 在本文中,研究上随体Oldroyd B流体在水平管内依时性流动。该问题可归结为无量纲速度分量的三阶偏微分方程的初边值问题。采用改进的Kantorovich方法,将该方程化为各级近似的二阶常微分方程组的初值问题。通过Laplace变换,求得其二阶常微分方程的解析解,在本文中,提出了变分解析解的新概念。获得了二级近似变分解析解,其中包括常压力梯度和周期性压力梯度两种情形。应用计算机符号处理和Laplace变换,可以获得任意近似下的变分解析解。
- OldroydB流体 /
- 非牛顿流体 /
- 依时性流体 /
- 变分一解析法 /
- 改进的Kantorovich方法
Abstract: In the present investigation the time dependent flow of an Oldroyd fluid B in a horizontal eylindrical pipe is stuided by the variational analytical approach developed by author.The tome dependent problem is mathematically reduced to a partial differential equation of third order.Using the improved variational approach due to Kantorovich the partial differential equation can be reduced to a system of ordinary differential equations for different approximations.The ordinary differential equations are solved by the method of the Laplace transform which is led to an analytical form of the solutions.
- Oldroyd fluid B /
- non-Newtonian fluid /
- time dependent flow /
- variational-analytical approach /
- improved approach dut to Kantorovich

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