Convective diffusion from a gas phase to a rotating disk

This paper presents a method for the analytical calculation of the flow velocity of the gas mixture and the concentration of the growth component during vapor-phase epitaxy in a reaction chamber with a rotating substrate holder disk. The concentration of the growth component is analyzed in relation to some epitaxy process parameters.     

Convective diffusion in fissured-porous media

The mixing of a dynamically neutral admixture added to a stream flowing through a homogeneous porous medium is described by an equation of the diffusion type with some effective diffusion coefficient which varies linearly with the filter velocity in the flow region in which Darcy's law is obeyed [1]. According to the ideas developed in a whole series of papers [2–4] this process, also called convective diffusion, is due to the irregular nature of the porous canals through which the liquid moves. Molecular effects also play a definite role in the mechanism of mixing, and their relative contribution is greater, the lower the filter velocity.This paper proposes equations for convective diffusion in fissuredporous media with due regard to the specific nature of mixing in these media. The solutions of some problems are given. In conclusion the author thanks Yu. P. Zheltov for suggesting the theme and guidance in the work, and G. I. Barenblatt and V. M. Entov for valuable comments.In conclusion the author thanks Yu. P, Zheltov for suggesting the theme and guidance in the work, and G. I. Barenblatt and V. M. Entov for valuable comments.     

Stability of thin film flowing down the outer surface of a rotating non-uniformly heated vertical cylinder

Nonlinear Dynamics - We investigated an incompressible viscous liquid film flow over a rotating vertical cylinder of radius R and of infinite length rotating with a uniform angular velocity...     

Convective diffusion in a periodic array of spheres for small reynolds numbers

It is shown that in flow past a system of spheres of radius a situated at the nodes of a cubic lattice with the period b in the direction of one of the principal translations of the lattice under the condition (a/b) · · P^1/31 (P is the Péclet number, P1), the concentration of dissolved material absorbed by the sphere surfaces diminishes logarithmically at distances large compared with b, but small compared with L=Pb²/4a. At distances considerably larger than L, the decrease is described by an exponential law which coincides with the law of concentration decrease at distances much larger than b in the case of a spatially homogeneous distribution of the spheres. We consider the flow of an incompressible fluid with the velocity U past a system of spheres of radius a. We assume that the Reynolds number R=Ua/ (where , the kinematic viscosity coefficient, is much larger than unity). Dissolved in the fluid is a material of concentration c which is absorbed by the sphere surfaces. The diffusion coefficient D is assumed to be sufficiently small for the Péclet number P=Ua/D to be much larger than unity. The spheres are situated at the nodes of a cubic lattice with the period b. As will be shown below, it is necessary that P(a/b)³1. Under these assumptions the concentration varies in a thin (of the order aP^–1/3) diffusion layer near the surface of each sphere. A diffusion wake is formed behind each sphere. The transverse dimensions of this wake for a sufficiently widely spaced lattice (aP^1/3 b) exceed the effective thickness of the diffusion boundary layer, which enables us to reduce the problem of concentration absorption on the surface of the system of spheres to the problem considered by Levich [1] concerning the convective diffusion of a material of constant constant concentration flowing past a single sphere.Hasimoto [2] considers the solution of the Stokes equation describing the motion of a viscous fluid past an array of spheres situated at the nodes of a cubic lattice. However, he does not give an expression for the velocity field applicable near the surface of some single sphere which is necessary to the solution of the diffusion problem.In the method of Lamb [3] (§336) and Burgers [4], in dealing with the flow of a viscous stream past a single sphere, one considers the equation of motion in space, including the interior of the sphere, and not just the solution of the equation in the space outside the sphere with boundary conditions at the sphere surface. At the center of the sphere one places a concentrated force and a system of multipoles whose magnitude is chosen in such a way as to ensure fulfillment of the required boundary conditions.This idea of introducing an effective potential is used in [2] to find the velocity field of a fluid flowing past an array of spheres. We propose a treatment of the effective potential method somewhat different from that of [2].The authors are grateful to V. G. Levich and V. S. Krylov for their comments.     

Convective instability in a two-layer system of reacting fluids with concentration-dependent diffusion

