Boundary layer laminarization on a thermally insulated surface with energy supply to the flow

A subsonic stream of gas flowing over a thermally insulated plate and having an elevated temperature in a thin layer adjacent to the surface is considered. This temperature distribution in the flow can be obtained by providing a volume energy supply near the leading edge of the plate. The results of calculating the position of the line of laminar-turbulent transition on the basis of linear stability theory and the e^N method are presented. It is shown that the presence of a heated layer of gas near the surface of the plate leads to an increase in the stability of the laminar flow and an extension of the laminar interval of the boundary layer. A nonmonotonic dependence of the length of the laminar interval on the thickness of the heated layer of gas is detected. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 58–61, September–October, 1988.     

Dynamics of a fluid sheet on a curved rigid wall with allowance for phase transformation on the free surface

The flow of a three-dimensional sheet on a curved wall is considered. Gravity and surface tension forces act on the sheet while a droplet stream falls on its free surface. The systems of equations of viscous incompressible fluid dynamics on a curved rigid surface and the boundary conditions with allowance for the falling droplet stream are formulated. The problems of steady axisymmetric motion of the sheet on cylindrical and conical surfaces are considered. The effect of the curvature of the rigid wall on the solution is examined. Kharkov. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 42–50, July–August, 1994.     

Circulation flow around airfoils by a steady plane-parallel flow of a heavy liquid of finite depth with a free surface

Steady problems of a circulation flow around bodies by a flow of a heavy liquid bounded by a free surface and a straight bottom are solved. The method of complex boundary elements is used, which is based on the integral Cauchy formula written for a complex-conjugate velocity. Results of numerical calculations of the flow around a circular contour and the Joukowski airfoil are presented. Shapes of the free surface and the most important hydrodynamic characteristics of the process (velocity circulation over the airfoil and the lifting force and its moment relative to the sharp edge of the airfoil) are given. Kemerovo State University, Kemerovo 650043. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 101–110, May–June, 2000.     

Approximate method for determining the maximum temperature during quasistationary heating of a piecewise-homogeneous half-space

A method is proposed to calculate the maximum temperature of the surface of a piecewise-homogeneous half-space heated by a uniformly moving, locally distributed heat flow. Analytical solutions of the corresponding quasistationary heat-conduction problems are obtained for small and large values of the Peclet number. These solutions are used to derive formulas for calculating the maximum temperature in the case of intermediate (moderate) values of the Peclet number. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 85–97, May–June, 2005.     

Eigenoscillations of an elastic body with a rough surface

Explicit presentations for the initial terms of the asymptotic solution of the spectral problem of the elasticity theory in a plane region with a rapidly oscillating boundary are obtained. Based on asymptotic formulas, two methods for problem modeling are proposed: with the use of Wenzel’s boundary conditions and with the use of the principle of a smooth image of a singularly perturbed boundary. Various approaches to justification of asymptotic presentations are discussed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 103–114, November–December, 2007.     

Motion of a hot wedge in a melting medium

In [1–3] a series of problems of the motion of heat sources at a temperature higher than the melting point of the surrounding medium was considered. The heat source could be a laser beam or a hot body. Here, the case of a thin wedge heated to a temperature higher than the melting point of the surrounding medium and moving at a constant velocity is investigated. The velocity is high enough for the molten layer formed to be thin. The problem is solved by the method of integral relations. The shape of the molten zone, the drag on the wedge and other flow characteristics of the melt are determined. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 52–57, September–October, 1988.     

