Baranovskii Evgenii S
Department of Applied Mathematics, Informatics and Mechanics, Voronezh State University, 394018 Voronezh, Russia.
Nanomaterials (Basel). 2023 Apr 19;13(8):1409. doi: 10.3390/nano13081409.
In this paper, we obtain new exact solutions for the unidirectional non-isothermal flow of a second grade fluid in a plane channel with impermeable solid walls, taking into account the fluid energy dissipation (mechanical-to-thermal energy conversion) in the heat transfer equation. It is assumed that the flow is time-independent and driven by the pressure gradient. On the channel walls, various boundary conditions are stated. Namely, we consider the no-slip conditions, the threshold slip conditions, which include Navier's slip condition (free slip) as a limit case, as well as mixed boundary conditions, assuming that the upper and lower walls of the channel differ in their physical properties. The dependence of solutions on the boundary conditions is discussed in some detail. Moreover, we establish explicit relationships for the model parameters that guarantee the slip (or no-slip) regime on the boundaries.
在本文中，我们考虑了传热方程中的流体能量耗散（机械能到热能的转换），得到了具有不可渗透固体壁面的平面通道中二级流体单向非等温流动的新精确解。假设流动与时间无关且由压力梯度驱动。在通道壁面上，给出了各种边界条件。具体而言，我们考虑了无滑移条件、阈值滑移条件（其中包括作为极限情况的纳维滑移条件（自由滑移））以及混合边界条件，假设通道的上壁和下壁在物理性质上有所不同。详细讨论了解对边界条件的依赖性。此外，我们建立了保证边界上滑移（或无滑移）状态的模型参数的显式关系。
