Development of liquid flow in a plane channel with moving permeable walls

We determined the laws that govern the change in hydraulic resistance in viscous incompressible liquid flow between parallel permeable and moving walls. The laws are of great practical interest. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No.2, pp. 200–204, March–April, 1997.     

Approximate method for calculating turbulent two-phase flow in a channel with permeable walls

Based on a model of a double-velocity and two-temperature medium the authors constructed a system of equations that describes plane or axisymmetric turbulent flow of a gas suspension in a channel with permeable walls. The system of equations of motion and heat transfer reduces to a system of ordinary differential equations, whose integration is much less difficult than solution of the initial system. The authors obtained the distribution of the velocity and local characteristics of turbulence in the channel with injection with allowance for the inverse effect of a condensed phase.     

Numerical solution of micropolar fluid flow in a channel with porous walls

In this paper, we have studied the effect of suction on the laminar flow of a micropolar fluid in the entrance region of a porous channel. The velocity and the microrotation at the entry of the channel are taken to be those of Poiseuille flow of a micropolar fluid through a non porous channel. The similarity variables introduced into the partial differential system, governing the flow, lead to a set of ordinary nonlinear differential equations. The boundary value problem governing the flow is solved by a numerical method based upon quasilinearisation, parametric differentiation and extrapolation. The velocity profiles and the stream lines, presented graphically, reveal several interesting conclusions.     

Motion of a disperse system in a channel with permeable walls

The effect of filtration of the liquid phase through the channel walls on the hydraulic resistance is considered in the case of flow in a round tube. Depending on the flow parameters there may be either an increase or a significant reduction (up to 50–60%) in the hydraulic resistance in comparison with flow in a tube with impermeable walls.     

Hydrodynamic flow stability of a fluid with a power-law rheological behavior in a channel with elastic walls

The stability of steady gradiental flow of a non-Newtonian fluid with a power-law rheological behavior in a channel with elastic walls is analyzed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 24, No. 6, pp. 1099–1102, June, 1973.     

Numerical solution of heat transfer in micropolar fluid flow in a channel with porous walls

Using the basic equations of heat conducting micropolar fluid, heat transfer through a channel of porous walls has been studied. The temperature distribution is obtained for different values of suction parameter $\text{S}$, convective parameter $\text{E}$ and micropolar parameter $\text{R}$.     

Hydrodynamic characteristics of turbulent flow of an incompressible fluid in a channel with porous walls

The effect of a transverse mass flux and a pressure gradient on the shaping of the flow structure in a channel with porous walls is investigated.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 4, pp. 588–593, April, 1977.     

Viscous liquid flow in a channel with sinusoidal walls

An approximate solution is obtained for the problem of flow of a viscous incompressible liquid within a plane channel formed by uniformly spaced sinusoidally curved walls.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 4, pp. 582–585, April, 1982.     

Stokes flow through a channel with wavy walls

Summary Stokes flow is solved through a channel with three-dimensional wavy walls enclosed by two wavy walls whose amplitude is proportional to the mean clearance of the channel multiplied by the small dimensionless parameter ɛ. The application of an analytical-numerical algorithm yields efficient formulas for the velocities and permeability. These formulas include ɛ in symbolic form. When ɛ increases, the Poiseuille flow (ɛ=0) is disturbed and eddies can arise above a critical value ɛ =ɛ_e. These results are also successfully compared to the ones derived by a fully numerical solution.     

Stability of fluid flow in a plane channel with uniform injection or suction through porous walls

The stability of laminar flow in a channel with porous walls is analyzed within the scope of the linear theory.Notation x distance from entrance cross section - y transverse coordinate measured from axis - u_x, u_y longitudinal and transverse velocity components of main flow - h half-width of channel - kinematic viscosity coefficient - U₀ average velocity in entrance cross section - V suction or injection rate (positive for suction) - U=U₀–V_x/h local average velocity - amplitude of flow disturbances - wave number - c complex phase velocity of disturbances - c_r real propagation velocity of disturbances, =y/h - Re=Uh/ Reynolds number of main flow - R=Vh/ injection or suction Reynolds number - m=U/¦V¦ injection rate parameter Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 436–440, September, 1981.     

Porous slider bearing with couple stress fluid

Summary Theoretical study of porous slider bearing with couple stress fluid as lubricant is made and the lubrication qualities of couple stress fluid are examined. The lower surface is covered by a thin porous material and the upper one, having arbitrary shape, moves in its own plane with constant velocity. Analytical expressions for load capacity, frictional force and the centre of pressure are derived. It yields increase in, load capacity and ensures the decrease in coefficient of friction. The problem is also discussed in the context of various geometries viz, (1) Rayleigh step bearings and (2) inclined slider bearings. Bounds on flow rate, frictional coefficient, centre of pressure and time-height relation are obtained and compared with classical case, Gross [1]. Suitable design parameters are predicted for the efficient lubrication of slider bearings.     

