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Oscillations of semi-infinite ice cover in an ideal incompressible fluid of finite depth under local time-periodic axisymmetric load type are considered. Ice cover is simulated by a thin elastic plate of constant thickness. An analytical solution of the problem is obtained using the Wiener-Hopf method. The asymptotic behavior of the amplitudes of oscillations of the plate and the liquid in the far field is studied. It is shown that the propagation of waves in the far field is uneven: in some directions the waves propagate at significantly greater amplitude.

This paper presents a mathematical model for carbon dioxide injection into a natural gas reservoir saturated with methane and water accompanied by formation of carbon dioxide hydrate in an extended region. The dependence of the coordinates of the boundaries of the region of phase transitions on the pressure of the injected gas and the initial parameters of the formation are investigated. It is established that the velocity of the near boundary of the region of hydrate formation decreases with increasing water saturation and initial temperature of the reservoir and the velocity of the far boundary of the region of phase transitions increases with increasing pressure of the injected gas and reservoir permeability. It is shown that at large initial temperatures of the reservoir, a regime is possible in which replacement of methane by carbon dioxide without hydrate formation occurs at the far interface, and at the near interface, water is completely transformed into a hydrated state.

This paper describes the results of an experimental study of heat transfer in the case of the flow of a helium-xenon mixture with a Prandtl number approximately equal to 0.23 and the flows of pure helium and air in heated tubes of circular or triangular cross sections with a constant density of the heat flux. The region of thermal stability is studied. The law of heat transfer on the stabilized region is compared with known relationships. The approach that helps to obtain an expression for calculating the heat transfer in heat transfers with circular and triangular cross sections, which operate in a mixture heating mode on the initial region is developed.

The effect of thermal radiation on an unsteady boundary layer flow and heat transfer in a Cu-water nanofluid over an exponentially shrinking porous sheet is investigated. With the use of suitable transformations, the governing equations are transformed into ordinary differential equations. Dual non-similarity solutions are obtained for certain values of some parameters. Owing to the presence of thermal radiation, the heat transfer rate is greatly enhanced, and the thermal boundary layer thickness decreases.

The problems of experimental studies of the boiling of superfluid helium (He-II) on a cylindrical heater placed in a porous body are considered. A diagram of the setup, a description of the experimental cell, control and measurement means, and video recording and data processing techniques are presented. The technique of the experiment and the results are described.

This paper studies the stability of steady convective flow in an inclined plane liquid layer bounded by ideally thermally conductive solid planes in the presence of a homogeneous longitudinal temperature gradient under stable stratification when the layer is inclined so that the temperature in its lower part is smaller than in the upper part.

Based on the thermal conduction equation that takes into account phase changes and the evolution of thermophysical parameters with temperature, laser-induced heating and melting of monocrystalline silicon are studied. The changes in the behavior of silicon temperature at different places within the irradiation spot and at different time instants are investigated by the finite element and finite difference methods for a wide range of energy and duration of millisecond laser pulses with the Gaussian spatial and temporal shapes. The numerical results are compared with the experimental measurements.

The temperature distribution in a reservoir with hydraulic fracture is studied by numerical modeling of transient temperature fields taking into account the Joule-Thomson effect and the adiabatic effect. It is shown that the presence of hydraulic fracture in the reservoir leads to a nonmonotonic temperature variation in the reservoir temperature: as the well pressure decreases, the temperature first decreases due to the adiabatic expansion of the fluid and then increases due to the Joule-Thomson effect. As the water-oil displacement front approaches the wellbore, the temperature decreases slightly due to the heat exchange processes in the fracture-reservoir system.

The dynamic equation of a viscoelastic floating ice plate under a triangular pulse load is solved analytically through the Hankel transformation and the Laplace transformation. The effects of physical and geometrical parameters of the problem on the displacement response as a function of time and spatial coordinate are discussed.

The elastic buckling analysis and the static postbuckling response of the Euler-Bernoulli microbeams containing an open edge crack are studied based on a modified couple stress theory. The cracked section is modeled by a massless elastic rotational spring. This model contains a material length scale parameter and can capture the size effect. The von Karman nonlinearity is applied to display the postbuckling behavior. Analytical solutions of a critical buckling load and the postbuckling response are presented for simply supported cracked microbeams. This parametric study indicates the effects of the crack location, crack severity, and length scale parameter on the buckling and postbuckling behaviors of cracked microbeams.