The development of convective instability in a two-layer system of miscible fluids placed in a narrow vertical gap has been studied theoretically and experimentally. The upper and lower layers are formed with aqueous solutions of acid and base, respectively. When the layers are brought into contact, the frontal neutralization reaction begins. We have found experimentally a new type of convective instability, which is characterized by the spatial localization and the periodicity of the structure observed for the first time in the miscible systems. We have tested a number of different acid–base systems and have found a similar patterning there. In our opinion, it may indicate that the discovered effect is of a general nature and should be taken into account in reaction–diffusion–convection problems as another tool with which the reaction can govern the movement of the reacting fluids. We have shown that, at least in one case (aqueous solutions of nitric acid and sodium hydroxide), a new type of instability called as the concentration-dependent diffusion convection is responsible for the onset of the fluid flow. It arises when the diffusion coefficients of species are different and depend on their concentrations. This type of instability can be attributed to a variety of double-diffusion convection. A mathematical model of the new phenomenon has been developed using the system of reaction–diffusion–convection equations written in the Hele–Shaw approximation. It is shown that the instability can be reproduced in the numerical experiment if only one takes into account the concentration dependence of the diffusion coefficients of the reagents. The dynamics of the base state, its linear stability and nonlinear development of the instability are presented. It is also shown that by varying the concentration of acid in the upper layer one can achieve the occurrence of chemo-convective solitary cell in the bulk of an almost immobile fluid. Good agreement between the experimental data and the results of numerical simulations is observed.     

Convective stability of a horizontal rotating fluid layer with distributed heat sources

The results of investigating the convective instability of a horizontal layer of rotating fluid, created by a temperature difference applied at the boundaries of the layer and by heat sources distributed according to various laws, are presented. It is shown that, when the other parameters of the problem are fixed, an increase in the internal heat release lowers the limits of both monotonic and oscillatory stability of the layer, increases the wave number and reduces the neutral oscillation frequency. An increase in source concentration towards the center of the layer intensifies the effect. As the strength of the internal heat sources and their concentration towards the center of the layer increase, the oscillating convection that develops at the stability limit when the Prandtl number is low and the rotation fairly fast is first replaced by monotonic convection and then ceases altogether.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 21–28, January–February, 1989.     

Convective boiling of halocarbon refrigerants flowing in a horizontal copper tube – an experimental study

An experimental study of convective boiling of refrigerants R-22, R-134a and R-404A in a 12.7 mm internal diameter, 2 m long, horizontal copper tube has been performed. Experiments involved a relatively wide range of operational conditions. Experiments were performed at the evaporating temperatures of 8°C and 15°C. Quality, mass velocity and heat flux varied in the following ranges: 5% to saturated vapor, 50–500 kg/(s m²); and 5–20 kW/m². Effects of these physical parameters over the heat transfer coefficient have been investigated. High quality experiments were also performed up to the point of the tube surface dryout, a mechanism which was investigated from the qualitative point of view. Two heat transfer coefficient correlations from the literature have been evaluated through comparisons with experimental data. Deviations varied in the range from −25% to 42%.     

Convective heat transfer to CO2 at a supercritical pressure flowing vertically upward in tubes and an annular channel

The Super-Critical Water-Cooled Reactor (SCWR) has been chosen by the Generation IV International Forum as one of the candidates for the next generation nuclear reactors. Heat transfer to water from a fuel assembly may deteriorate at certain supercritical pressure flow conditions and its estimation at degraded conditions as well as in normal conditions is very important to the design of a safe and reliable reactor core. Extensive experiments on a heat transfer to a vertically upward flowing CO₂ at a supercritical pressure in tubes and an annular channel have been performed. The geometries of the test sections include tubes of an internal diameter (ID) of 4.4 and 9.0 mm and an annular channel (8 × 10 mm). The heat transfer coefficient (HTC) and Nusselt numbers were derived from the inner wall temperature converted by using the outer wall temperature measured by adhesive K-type thermocouples and a direct (tube) or indirect (annular channel) electric heating power. From the test results, a correlation, which covers both a deteriorated and a normal heat transfer regime, was developed. The developed correlation takes different forms in each interval divided by the value of parameter Bu. The parameter Bu (referred to as Bu hereafter), a function of the Grashof number, the Reynolds number and the Prandtl number, was introduced since it is known to be a controlling factor for the occurrence of a heat transfer deterioration due to a buoyancy effect. The developed correlation predicted the HTCs for water and HCFC-22 fairly well.     

Convective motions in a porous medium heated from below

Convective motions in a porous medium filling a horizontal cylinder with a cross section of arbitrary shape and heated from below are studied. The small-parameter method is used to obtain infinitely many stationary motions forming a one-parameter family. For small values of the parameter, all of these motions are stable with respect to small perturbations. The article also discusses the case of heating which is not strictly vertical. It is found that in this case only one stationary motion is stable.     

Convective diffusion to a drop under arbitrary conditions of absorption. Diffusion boundary layer approximation

The diffusion boundary layer approximation is used to investigate the stationary convective diffusion of substance dissolved in a flow to a spherical drop under arbitrary conditions of absorption on its surface, in particular when a chemical reaction of arbitrary order takes place on the surface. An integral equation is obtained for the local diffusion flux to the surface of the drop. It is shown that 1) the total Sherwood number increases with increasing rate of the reaction and decreases with increasing exponent of the reaction rate; 2) with increasing Péclet number, saturation occurs (i.e., the total diffusion flux to the surface of the drop tends to a limiting value, which depends only on the reaction kinetics). The case of total absorption of diffusing, substance on the surface of reacting solid and liquid particles in a homogeneous Stokes flow at large Péclet numbers was investigated in [1]. The problem of convective diffusion to the surface of a solid spherical particle in the case of mixed kinetics was considered in [2, 3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 64–69, November–December, 1979.     