A model of liquid flow in a channel with elastic walls

It is suggested to describe a liquid flow in a cylindrical round channel with elastic walls in terms of a two-fluid model used to describe the flow of He II in narrow capillaries near absolute zero. The idea is based on a similar (phonon-like) shape of the spectrum of elementary excitations at small wavenumbers k. The calculations show that the density ρ_n of a normal (i.e., viscous) liquid component (water in a steel tube) at 300 K is about 50 times smaller than the total density. This explains the paradox related to flow in a round tube for which anomalously large Reynolds numbers (Re∼10⁵) are observed. Since Re∼ρ_n, real Reynolds numbers must also be about 50 times as small, that is, on the same order of magnitude as those for a flow between planes under otherwise equal conditions. A physical reason for the appearance of superfluidity at high (∼300 K) temperatures is a decrease in repulsion between small density fluctuations in the liquid, which is related to their interaction being screened by elastic waves in the channel walls.     

Free convection effects on the oscillatory flow of a couple stress fluid through a porous medium

Summary Effects of free convection currents on the oscillatory flow of a polar fluid through a porous medium, which is bounded by a vertical plane surface of constant temperature, have been studied. The surface absorbs the fluid with a constant suction and the free stream velocity oscillates about a constant mean value. Analytical expressions for the velocity and the angular velocity fields have been obtained, using the regular perturbation technique. The effects of Grashof numberG; material parameters and ; Prandtl numberP; permeability parameterK and frequency parametern on the velocity and the angular velocity are discussed. The effects of cooling and heating of a polar fluid compared to a Newtonian fluid have also been discussed. The velocity of a polar fluid is found to decrease as compared to the Newtonian fluid.List of symbols C _p specific heat at constant pressure - g acceleration due to gravity - G Grashof number - K ⁺ permeability of the porous medium - K dimensionless permeability - P Prandtl number - t ⁺ time - t dimensionless time - T _w ⁺ mean temperature of the surface - T ⁺ temperature of the fluid - T ⁺ temperature of the fluid away from the surface - density of the fluid - viscosity - _r rotational viscosity - C _a ,C _d coefficients of couple stress viscosities - I a scalar constant of dimension equal to that of the moment of inertia of unit mass - x ⁺,y ⁺ coordinate system - u ⁺,v ⁺ velocity components in thex ⁺ andy ⁺ directions - u dimensionless velocity in thex ⁺-direction - ⁺ angular velocity component - dimensionless angular velocity - n ⁺ frequency of oscillations - n dimensionless frequency - perturbation parameter - U a constant velocity - u ₀ mean velocity - u ₁ fluctuating part of the velocity - ⁰ mean angular velocity - ¹ fluctuating part of the angular velocity - T ₀ mean temperature - T ₁ fluctuating part of the temperature - ⁰ coefficient of the volume expansion - kinematic viscosity - ^r rotational kinematic viscosity - , material parameters characterizing the polarity of the fluid - v ₀ suction velocity - density of the fluid far from the surface - y dimensionless coordinate normal to the surface     

Effect of variation of the physical properties of the gas on the stability of laminar nonisothermal flow in a channel with permeable walls

An investigation is made into the stability relative to small perturbations of a quasideveloped gas flow with variable physical properties in a plane channel in the presence of heating or cooling.     

Particle deposition on channel walls in a turbulent flow

The process of admixture deposition from a turbulent flow for different values of the particle reflection coefficient from the wall is analyzed. A generalizing formula is proposed for the computation of the deposition rate on a completely absorbing surface in a broad range of variation of the particle inertia.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 59, No. 5, pp. 735–742, November, 1990.     

Viscous liquid flow in the initial portion of a permeable channel with transverse slot

The problem of flow in the initial segment of a permeable channel with transverse impermeable slot is solved. Behavior of the solution with change in geometric parameters and characteristic injection Reynolds number is analyzed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 4, pp. 561–564, April, 1988.     

Hydromagnetic flow and heat transfer of a second-grade viscoelastic fluid in a channel with oscillatory stretching walls: application to the dynamics of blood flow

The characteristics of flow and heat transfer of a fluid in a channel with oscillatory stretching walls in the presence of an externally applied magnetic field are investigated. The fluid considered is a second-grade viscoelastic electrically conducting fluid. The partial differential equations that govern the flow are solved by developing a suitable numerical technique. The computational results for the velocity, temperature and the wall shear stress are presented graphically. The study reveals that flow reversal takes place near the central line of the channel. This flow reversal can be reduced to a considerable extent by applying a strong external magnetic field. The results are found to be in good agreement with those of earlier investigations.     

Turbulent fluid flow in a circular pipe with uniform blowing through porous walls

The average and fluctuating incompressible fluid flow characteristics in a circular pipe with blowing are computed on the basis of a three-parameter model of turbulence.Translated from Izhenerno-Fizicheskii Zhurnal, Vol. 41, No. 5, pp. 791–795, November, 1981.