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The presented work is devoted to one problem of hydrodynamic stability of a thermoviscous fluid. The stability of the flow of a 45 $$\%$$ aqueous solution of propylene glycol in a plane channel with a linear temperature distribution was considered. The solution of the obtained generalized Orr-Sommerfeld equation was carried out using the spectral method of expanding the sought functions in terms of the first kind Chebyshev polynomials. As a result of calculations, the distributions of eigenvalues were constructed for different parts of the curve of the dependence of viscosity on the temperature of the liquid under consideration, in each case the critical Reynolds numbers and eigenfunctions were determined. It was found that taking into account the dependence of the viscosity on the temperature of the liquid leads to an increase in the region of unstable flow regimes in the channels of heat exchangers.

The upgrade of the technology of steel teeming on billet continuous-casting machines (CCMs) includes equipment upgrades, optimization of equipment operation modes and technological parameters of teeming and is one of the main trends in modern metallurgy. The aim of developing this trend is to increase the production capacity and utilization coefficient of CCMs, make the teeming a more stable process, and improve the quality of billets. This study provides a comparative analysis of the state of billet CCMs run at different iron and steel works as well as outlines the prospects for their advancement.

In this work we study the effect of the exponential temperature dependence of the incompressible fluid viscosity on the critical parameters of the flow hydrodynamic stability in a flat channel at various specified values of the wall temperature. The temperature field perturbations are thought to be absent. The eigenvalue spectra for the generalized Orr-Sommerfeld equation are constructed at sufficiently large Peclet numbers. The spectra structure, neutral stability curves, and the critical Reynolds number are shown to largely depend on the fluid properties that are determined by the exponential viscosity function.

The flow of a viscous model fluid in a flat channel with a non-uniform temperature field is considered. The problem of the stability of a thermoviscous fluid is solved on the basis of the derived generalized Orr-Sommerfeld equation by the spectral decomposition method in Chebyshev polynomials. The effect of taking into account the linear and exponential dependences of the fluid viscosity on temperature on the spectral characteristics of the hydrodynamic stability equation for an incompressible fluid in a flat channel with given different wall temperatures is investigated. Analytically obtained profiles of the flow rate of a thermovisible fluid. The spectral pictures of the eigenvalues of the generalized Orr-Sommerfeld equation are constructed. It is shown that the structure of the spectra largely depends on the properties of the liquid, which are determined by the viscosity functional dependence index. It has been established that for small values of the thermoviscosity parameter the spectrum compares the spectrum for isothermal fluid flow, however, as it increases, the number of eigenvalues and their density increase, that is, there are more points at which the problem has a nontrivial solution. The stability of the flow of a thermoviscous fluid depends on the presence of an eigenvalue with a positive imaginary part among the entire set of eigenvalues found with fixed Reynolds number and wavenumber parameters. It is shown that with a fixed Reynolds number and a wave number with an increase in the thermoviscosity parameter, the flow becomes unstable. The spectral characteristics determine the structure of the eigenfunctions and the critical parameters of the flow of a thermally viscous fluid. The eigenfunctions constructed in the subsequent works show the behavior of transverse-velocity perturbations, their possible growth or decay over time.

