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研究三阶流体在重力作用下,沿着一个倾斜等温的,带绝热自由表面时薄膜流动的热临界机理.假设是Arrhenius动力学意义下的发热反应,同时不计物质消耗.得到了动量和能量守恒的非线性控制方程,并以MAPLE为工具,基于一种特殊形式的Hermite-Padé近似技术,使用一种全新的数值逼近方法解之.这种半数值方法比之传统的方法,如有限差分法、频谱法、打靶法等,具有一定的优势.得到了解函数的解析结构,并对全部流动结构的重要性能,包括速度场、温度场、热临界和分岔加以讨论.
The thermal critical mechanism of the third-order fluid flow along a tilted isothermal, adiabatic free surface is studied under the action of gravity.It is assumed that it is an exothermic reaction in the sense of Arrhenius kinetics, without considering the material consumption, and the conservation of momentum and energy And using MAPLE as a tool, based on a special form of Hermite-Padé approximation, a new numerical approximation method is used to solve the problem. Compared with the traditional methods, such as the finite difference method , Spectrum method, shooting method, etc. The analytic structure of the analytic function is obtained, and the important properties of all the flow structures including velocity field, temperature field, thermal criticality and bifurcation are discussed.