Том 58, № 4 (2017)

A method of generation of electromagnetic energy and magnetic flux in a magnetic cumulation generator is proposed. The method is based on dynamic variation of the circuit coupling coefficient. This circuit is compared with other available circuits of magnetic energy generation with the help of magnetic cumulation (classical magnetic cumulation generator, generator with transformer coupling, and generator with a dynamic transformer). It is demonstrated that the proposed method allows obtaining high values of magnetic energy. The proposed circuit is found to be more effective than the known transformer circuit. Experiments on electromagnetic energy generation are performed, which demonstrate the efficiency of the proposed method.

The group analysis method is applied to a system of integro-differential equations corresponding to a linear thermoviscoelastic model. A recently developed approach for calculating the symmetry groups of such equations is used. The general solution of the determining equations for the system is obtained. Using subalgebras of the admitted Lie algebra, two classes of partially invariant solutions of the considered system of integro-differential equations are studied.

This paper derives a new system of equations for the simulation of the long-wave perturbation dynamics on the surface of a thin horizontal layer of heavy viscous fluid moving under the action of turbulent gas flow. In the case of small Reynolds numbers of the fluid, this system of equations is used to derive an evolution equation for the value of deviation of the film thickness from the unperturbed level. Some solutions of this equation are given.

Electrokinetic processes in the vicinity of inhomogeneous ion-selective surfaces (electrodes, membranes, microchannels, and nanochannels) consisting of alternating conducting and nonconducting regions in the presence of a normal-to-surface electric current are numerically studied. An increase in the electric current density is observed in the case of some particular alternation of conducting and nonconducting regions of the surface. The current–voltage characteristics of homogeneous and inhomogeneous electric membranes are found to be in qualitative agreement. Various physical phenomena leading to the emergence of a supercritical current in homogeneous and inhomogeneous membranes are detected.

This paper presents a mathematical model for the injection of carbon dioxide into a natural gas reservoir saturated with methane and water accompanied by the 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 reservoir 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 high 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 incorporated into gas hydrate.

The effect of thermal radiation on an unsteady boundary layer flow and heat transfer in a copper–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.

This paper studies the stability of steady convective flow in an inclined plane fluid layer bounded by perfectly heat-conducting solid planes in the presence of a homogeneous longitudinal temperature gradient under stable stratification where the layer is inclined so that the temperature in its lower part is lower than in the upper part.

The temperature distribution in a reservoir with a 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 a hydraulic fracture in the reservoir leads to a nonmonotonic change 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 heat exchange in the fracture–reservoir system.

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 Kármán 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.

This paper considers the inverse problem of determining the inhomogeneity laws of the coating of an elastic cylinder that provide minimum reflection of a plane acoustic wave in a particular angular sector and in a given frequency range. A functional that expresses the reflection intensity is constructed by direct solution of the direct problem, and an algorithm for minimizing this functional is proposed. Analytical expressions describing the mechanical parameters of the inhomogeneous coating are obtained.

The dynamic response of a clamped L-connected plate and an actively controlled vibratory power flow are studied. The vibratory power flow is suppressed by a piezoelectric patch, which is bonded on the L-connected plate. The electric patch is considered as an actuator. The feedforward least mean square algorithm is used to deduce the optimal piezoelectric patch control moment. Actuator operation with close-to-optimal moments is studied with allowance for the presence of in-plane waves.