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The flow around a stationary process sphere by an accelerating flow of a pseudoplastic fluid at Reynolds numbers Re = 0-200 and dimensionless acceleration Ga = 10-10⁴ is studied by numerical simulation. It is shown that the analytical expression of the force of the added mass for an ideal fluid is appropriate for a pseudoplastic fluid. An expression for calculating the hereditary force of the type of the Basset force for a pseudoplastic fluid is proposed.

The plane consolidation problem for elastic half-space under an instantaneously applied vertical load is solved in the general case assuming that the following Terzaghi hypothesis holds.

A mathematical model is proposed to describe the substitution of carbon dioxide for methane in gas hydrate upon injection of liquid carbon dioxide into a porous medium initially saturated with methane and its hydrate. Self-similar solutions of the axisymmetric problems that describe the distribution of the main parameters of the bed are constructed. It is shown that there are solutions, according to which the process can occur both with and without boiling of carbon dioxide. Diagrams of the existence of each type of solution are constructed.

The interaction of the cooling systems of permeable materials with a high-temperature gas flow is considered. The effect of the porosity and thermal properties of some metals on heat transfer is investigated.яIt is found that increasing the thermal conductivity of the material leads to a decrease in the temperature of the heat-shielding coating and increasing the porosity to a more uniform distribution of the coolant applied on the surface and to a decrease in the heat loads on the structure to be protected.

This research is aimed at studying the two-phase flow pattern of a top heat mode closed loop oscillating heat pipe with check valves. The working fluids used are ethanol and R141b and R11 coolants with a filling ratio of 50% of the total volume. It is found that the maximum heat flux occurs for the R11 coolant used as the working fluid in the case with the inner diameter of 1.8 mm, inclination angle of -90 ͦ, evaporator temperature of 125gr, and evaporator length of 50 mm. The internal flow patterns are found to be slug flow/disperse bubble flow/annular flow, slug flow/disperse bubble flow/churn flow, slug flow/bubble flow/annular flow, slug flow/disperse bubble flow, bubble flow/annular flow, and slug flow/annular flow.

A method and an experimental setup are developed for determining the intensity of evaporation from the free surface of water. During the measurement, the ambient air velocity and the water temperature can be varied. The mass and temperature of water, as well as the temperature, pressure, and humidity of the ambient air are measured as functions of time. The evaporation rates are calculated from the measured and recorded data in the cases of natural and forced convection.

The torsional and longitudinal flexural vibrations of orthotropic corrugated shells are investigated. Relations, including the equation of motion in forces and moments and the Hooke's law relations are obtained using the Kirchhoff-Love hypotheses. The influence of geometric parameters of the shell (amplitude and length of the corrugation) on the natural frequencies and natural vibrations modes are studied for fixed-end shells.It is found that during torsional vibrations, increasing the amplitude of the corrugation and increasing the number of corrugations leads to a decrease in the resonant frequencies. In the case of torsional and longitudinal flexural vibrations, the influence of the corrugation amplitude on the natural vibration modes is investigated.

The previously proposed method of one-dimensional deformation of soil is used to solve the problems of joint seismic vibrations of an underground pipeline and elastic soil under nonideal contact under the assumption that there is slip on the contact surface and that resulting shear stresses on it are proportional either to the relative displacement of soil particles and pipeline or to the relative speed of motion movement. The dependence of the maximum stress in the pipeline on the coefficients under boundary conditions is investigated. For supersonic flow around the pipe, resonance is observed with decreasing shear stress on the contact surface.

The Ramberg-Osgood stress-strain relation is used to perform a theoretical springback analysis in the problem of bending of a narrow rectangular strip made of a strain-hardening material. The maximum strip thickness is 5 mm, and its length is significantly greater than the thickness. Based on the elasticity and plasticity deformation theory and also on the Tresca and von Mises yield criteria, an expression for the springback ratio is derived. The springback ratio depends on the ratio of the yield stress to Young's modulus, Poisson's ratio, strain hardening coefficient, and sheet thickness.

The boundary-value problem of the elasticity theory for a cylinder with cylindrical cavities forming a hexagonal structure is under consideration. The solution is constructed in the form of a superposition of accurate basic equations of the Lame equations for a cylinder in the coordinate systems associated to the centers of the body surfaces. The boundary conditions of the problem are satisfied exactly with the help of the generalized Fourier method. The problem is reduced to an infinite system of linear algebraic equations with a Fredholm operator in the space l₂. The resolving system is solved numerically by the reduction method. The numerical analysis of stresses in the regions of their greatest concentration is carried out.