Melting heat transfer in steady laminar flow over a moving surface

The steady laminar boundary layer flow and heat transfer from a warm, laminar liquid flow to a melting surface moving parallel to a constant free stream is studied in this paper. The continuity, momentum and energy equations, which are coupled nonlinear partial differential equations are reduced to a set of two nonlinear ordinary differential equations, before being solved numerically using the Runge–Kutta–Fehlberg method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented for different values of the governing parameters. Effects of the melting parameter, moving parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined. It is found that the problem admits dual solutions.     

Direct numerical simulation of a liquid sheet in a compressible gas stream in axisymmetric and planar configurations

A thin liquid sheet present in the shear layer of a compressible gas jet is investigated using an Eulerian approach with mixed-fluid treatment for the governing equations describing the gas–liquid two-phase flow system, where the gas is treated as fully compressible and the liquid as incompressible. The effects of different topological configurations, surface tension, gas pressure and liquid sheet thickness on the flow development of the gas–liquid two-phase flow system have been examined by direct solution of the compressible Navier–Stokes equations using highly accurate numerical schemes. The interface dynamics are captured using volume of fluid and continuum surface force models. The simulations show that the dispersion of the liquid sheet is dominated by vortical structures formed at the jet shear layer due to the Kelvin–Helmholtz instability. The axisymmetric case is less vortical than its planar counterpart that exhibits formation of larger vortical structures and larger liquid dispersion. It has been identified that the vorticity development and the liquid dispersion in a planar configuration are increased at the absence of surface tension, which when present, tends to oppose the development of the Kelvin–Helmholtz instability. An opposite trend was observed for an axisymmetric configuration where surface tension tends to promote the development of vorticity. An increase in vorticity development and liquid dispersion was observed for increased liquid sheet thickness, while a decreasing trend was observed for higher gas pressure. Therefore surface tension, liquid sheet thickness and gas pressure factors all affect the flow vorticity which consequently affects the dispersion of the liquid.      

Skin friction measurements on reflective surfaces using nematic liquid crystal

 A new liquid crystal technique for full surface skin friction measurements is introduced. With the new technique, the transmission of light through nematic liquid crystal viewed in reflection provides a quantitative measurement of the skin friction. The measurement technique is discussed with the aid of a model which describes the rotation dynamics of the liquid crystal molecules. Calibration experiments performed in a laminar flow duct demonstrate that the model captures the essential physics of the new technique. The measurement of skin friction downstream of a three dimensional roughness element in an incompressible laminar boundary layer is then presented as a demonstration of the utility of the technique. Received: 5 June 1998/Accepted: 13 November 1998     

Experimental study on influence of microscale effects on liquid flow characteristic in microtubes

Using deioned water as a working fluid, the influence of the microscale effects on liquid flow resistance in microtubes with inner diameters of 19.6 and 44.2 μm, respectively, is experimentally studied. The temperature rise resulted from the microscale effects, such as viscous dissipation, electric double layer, wall rough on the wall surface, etc., is obtained by an IR camera with a special magnified lens adopting micro-area thermal image technology and the corresponding pressure drop and the flux are also measured, so the relationship among friction factor, temperature rise and Reynolds number is obtained. Investigation shows that experimental data are almost equal to those of Hagen–Poiseuille when Reynolds number is low. With the increase of Reynolds number, the values of the friction factor depart from that of classical theory due to the microscale effects. Moreover, the values of the experimental friction factor considering various microscale effects is the maximal 10–15% deviation from that of friction factor without considering various microscale effects with further increase of Reynolds number.     

Friction and Heat Transfer in a Laminar Separated Flow behind a Rectangular Step with Porous Injection or Suction

Results of a numerical study of a laminar separated flow behind a rectangular step on a porous surface with uniform injection or suction are described. Two cases are considered: an unconfined flow past a step and flow evolution in a confined channel (duct). It is shown that mass transfer on the surface causes strong changes in the flow structure and substantially affects the position of the reattachment point, as well as friction and heat transfer. More intense injection leads first to an increase in the separation-zone length and then to its rapid vanishing due to boundary-layer displacement. Vice versa, suction at high Reynolds numbers Re _s > 100 reduces the separation-zone length. The duct flow has a complicated distribution of friction and heat-transfer coefficients along the porous surface owing to the coupled effect of the transverse flow of the substance and changes in the main flow velocity due to mass transfer. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 18–28, January–February, 2006.     

Force interaction of a sphere and a viscous liquid in the presence of a wall

The problem of the force interaction of a vibrating sphere and a viscous liquid bounded from outside by a rigid wall at rest is studied under the assumption that the largest displacement of the sphere is small compared to its radius and the radius of the sphere is small compared to the distance between the sphere and the wall surface. The liquid flow and the force exerted by the liquid on the sphere are determined. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol 41, No. 1, pp. 57–62, January–February, 2000.     

