摘要
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 criticality for a mauve gravity driven thin film flow of a third grade fluid with adiabatic flee surface down an inclined isothermal plane is investigated. It was assumed that the reaction is exothermic under Arrhenius ldnetics,neglecting the consumption of the material. The governing non-linear equations for conservation of momentum and energy were obtained and solved using a new computational approach based on a special type of Hermite-Pade approximation technique implemented on MAPLE. This semi-numerical scheme offers some advantages over solutions obtained by using traditional methods such as finite differences, spectral method, shooting method, etc. It reveals the analytical structure of the solution function and the important properties of overall flow structure including velocity field, temperature field, thermal criticality and bifurcations were discussed.
出处
《应用数学和力学》
CSCD
北大核心
2009年第3期353-359,共7页
Applied Mathematics and Mechanics
基金
南非Thuthuka计划国家研究基金资助