Interaction between a distributed source and the free surface of a viscous fluid

A self-similar solution of the Navier-Stokes equations describing steady-state axisymmetric viscous incompressible fluid flow in a half-space is investigated. The motion is induced by sources or sinks distributed over a vertical axis with a constant density. The horizontal plane bounding the fluid is a free surface. It is found that in the presence of sources a solution of the above type exists and is unique for any value of the Reynolds numberR > 0, but in the case of sinks only on the interval –2 R < 0. The results of calculating the self-similar solutions are presented. The asymptotics of the solutions are found asR 0 andR .Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 53–65, March–April, 1996.     

Effects of fluid recirculation on mass transfer from the arterial surface to flowing blood

The effect of disturbed flow on the mass transfer from arterial surface to flowing blood was studied numerically,and the results were compared with that of our previous work.The arterial wall was assumed to be viscoelastic and the blood was assumed to be incompressible and non-Newtonian fluid,which is more close to human arterial system.Numerical results indicated that the mass transfer from the arterial surface to flowing blood in regions of disturbed flow is positively related with the wall shear rates and it is significantly enhanced in regions of disturbed flow with a local minimum around the reattachment point which is higher than the average value of the downstream.Therefore,it may be implied that the accumulation of cholesterol or lipids within atheromatous plaques is not caused by the reduced efflux of cholesterol or lipids,but by the infiltration of the LDL(low-density lipoprotein) from the flowing blood to the arterial wall.     

Correct modeling for gaussian distributed heat source on a finite thin rod

One of the main problems which arise during the computation of welding processes is the development of a proper mathematical model for the distribution of heat Power Density of a moving heat source. Though there has been an extensive research done following Pavelic who had proposed a formula of a Circular Source of Heat (see Fassani (J Brazilian Soc Mech Sci 25:302–305, 2003) in 1969 for the first time, no one has yet been able to give a crucial scientific idea for determining the heat source parameters of Gaussian distributed spatial heat source. Due to lack of clear mathematical modeling of Gaussian distributed heat Power Density, an accurate formula needs to be developed. In this paper, I have proposed a completely new idea to define Gaussian distributed spatial heat source for the one dimensional case. A simple and relevant method has been adopted to elucidate the new idea.     

Convective heat transfer from a suddenly-developed horizontal hot spot

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 112–116, July–August, 1989.     

Periodic flow boiling in a non-uniformly heated microchannel heat sink

Hydrodynamic and thermal characteristics of flow boiling in a non-uniformly heated microchannel were studied. Experiments were performed with a single microchannel and a series of microheaters to study the microscale boiling of water under axially non-uniform heat input conditions. A simultaneous real time visualization of the flow pattern was performed with the measurement of experimental parameters. Tests were performed over a mass flux of 309.8 kg/m² s, and heat flux of 200–600 kW/m². Test results showed different fluctuations of heated wall temperature, pressure drop, and mass flux with variations of the heat input along the flow direction. The unique periodic flow boiling in a single microchannel was observed at all heat flux conditions except for the increasing heat input distribution case which is the nearly uniform effective heat input distribution condition. The instability is correlated with flow pattern transition. For the nearly uniform effective heating condition, no fluctuation of the wall temperature, pressure drop, or mass flux was observed. We can relieve the instability by increasing total heat input along the flow direction and predict the instability using the transition criteria and flow pattern map.     

Convective heat transfer from a rotating or nonrotating axisymmetric body

An analysis of steady laminar mixed-convection heat transfer from a rotating or nonrotating axisymmetric body is presented. A mixed-convection parameter is proposed to serve as a controlling parameter that determines the relative importance of the forced and the free convection. In addition, a rotation parameter is introduced to indicate the relative contributions of the flow forced convection and the rotational forced convection. The values of both these two parameters lie between 0 and 1. Furthermore, the coordinates and dependent variables are transformed to yield computationally efficient numerical solutions that are valid over the entire range of mixed convection from the forced-convection limit (rotating or nonrotating bodies) to the pure free-convection limit (non-rotating bodies) and the entire regime of forced convection from the pure flow forced-convection limit (nonrotating bodies) to pure rotational forced-convection limit (rotating bodies). The effects of mixed-convection intensity, body rotation, fluid suction or injection, and fluid Prandtl number on the velocity profiles, the temperature profiles, the skin-friction parameter, and heat transfer parameter are clearly illustrated for both cases of buoyancy assisting and opposing flow conditions.