Fully Coupled THMC Modeling of Wellbore Stability with Thermal and Solute Convection Considered

Wellbore stability analysis is an important topic in petroleum geomechanics. Analytical and numerical analysis of wellbore stability involves the study of interactions among pressure, temperature and chemical changes, and the mechanical response of the rock, a coupled thermal–hydraulic–mechanical–chemical (THMC) process. Thermal and solute convection have usually been overlooked in numerical models. This is appropriate for shales with extremely low permeability, but for shales with intermediate and high permeability (e.g., shale with a disseminated microfissure network), thermal and solute convection should be considered. The challenge of considering advection lies in the numerical oscillation encountered when implementing the traditional Galerkin finite element approach for transient advection–diffusion problems. In this article, we present a fully coupled THMC model to analyze the stress, pressure, temperature, and solute concentration changes around a wellbore. In order to overcome spurious spatial temperature oscillations in the convection-dominated thermal advection–diffusion problem, we place the transient problem into an advection– diffusion-reaction problem framework, which is then efficiently addressed by a stabilized finite element approach, the subgrid scale/gradient subgrid scale method (SGS/GSGS).     

Temperature dependent viscosity and thermal conductivity effects on combined heat and mass transfer in MHD three-dimensional flow over a stretching surface with Ohmic heating

An analysis has been carried out to obtain the flow, heat and mass transfer characteristics of a viscous electrically conducting fluid having temperature dependent viscosity and thermal conductivity past a continuously stretching surface, taking into account the effect of Ohmic heating. The flow is subjected to a uniform transverse magnetic field normal to the plate. The resulting governing three-dimensional equations are transformed using suitable three-dimensional transformations and then solved numerically by using fifth order Runge–Kutta–Fehlberg scheme with a modified version of the Newton–Raphson shooting method. Favorable comparisons with previously published work are obtained. The effects of the various parameters such as magnetic parameter M, the viscosity/temperature parameter θ _r , the thermal conductivity parameter S and the Eckert number Ec on the velocity, temperature, and concentration profiles, as well as the local skin-friction coefficient, local Nusselt number, and the local Sherwood number are presented graphically and in tabulated form.     

Theories of ideal plasticity with a singular yield surface

Specific features of the theories of ideal plasticity which are based on the Tresca yield criterion and the maximum reduced stress criterion are discussed. An analysis is carried out in terms of the canonical basis of the deviatoric stress tensor. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 181–188, March–April, 1999.     

Mass transfer effects on the non-Newtonian fluids past a vertical plate embedded in a porous medium with non-uniform surface heat flux

 The present study is devoted to investigate the influences of mass transfer on buoyancy induced flow over vertical flat plate embedded in a non-Newtonian fluid saturated porous medium. The Ostwald–de Waele power-law model is used to characterize the non-Newtonian fluid behavior. Similarity solution for the transformed governing equations is obtained with prescribed variable surface heat flux. Numerical results for the details of the velocity, temperature and concentration profiles are shown on graphs. Excess surface temperature as well as concentration gradient at the wall associated with heat flux distributions, which are entered in tables, have been presented for different values of the power-law index n, buoyancy ration B and the exponent λ as well as Lewis number Le. Received on 26 April 2000     

Interaction of surface radiation with combined conduction and convection from a discretely heated L-corner

Prominent results pertaining to the problem of multi-mode heat transfer from an L-corner equipped with three identical flush-mounted discrete heat sources in its left leg are given here. The heat generated in the heat sources is conducted along the two legs of the device before being dissipated by combined convection and radiation into air that is considered to be the cooling agent. The governing equations for temperature distribution along the L-corner are obtained by making appropriate energy balance between the heat generated, conducted, convected and radiated. The non-linear partial differential equations thus obtained are converted into algebraic form using a finite-difference formulation. The resulting equations are solved simultaneously by Gauss–Seidel iterative solver. A computer code is specifically written to solve the problem. The computational domain is discretised using 101 grids along the left leg, with 15 grids taken per heat source, and 21 grids along the bottom leg. The effects of surface emissivity, convection heat transfer coefficient, thermal conductivity and aspect ratio on local temperature distribution, peak device temperature and relative contributions of convection and radiation to heat dissipation from the L-corner are studied in detail. The point that one cannot overlook radiation in problems of this class has been clearly elucidated.     

Control of the surface of a sectioned bimorph plate

Rostov State University. Rostov State Technical University, Rostov-on-Don 344000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 36, No. 4, pp. 131–136, July–August, 1995.     