Wave regimes on a nonisothermal film of a viscous liquid flowing down a vertical plane

A thin film flow of a viscous liquid flowing down a vertical wall in the field of the gravity force is studied. The values of temperatures on the solid wall and on the free surface are constant. The viscosity and thermal diffusivity are functions of temperature. An equation that describes the evolution of surface disturbances is derived for small flow rates in the long-wave approximation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 89–97, March–April, 2008.     

On local perturbations of a boundary layer with small skin friction

This paper studies the effect of two-dimensional surface irregularities on the flow in a plane steady boundary layer with small skin friction in an incompressible fluid. A detailed analysis is carried out for the flow regime with a given pressure gradient determined on the scale of the small irregularity by its shape. It is shown that there is a critical value of the height (depth) of the irregularity at which the skin friction first becomes zero, and the nonuniqueness of the corresponding solution is established. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 87–97, November–December, 1998. The work was financially supported by the Russian Foundation for Basic Research (project No. 97-01-00354).     

Strain-rate intensity factor in compression of a layer of a plastic material between cylindrical surfaces

A model problem for a rigid perfectly/plastic material is obtained. Based on this solution, it is possible to estimate the influence of the friction surface curvature and one of the types of additional rotational motion of the friction surface on the strain-rate intensity factor. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 171–180, May–June, 2009.     

Modeling of heat transfer in a turbulent flow around a heat-conducting plate with local regions of heating

A solution of the coupled nonstationary boundary-value problem of turbulent flow around a flat heat-conducting plate of finite thickness having local regions with volume heat sources is given. For modeling the heat transfer in the boundary layer, thek-ε turbulence model is used. It is shown that the thermal conductivity of the plate material significantly affects the surface distributions of both temperature and local friction. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 79–86, November–December, 1998. The work received financial support from the International Scientific and Engineering Center (project No.199).     

Flow of a thin layer of a viscous liquid over a dry surface

The problem of flow of a thin layer of a viscous liquid over a dry surface is formulated (ignoring surface tension). Examples of calculations are given. The results are compared with a solution using an appropriate one-dimensional model that admits an exact solution. Singularities of the solution are analyzed. Deceased. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 47–51, March–April, 1998.     

Convective structures in a thin layer of an evaporating liquid under an airflow

Evolution of convective structures in a thin layer of an evaporating liquid (ethanol) located under a turbulent boundary layer of an airflow is studied experimentally and theoretically. Evolution of the structures is examined under conditions of an increased flow velocity. A transition is found from convective cells formed in the absence of the flow to convective rolls elongated in the streamwise direction. The theoretical analysis is performed within a two-dimensional model of the flow in the liquid layer. The boundary conditions on the liquid surface are obtained with the use of self-similar solutions for mean fields in the airflow. The onset and evolution of a periodic system of rolls are simulated numerically. Theoretical conclusions are compared with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 3–14, July–August, 2007.     

Boiling heat transfer characteristics of nanofluids jet impingement on a plate surface

The jet boiling heat transfer of a bar water–CuO particle suspensions (nanofluids) jet impingement on a large flat surface was experimentally investigated. The experimental results were compared with those from water. The quantificational effects of the nanoparticles concentration and the flow conditions on the nucleate boiling heat transfer and the critical heat flux (CHF) were investigated. The experimental data showed that the jet boiling heat transfer for the water–CuO nanofluid is significantly different from those for water. The nanofluids have poor nucleate boiling heat transfer compared with the base fluid due to that a very thin nanoparticle sorption layer was formed on the heated surface. The CHF for the nanofluid increased compared with that of water. The reasons were that the solid–liquid contact angle decreased due to a very thin sorption layer on the heated surface and the jet and agitating effect of the nanoparticles on the subfilm layer enhance supply of liquid to the surface.     

Nonsimilar boundary-layer flow over a stationary permeable plate in a rotating fluid with a magnetic field

Summary  The nonsimilar boundary-layer flow and heat transfer over a stationary permeable surface in a rotating fluid in the presence of magnetic field, mass transfer and free stream velocity are studied. The parabolic partial differential equations governing the flow have been solved numerically by using a difference–differential method. For small streamwise distance, these partial differential equations are also solved by a perturbation technique with Shanks transformation. For uniform mass transfer, analytical solutions are obtained. The surface skin friction coefficients and the Nusselt number increase with the magnetic field, suction and streamwise distance from the leading edge of the plate except the skin friction coefficient in the y-direction which decreases with the increasing magnetic field. Received 4 December 2001; accepted for publication 24 September 2002     

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.     

