Vol 53, No 1 (2018): Suppl

A plane isothermal problem of the internal contact between elastic cylindrical bodies separated by a thin layer of a viscous lubricating fluid under constant load and reverse motion is considered. To determine the deformations of the contacting bodies, solutions of the plane problems of the elasticity theory for a cylinder and a space with a cylindrical cut are used. Extreme cases of low load, high load, small and long periods of reverse motion are considered. The dependences of lubricant layer thickness and pressure on the angular coordinate at different times, as well as the dependence of the eccentricity and the minimum lubricant layer thickness on time are presented. It is shown that the minimum lubricant layer thickness as a function of time exhibits a decrease when braking the cylinder and continues to decrease for some time after a change in the direction of rotation and an increase in speed. It has been established that at the times when the speed is low, under high loads, the gap has narrow spots at the boundaries of the high-pressure area, preventing the lubricant from leaking out of the gap. At a low load and a long period of reverse motion, the maximum pressure in the lubricant layer can increase more than twice.

Based on the determination of the temperature perturbation front and additional boundary conditions, an approximate analytical solution is obtained for the stationary heat exchange problem when fluid flows in a cylindrical channel with a constant parabolic velocity profile (the Gretz–Nusselt problem), which allows us to investigate the temperature distribution in the fluid in a wide range of distances from the pipe inlet, including small and very small distances. Based on the data of numerical calculations of temperature change at a certain value of the spatial variable using the solution obtained by solving the inverse heat conduction problem, the Peclet number was found (in the case where it is unknown in the solution obtained), from which we can determine the velocity profile and the flow rate of the liquid. Graphs of the distribution of isotherms and the their velocities in space over time are plotted.

In this paper, we study the exact stationary solution of the Oberbeck–Boussinesq equations describing the joint flow of a viscous heat-conducting liquid and the cocurrent flow of a gas-vapor mixture in a flat horizontal layer. The initial formulation of the problem takes into account mass transfer through the interphase interface due to evaporation, vapor diffusion in the gas phase in the presence of diffusion heat conduction, and a longitudinal temperature gradient at the solid impermeable boundaries of the channel. The effect of the layer thickness of working media on the characteristics of the main flow under conditions of equal thermal load on the channel walls was studied. Based on the linear theory, the stability of the exact solution is studied, typical forms of perturbations and their dynamics are determined with a change in the linear dimensions of a system, and neutral curves and maps of the instability regimes are plotted.

The induction of uncompensated volume charge in a weakly conducting liquid flowing in a flat microchannel by a highly nonuniform electric field is modeled and investigated; the flow regime is limited to moderate Debye numbers. The effects associated with the immediate impact of the electric field on the bulk dissociation kinetics are analyzed.

Hydrodynamic and thermodynamic equations for the atmosphere are considered in the meteorological and climatic scales in which the inertial forces are negligibly small in comparison with gravity. In this case, the inertia of the horizontal velocity and temperature has an effect. For such a vertically quasi-static flow, an equation for the vertical velocity distribution asymptotically exact in density, temperature, and horizontal velocity is obtained. A closed system of hydro- and thermodynamic equations is presented in which the pressure at each point is determined by the weight of the air column above this point. It is this system of equations that should be used to calculate the climatic and meteorological processes in which the inertia of the horizontal velocity and the inertialess vertical velocity play an essential role.