Non-Newtonian rivulet-flows on unsteady heated plane surface

IF 3.2 3区工程技术 Q2 MECHANICS International Journal of Non-Linear Mechanics Pub Date : 2024-12-06 DOI:10.1016/j.ijnonlinmec.2024.104984

S.V. Ershkov , E.S. Baranovskii , E.Yu. Prosviryakov , A.V. Yudin

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Abstract

In this illuminating study, a new distinct family of semi-analytical solutions for the nonlinear system describing the rivulet flow of viscoplastic fluid (with the non-zero critical maximal level of plasticity τ_s), is presented with updating to the case of rivulet flowing on inclined heated plane surface which can be considered as the stretching plane linearly dependent on time t due to thermal expansion. Therefore, purely non-Newtonian case of solution {

\vec{v} = (v_{x}, v_{y}), p

} of viscoplastic flow has been highlighted. It is worthnoting that the obtained unsteady solutions are fully decribed by Riccati-type ODE which means a possible jumping of rivulet flowing: sudden accelerating or decelerating of the flow at approriate moment of time. Approximate general mode for rivulet flow is obtained. Profile of pressure can be retrieved from two partial differential equations of the 1st order, depending of function τ_s of plasticity.

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非定常加热平面上的非牛顿小流

在这一具有启发意义的研究中，提出了描述粘塑性流体（具有非零临界最大塑性水平τs）流的非线性系统的一组独特的半解析解，并更新了流在倾斜加热平面上流动的情况，该平面可视为由于热膨胀而线性依赖于时间t的拉伸平面。因此，粘塑性流动的纯非牛顿解{v→=vx,vy，p}的情况得到了强调。值得注意的是，所得到的非定常解是由riccati型ODE完全描述的，这意味着水流可能出现跳跃，在适当的时刻突然加速或减速。得到了溪流流动的近似一般模式。根据塑性函数τs，可以从两个一阶偏微分方程中得到压力剖面。

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来源期刊

International Journal of Non-Linear Mechanics 物理-力学

CiteScore

5.50

自引率

9.40%

发文量

192

审稿时长

67 days

期刊介绍： The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.