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利用现代数学理论对具有幂律速度的无限延伸平板边界层问题进行了研究。通过引入适当的相似变换将原边界层方程转化为一类奇异非线性两点边界值问题,利用泛函分析中的控制收敛定理,Schauder不动点定理和近代微分方程理论中的奇异摄动理论和单调逼近技巧,给出了奇异非线性边值问题的负解的存在性和唯一性的严格证明,并给出了无量纲剪切应力和无量纲切向速度的估计公式。 相似文献
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研究了一类奇异非线性两点边值问题-y″=f(x,y),0≤k<x<1,y′(k)=C,y(1)+Dy′(1)=η(D>0)的正确的存在性和住性,其中假定函数f(x,y)关于变量y具有奇性(limf(x,y)=+∞)。 相似文献
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研究了运动的粘性导电流体中可渗透收缩壁面上非稳态磁流体边界层流动,利用解析和数值方法对问题进行了研究,并考虑了壁面速度滑移的影响.提出了一个新的解析方法(DTM-BF),并将其应用于求解带有无穷远边界条件的非线性控制方程的近似解析解.对所有的解析结果和数值结果进行了对比,结果显示两者非常吻合,从而证明了DTM-BF方法的有效性.另外,对不同的参数,得到了控制方程双解和单解的存在范围.最后,分别讨论了滑移参数、非稳态参数、磁场参数、抽吸/喷注参数和速度比例参数对壁面摩擦、唯一解速度分布和双解速度分布的影响. 相似文献
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The flow of a micropolar fluid in a semi-porous channel with an expanding or contracting wall is investigated. The governing equations are reduced to ordinary ones by using similar transformations. To get the analytic solution to the problem, the homotopy analysis method (HAM) is employed to obtain the expressions for velocity fields. Graphs are sketched and discussed for various parameters, especially the effect of the expansion ratio on velocity and micro-rotation fields. 相似文献
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利用单调逼近方法给出了源于流体边界层理论中的一类奇异边值问题正解的存在性和唯一性的充分条件,同时给出了用压力梯度参数表示的壁摩擦的估计公式;并且数值结果证明了估计公式的可靠性和有效性。 相似文献
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Bifurcation Behaviour in the Reverse—Flow Boundary Layer with Special Injection or Suction
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Bifurcation solutions are numerically presented for reverse flow boundary layer equations with special suction/injection by utilizing similarity transformation and shooting technique.The results indicate that both superior solution and inferior solution are noticeable.The skin friction and shear stress for the superior solution decrease with the increases of the ratio of surface velocity to free stream velocity and suction/injection.The behaviour is opposite to that for the inferior solution.Both the skin frictions for the superior and inferior solutions decrease with increasing the power law parameter.The inferior solution approaches the superior solution with increasing the velocity ratio and suction/injection.When power law is unit and suction/injection is zero,the superior solution approaches the classical Blasius solution as the velocity ratio approaches zero. 相似文献