Baranovskii Evgenii S
Department of Applied Mathematics, Informatics and Mechanics, Voronezh State University, 394018 Voronezh, Russia.
Polymers (Basel). 2025 Aug 29;17(17):2343. doi: 10.3390/polym17172343.
In the present article, we study a nonlinear mathematical model for the steady-state non-isothermal flow of a dilute solution of flexible polymer chains between two infinite horizontal plates. Both plates are assumed to be at rest and impermeable, while the flow is driven by a constant pressure gradient. The fluid rheology model used is FENE-P type. The flow energy dissipation (mechanical-to-thermal energy conversion) is taken into account by using the Rayleigh function in the heat transfer equation. On the channel walls, we use one-parameter Navier's conditions, which include a wide class of flow regimes at solid boundaries: from no-slip to perfect slip. Moreover, we consider the case of threshold-type slip boundary conditions, which state the slipping occurs only when the magnitude of the shear stresses overcomes a certain threshold value. Closed-form exact solutions to the corresponding boundary value problems are obtained. These solutions represent explicit formulas for the calculation of the velocity field, the temperature distribution, the pressure, the extra stresses, and the configuration tensor. The results of the work favor better understanding and more accurate description of complex dynamics and energy transfer processes in FENE-P fluid flows.
在本文中，我们研究了一个非线性数学模型，用于描述柔性聚合物链稀溶液在两个无限水平平板之间的稳态非等温流动。假定两个平板均静止且不可渗透，而流动由恒定压力梯度驱动。所使用的流体流变模型为FENE - P型。通过在传热方程中使用瑞利函数来考虑流动能量耗散（机械能到热能的转换）。在通道壁上，我们使用单参数纳维条件，其涵盖了固体边界处的广泛流动状态：从无滑移到完全滑移。此外，我们考虑阈值型滑移边界条件的情况，即只有当剪应力的大小超过某个阈值时才会发生滑移。获得了相应边值问题的闭式精确解。这些解给出了用于计算速度场、温度分布、压力、额外应力和构型张量的显式公式。这项工作的结果有助于更好地理解和更准确地描述FENE - P流体流动中的复杂动力学和能量传递过程。