The viscous model fluid flow in a plane channel with a linear temperature profile is considered. The problem of the thermoviscous fluid flow stability is solved on the basis of the previously obtained generalized Orr–Sommerfeld equation by the spectral method of decomposition into Chebyshev polynomials. We study the effect of taking into account the linear and exponential dependences of the viscosity of a liquid on temperature on the eigenfunctions of the hydrodynamic stability equation and on perturbations of the transverse velocity of an incompressible fluid in a plane channel when various wall temperatures are specified. Eigenfunctions are found numerically for two eigenvalues of the linear and exponential dependence of viscosity on temperature. Presented pictures of their own functions. The eigenfunctions demonstrate the behavior of the transverse velocity perturbations, their possible growth or attenuation over time. For the given eigenfunctions, perturbations of the transverse flow velocity of a thermoviscous fluid are obtained. It is shown that taking the temperature dependence of viscosity into account affects the eigenfunctions of the equations of hydrodynamic stability and perturbations of the transverse flow velocity. Perturbations of the transverse velocity significantly affect the hydrodynamic instability of the fluid flow. The results show that when considering the unstable eigenvalue over time, the velocity perturbations begin to grow, which leads to turbulence of the flow. The maximum values of the eigenfunctions and perturbations of the transverse velocities are shifted to the hot wall. It is seen that for an unstable eigenvalue, the perturbations of the transverse flow velocity increase over time, and for a stable one, they decay.

In this paper, the problem of the possibility of regulating hydraulic resistance due to local thermal action is considered. The flow of an incompressible liquid with a temperature dependence of the viscosity in a plane channel with a variable cross section and an inhomogeneous temperature field is investigated. The flow velocities profiles of a thermoviscous liquid for a narrowed channel are obtained numerically. Using the example of a thermoviscous liquid flow in a plane channel with a sharp expansion, it is shown that the temperature factor exerts a significant influence on the value of the local resistance coefficient for the variable channel cross-section.

In the paper the results of numerical modeling of the flow of an incompressible fluid with a non-monotonic dependence of the viscosity on the temperature in a channel are presented. On the channel’s walls the heat exchange is specified that are written mathematically in the form of the boundary conditions of the third kind on the basis of the Newton– Richman convective heat exchange law. The regimes of flow stabilization in the channel depending on the Nusselt numbers have been studied. Four different types of unsteady processes are discovered and it has been shown that they are determined by the different heat exchange intensity.

Since the turn of the century, continuous bar-casting machines have been widely established, primarily at mini mills. The continuous bar-casting machines already in operation in Ukraine and Moldova are considered, along with the prospects for the construction of new mini mills and the expanded production of continuous-cast bar.

Results of numerical simulations of the thermal action on a high-viscosity hydrocarbon fluid with temperature-dependent viscosity and thermal conductivity are presented. A system of equations of thermal convection in the Boussinesq approximation is used as the constitutive equations to describe the convection of the hydrocarbon fluid. The dynamics of the temperature field and convective structures in the fluid is studied. The spatial motion of the fluid is found to be locally nonuniform; the motion is accompanied by vortex flows; as a result, two regions with significantly different temperatures are formed in the medium.

In a collaboration with the Moldavian Metallurgical Plant, VNIIMETMASh has used the results of studies of the design elements of continuous-caster molds to develop and succesfully produce a new liner for such molds — the VM-sinus. The main feature of this liner is the presence of convexity on the central sections of its walls. The convexity makes it possible to center the solidifying skin of the casting inside the liner when the skin is just beginning to form. Gradual straightening of the sinusoidal sections of the skin miminizes the size of the gas-filled gap between the skin and the walls of the liner. Gap size is minimized not only along the surfaces of the liner, but also at the corners. The new liners are being made at the pilot plant operated by VNIIMETMASh.

One of the main goals in the improvement of continuous casting technology is to improve the quality of the cast semifinished products. The most common surface defects on these products (folds, bleeders, coarse traces of mold oscillation, hanger tears) are related to the stability of operation of the mold oscillation mechanism and its drive and the accuracy with which the prescribed level of metal is maintained in the mold. Research done by the consortium MMZ-NKMZ-VNIIMETMASh on the development of a spring-based mold oscillation mechanism has made it possible to gain valuable experience in this area, design new components and oscillation mechanisms, and arrive at a better understanding of the technological aspects of their operation and the service requirements of such mechanisms on high-speed continuous casters. The Moldavian plant plans to continue its tests of an experimental oscillation mechanism with spring connectors in order to further improve the surface quality of continuous-cast semifinished products and stabilize the casting operation.