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The dynamic behavior of the magma melt saturated with a strongly compressed gas at a high temperature, which is located between two rigid boundaries aligned symmetrically with respect to the vertical axis, is considered. A constant pressure is maintained at the channel bottom, while the pressure in the medium is initially distributed in accordance with the hydrostatic law. The top of the channel is hermetically sealed with a plug, which is affected by a constant pressure equal to the atmospheric value. The state of the melt after instantaneous removal of the plug is studied.

The problem of gas pressure equalization in a porous medium filling a tube with a closed end upon impact is solved.In this case, the initial filtration velocity behind the shock wave should be specified as initial data, in addition to the impact pressure.It is shown that the pressure surge decays at a finite distance and pressure equalization occurs in a finite time. Approximate submodels of discontinuous and smooth solutions are obtained.

An analytical study of the entropy generation rate and heat transfer in a flow of immiscible couple stress fluids between two horizontal parallel plates under a constant pressure gradient is performed. Both plates are kept at different and constant temperatures higher than that of the fluid. The Stokes couple stress flow model is employed. The classical no-slip condition is prescribed at the plates, and continuity of the velocity, rotation, couple stress, shear stress, temperature, and heat flux is imposed at the interfaces. The velocity and temperature distributions are found analytically, and they are used to compute the entropy generation number and Bejan number. The effects of the couple stress parameter and Reynolds number on the velocity, temperature, entropy generation number, and Bejan number are investigated. It is observed that the friction near the plates in couple stress fluids decreases as the couple stress increases.

Forced oscillations of a cylindrical drop of an inviscid liquid surrounded by another liquid and bounded in the axial direction by rigid planes are investigated.The system is affected by vibrations whose force is directed parallel to the axis of symmetry of the drop. The speed of motion of the contact line is proportional to the deviation of the contact angle from the value at which the drop is in equilibrium. Linear and nonlinear oscillations are considered. The conditions of the occurrence of resonance are determined.

The self-gravitating instability of the present model is discussed by using a simple linear theory. The problem is formulated for a rotating fluid layer, and a dispersion relation valid for all kinds of perturbations is derived and discussed. The self-gravitating force is found to be a destabilizing factor for a small range of wavenumbers, while it is stabilizing in other ranges, depending on the density ratio of the fluids. For high values of the angular velocity, the rotational force produces a stabilizing effect and can suppress the self-gravitating instability. In the absence of the self-gravitating force, the model of a rotating fluid layer is marginally stable

A flow past a heterogeneous porous sphere is investigated by using the perturbation theory. The flow through the sphere is divided into two zones, which are fully saturated with the viscous fluid, and the flow in these zones is governed by the Brinkman equation. The space outside the sphere, where a clear fluid flows, is also divided into two zones: the Navier-Stokes zone and the Oseen flow zone. The solutions on the interface inside the sphere are matched with the condition proposed by Merrikh and Mohammad. The stream function in the Navier-Stokes zone is matched with that on the sphere surface by the condition proposed by Ochoa-Tapia and Whitaker. It is found that the drag on the spherical shell decreases as the permeability toward the sphere boundary increases.

A similarity solution for a steady laminar mixed convection boundary layer flow of a nanofluid near the stagnation point on a vertical permeable plate with a magnetic field and a buoyancy force is obtained by solving a system of nonlinear ordinary differential equations. These equations are solved analytically by using a new kind of a powerful analytic technique for nonlinear problems, namely, the homotopy analysis method (HAM). Three different types of nanoparticles, namely, copper Cu, alumina Al₂O₃, and titanium oxide TiO₂, with water as the base fluid are considered. The influence of the volume fraction of nanoparticles, permeability parameter, magnetic parameter, and mixed convection parameter on the surface shear stress and surface heat transfer, as well as on the velocity and temperature profiles, is considered. It is observed that the skin friction coefficient and the local Nusselt number increase with the nanoparticle volume fraction for all types of nanoparticles considered in this study. The greatest values of the skin friction coefficient and the local Nusselt number are obtained for Cu nanoparticles.

Schlieren visualization is used to study the generation of Mach waves and impact noise in a wide range of frequencies by single supersonic jets and by groups of jets in the Mach number range M=1-4.

A two-dimensional magnetohydrodynamic boundary layer flow of the Eyring-Powell fluid on a stretching surface in the presence of thermal radiation and Joule heating is analyzed. The Soret and Dufour effects are taken into account. Partial differential equations are reduced to a system of ordinary differential equations, and series solutions of the resulting system are derived. Velocity, temperature, and concentration profiles are obtained. The skin friction coefficient and the local Nusselt and Sherwood numbers are computed and analyzed.

Two problems on flat damping surface waves in an inhomogeneous medium are under consideration: the problem of propagation of the waves similar to the Rayleigh waves in an isotropic elastic half-space bordering with the layer of an ideal incompressible fluid, and the problem of propagation of the waves to the Love waves in a semi-infinite saturated porous medium bordering with the layer of an isotropic elastic medium.