Combined convection along a non-isothermal wedge in a porous medium

A boundary layer analysis has been presented for the combined convection along a vertical non-isothermal wedge embedded in a fluid-saturated porous medium. The transformed conservation laws are solved numerically for the case of variable surface temperature. Results are presented for the details of the velocity and temperature fields as well as the Nusselt number. The wedge angle geometry parameter m ranged from 0 to 1.     

Motion of a viscoplastic liquid in a porous inhomogeneous medium

Equations of motion are derived for a viscoplastic liquid in a nonuniform medium of type 2 (piecewise uniform) or type 3 (with a variable filtration coefficient) [1] on the assumption that the motion is of steady-state type. Solutions are presented for a parallel flow and a flow with axial symmetry.     

Motion of a thin plate in an elastic medium

A solution to the problem of motion of a thin rigid plate in an elastic medium is obtained using the Smirnov-Sobolev method for solving a two-dimensional wave equation.     

Mixed convection flow over a vertical wedge embedded in a highly porous medium

 The steady mixed convection flow over a vertical wedge with a magnetic field embedded in a porous medium has been investigated. The effects of the permeability of the medium, surface mass transfer and viscous dissipation on the flow and temperature fields have been included in the analysis. The coupled nonlinear partial differential equations governing the flow field have been solved numerically using the Keller box method. The skin friction and heat transfer are found to increase with the parameters characterizing the permeability of the medium, buoyancy force, magnetic field and pressure gradient. However the effect of the permeability and magnetic field on the heat transfer is very small. The heat transfer increases with the Prandtl number, but the skin friction decreases. The buoyancy force which assists the forced convection flow causes an overshoot in the velocity profiles. Both the skin friction and heat transfer increase with suction and the effect of injection is just the reverse. Received on 21 May 1999     

Motion of a nonisothermal multicomponent sorbable mixture in a porous medium

The numerical solutions of a system of quasilinear equations in partial derivatives, describing the motion of a nonisothermal multicomponent sorbable gas mixture (or mixture of liquids) through a porous saturated medium consisting of porous grains and incapable of undergoing deformation, are analyzed; the conditions for the convergence of the iteration process used in solving the difference scheme and for the stability of the numerical solutions are obtained; the necessary and sufficient conditions for the existence of solutions of the traveling-wave type, permitted by the system of equations of motion, are also analyzed.     

Motion of the interface of two fluids in a porous medium

In this study we obtain the Integro-differential equation for the motion of the interface of two incompressible fluids in various well areal arrangement systems. The solution of the equation is presented for a five-point system in the form of a power series with respect to time. Formulas are assumed which describe the motion of the particles belonging to the interface along invariant streamlines for five-point, seven-point, and nine-point well arrangement systems. The stratum sweeping coefficients for the fluid which is displacing the stratum oil are calculated (under conditions of the five-point system) at the instant when the fluid breaks through into the operation wells. The results of the calculations are compared with experimental data [1].The author wishes to thank V. L. Danilov for valuable counsel and comments.     

Motion of a cylinder in a viscous electroconductive medium with a magnetic field

The method of force sources is used to consider the planar problem of the motion of a circular cylinder in a viscous electroconductive medium with a magnetic field. The conventional and magnetic Reynolds numbers are assumed to be small. Expressions are obtained for the hydrodynamic reaction forces of the medium, acting on the moving cylinder. It is shown that as a result of the flow anisotropy in the medium, caused by the magnetic field, in addition to the resistance forces on bodies moving at an angle to the field, there are deflecting forces perpendicular to the velocity vector. The velocity field disturbances at great distances from the moving cylinder are determined.The problems of viscous electroconductive flow about solid bodies in the presence of a magnetic field constitute one of the divisions of magnetohydrodynamics. Motion of an electroconductive medium in a magnetic field gives rise to inductive electromagnetic fields and currents which interact with the velocity and pressure hydrodynamic fields in the medium [1, 2]. Under conditions of sufficiently strong interaction, the number of independent flow similarity parameters in MHD is considerably greater than in conventional hydrodynamics. This circumstance complicates the theoretical analysis of MHD flow about bodies, and therefore we must limit ourselves to consideration of individual particular flow cases.Here we consider the linear problem of the motion of an infinite circular cylinder in a viscous incompressible medium with finite electroconductivity located in a uniform magnetic field.There are many studies devoted to the flow of a viscous electroconductive medium with a magnetic field about solid bodies (see, for example, [3–5]). Because of this, some of the results obtained here include previously known results, which will be indicated below. In contrast to the cited studies, the examination is made by the method of force sources, suggested in [6]. This method permits obtaining integral equations for the distribution of the forces acting on the surface of the moving body. Their solution is obtained for small Reynolds and Hartmann numbers. Then the nature of the velocity disturbances at great distances from the body are determined. These results are compared with conventional viscous flow about a cylinder in the Oseen approximation.     

Motion of a gas mixture through a porous medium with sorption

Solutions are investigated of a system of linear partial differential equations describing the motion of a gaseous (liquid) mixture through an undeformable homogeneous porous medium with sorption at interfaces between gaseous (liquid) and solid phases, the kinetics of which are described by a linear equation. If the porous medium consists of spherical granules, the problem is solved in quadratures. For the case of symmetric granules with arbitrary symmetry parameter, various approximate solutions are obtained; first and central moments are used as criteria for the accuracy of the approximations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 95–100, September–October, 1970.     

Motion of a rigid plastic cantilever in a damping medium under transverse impact

The motion of a rigid plastic cantilever beam which is surrounded by a damping medium and struck transversely at the tip by a moving mass is studied. The elementary theory, which disregards effects due to rate of straining and geometry changes is used. The governing equations of motion are integrated numerically. For comparison the case of discrete damping provided at the tip only is also solved. Results are presented for a wide range of parameters.     

New analysis of contact melting of phase change material around a hot sphere

The process of contact melting of the solid phase change material (PCM) around a hot sphere, which is driven by the temperature difference between the PCM and the sphere, is analyzed in this paper. Considering the difference of the normal angle between the sphere surface and the solid–liquid interface of the melting PCM, the fundamental equations of the melting process are derived with the film theory. The new film thickness and pressure distribution inside the liquid film and the variation law of the normal angle of the solid–liquid interface and the melting velocity of the sphere are also obtained. It is found that (1) while normal angle at sphere surface φ is within a certain value φ₀, which is related to Ste number and the outside force F, it has no obvious effect on the pressure distribution inside the liquid film and the numerical results by the present model are in accordance with the analytical results in the published literature, (2) the film thickness at φ = ±90° is constringent to a certain value and not the infinity, (3) the analytical results can be employed approximately to analyze the contact melting process except for the film thickness at φ = ±90°.     

Motion of a multicomponent sorbed mixture in a porous medium when the medium is preliminarily saturated with certain components of the mixture

The numerical and invariant solutions of a system of quasilinear equations in partial derivatives, describing the motion of a multicomponent sorbed gas (or liquid) mixture through a porous medium previously saturated by certain sorbed components of the mixture, are analyzed; in the presence of Langmuir sorption isotherms, invariant solutions are obtained in the form of Riemann invariants.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 50–56, January–February, 1976.