Численное моделирование двумерного течения микрополярной жидкости в замкнутой полости с учётом полной функции диссипации, Numerical simulation of two-dimensional flow of a micropolar fluid in an enclosed cavity with the full dissipation function

<jats:p>The paper studies numerically a steady two-dimensional flow of incompressible micropolar fluid in a square cavity with a moving top wall. The steady solution is obtained by the time-marching method - time integration of the full system of unsteady Eringen equations. A distinctive feature of this work is a detailed calculation and analysis of the total dissipation function, which includes three mechanisms: classical viscous dissipation, dissipation due to microrotation gradients, and dissipation resulting from the interaction between macroscopic vorticity and the microrotation field. A numerical algorithm is developed based on the Chorin–Temam projection method; its correctness is verified by comparison with the classical Newtonian limit. A parametric study is carried out over wide ranges of the governing dimensionless parameters - the Reynolds number, the micropolarity parameter, and the microscale parameter. It is shown that the integral dissipation increases with the Reynolds number and the micropolarity parameter, although there are local non-monotonicities due to a nonlinear interaction of dissipative mechanisms. The influence of the microscale parameter is found to be considerably weaker than that of the other two parameters. It is shown that as the Reynolds number increases, the thickness of the boundary layer at the moving wall decreases, and the microrotation velocity maximum diminishes and is localized in the near-wall layers. Analysis of the velocity and microrotation distributions confirms the formation of thin boundary layers near solid walls, where dissipation is maximal. Micropolar effects lead to a marked increase in dissipation compared with a classical Newtonian fluid, which demonstrates the importance of considering the internal rotational degrees of freedom in the energy balance. The results may find application in microfluidics and modeling of complex fluid flows.</jats:p>