Single cavitation bubble generation and observation of the bubble collapse flow induced by a pressure wave

This study utilizes a U-shape platform device to generate a single cavitation bubble for a detailed analysis of the flow field characteristics and the cause of the counter jet during the process of bubble collapse caused by sending a pressure wave. A high speed camera is used to record the flow field of the bubble collapse at different distances from a solid boundary. It is found that a Kelvin–Helmholtz vortex is formed when a liquid jet penetrates the bubble surface after the bubble is compressed and deformed. If the bubble center to the solid boundary is within one to three times the bubble’s radius, a stagnation ring will form on the boundary when impinged by the liquid jet. The fluid inside the stagnation ring will be squeezed toward the center of the ring to form a counter jet after the bubble collapses. At the critical position, where the bubble center from the solid boundary is about three times the bubble’s radius, the bubble collapse flow will vary. Depending on the strengths of the pressure waves applied, the collapse can produce a Kelvin–Helmholtz vortex, the Richtmyer–Meshkov instability, or the generation of a counter jet flow. If the bubble surface is in contact with the solid boundary, the liquid jet can only move inside-out without producing the stagnation ring and the counter jet; thus, the bubble collapses along the radial direction. The complex phenomenon of cavitation bubble collapse flows is clearly manifested in this study.     

Stability of a laminar rivulet liquid flow in a cylindrical duct in the approximation of one-dimensional waves

The problem of the stability of a viscous laminar liquid flow with a liquid free surface in an inclined duct is theoretically considered. Since the dependence of the flow rate on the free-surface height is not monotonic (the highest flow rate in a cylindrical duct is observed at H_*=1.7R), primary attention is given to the region H>H_*. It is proved that there is aw region of instability: for an arbitrarity low Reynolds number, there is a free-surface level above which the flow becomes unstable against one-dimensional disturbances. When the height of the liquid layer is close to the vertical dimension of the duct, the one-dimensional disturbances propagate mainly upstream (for moderate Reynolds numbers). Hence it follows that there is not steady regime of liquid flow from a fully filled duct with an open end. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 90–96, May–June, 1999.     

Effects of Viscous Dissipation on Unsteady Free Convection in a Fluid Past a Vertical Plate Immersed in a Porous Medium

The effects of viscous dissipation on unsteady free convection from an isothermal vertical flat plate in a fluid saturated porous medium are examined numerically. The Darcy–Brinkman–Forchheimer model is employed to describe the flow field. A new model of viscous dissipation is used for the Darcy–Brinkman–Forchheimer model of porous media. The simultaneous development of the momentum and thermal boundary layers are obtained by using a finite difference method. Boundary layer and Boussinesq approximation have been incorporated. Numerical calculations are carried out for various parameters entering into the problem. Velocity and temperature profiles as well as local friction factor and local Nusselt number are shown graphically. It is found that as time approaches infinity, the values of friction factor and heat transfer coefficient approach steady state.     

Motion of a flexible finite-length filament in a flow of a viscous fluid

The two-dimensional problem of the configuration of a flexible filament of finite length in a deformable viscous fluid is solved. The flexuural stresses in the filament and the inertial and gravitational forces are not taken into account. The equilibrium equations are obtained. The friction force that acts on the filament surface from the side of the viscous fluid is proportional to the flow rate. The specific features of the evolution of a bent filament under the conditions of pure and simple shear of a fluid are studied numerically. Analytical solutions are obtained for the evolution of a rectilinear filament; in particular, the stretching force in the filament is found. For the indicated types of flow, the stability of a rectilinear filament against small perturbations is investigated. Volzhskii Polytechnical Institute at the Volgograd State Technical University, Volgograd 404121. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 144–153, March–April, 2000.     

Explosive discharge of a gas-saturated liquid from channels and tanks

A mathematical model for the discharge of a gas-saturated liquid from cylindrical channels is developed. Two limiting cases of linear and quadratic, relations between the flow friction force and the flow velocity are considered. It is established that the process of evacuation, from a semi-infinite channel consists of two stages. In the initial stage, the flow drag can be ignored, and the process of discharge is described by a Riemann wave solution. For the next stage, in which inertia is insignificant, nonlinear equations are obtained and self-similar solutions are constructed for them. The problem of flow through a slot in a tank of finite volume is solved. It is shown that the discharge proceeds either in a gas-dynamic choking regime or in a subsonic regime, depending on the conditions inside the tank and at the outlet. Examples of numerical calculations are given. Institute of Mechanics, Ufa Scientific Center, Russian Academy of Sciences, Ufa 450000 Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 64–73, January–February, 1999.