Comparison of four different versions of the variable metric method for solving inverse heat conduction problems

In this study, four different versions of the variable metric method (VMM) are investigated in solving standard one-dimensional inverse heat conduction problems in order to evaluate their efficiency and accuracy. These versions include Davidon–Fletcher–Powell (DFP), Broydon–Fletcher–Goldfarb–Shanno (BFGS), Symmetric Rank-one (SR1), and Biggs formula of the VMM. These investigations are carried out using temperature data obtained from numerical simulations.     

Reliable treatment of a new analytical method for solving MHD boundary-layer equations

The purpose of this study is to implement a new analytical method which is a combination of the homotopy analysis method (HAM) and the Padé approximant for solving magnetohydrodynamic boundary-layer flow. The solution is compared with the numerical solution. Comparisons between the HAM–Padé and the numerical solution reveal that the new technique is a promising tool for solving MHD boundary-layer equations. The effects of the various parameters on the velocity and temperature profiles are presented graphically form. Favorable comparisons with previously published works (Crane, J. Appl. Math. Phys. 21:645–647, 1970, and Vajravelu and Hadjinicolaou, Int. J. Eng. Sci. 35:1237–1244, 1997) are obtained. It is predicted that HAM–Padé can have wide application in engineering problems (especially for boundary-layer and natural convection problems).     

Some primal problems of the axisymmetric theory of elasticity for space with a flat slit bounded by a circle

We consider the first and second primal problems of the axisymmetric theory of elasticity for space with a round slit and a mixed problem in which forces are specified on one side of the slit and displacements are specified on the other side. The problems reduce to conjugation problems for generalized analytic functions on rectilinear segments, whose solution is obtained in closed form. Institute of Applied Mechanics, Russian Academy of Sciences, Moscow 117334. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1 pp. 144–151, January–February, 2000.     

Effect of surface and internal waves on the hydrodynamic characteristics of a contour in the linear approximation

A method of solving the problem of the motion of an elliptic contour in a three-layer fluid is developed within the framework of the linear theory. The results of calculating the hydrodynamic contour loads and the shape of the interfaces are presented for the following problems: the motion of a contour beneath an interface between two media and in a two-layer fluid both beneath a rigid lid and a free surface. On the basis of the numerical experiment it is concluded that surface and internal waves have a significant effect on the hydrodynamic characteristics of the contour. Omsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 121–127, May–June, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00093).     

Evolution of perturbations on the surface of a viscoelastic liquid

The stability of a layer of a viscoelastic liquid on an inclined plane is studied within the framework of the model with a time-dependent “memory” in the presence of surface tension. It is shown analytically and numerically that these flows can be stable or unstable depending on the Reynolds number. Profiles of the free surface are found as functions of the Reynolds and Weber numbers. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 86–91, May–June, 2000.     

Exhaustion of a thin film of a nonlinear-viscous fluid from a slot with slipping relative to the underlying surface

The problem of exhaustion of a thin film of a non-Newtonian fluid with a power rheological law from a slotted orifice is solved with account of film slipping relative to the underlying surface. By the method of group analysis with transformation of the parameters entering the problem, an asymptotic formula for the film profile is obtained and a law of motion of the film edge with small slipping is derived. Kazan' State University, 420008 Kazan'. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 71–76, March–April, 2000.     

Numerical simulation of stabilization of the boundary layer on a surface with a porous coating in a supersonic separated flow

Stability of a supersonic (M _∞ = 5.373) boundary layer with local separation in a compression corner with a passive porous coating partly absorbing flow perturbations is considered by solving two-dimensional Navier-Stokes equations numerically. The second mode of disturbances of a supersonic boundary layer is demonstrated to be the most important one behind the boundary-layer reattachment point. The possibility of effective stabilization of these disturbances behind the reattachment point with the use of porous coatings is confirmed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 39–47, March–April, 2007.