Laminar Flow Of Viscous Fluid Research Articles

Plane-Parallel Laminar Flow of Viscous Fluid in the Transition Zone of the Inlet Section

A study was conducted to analyze how hydrodynamic parameters change in the entrance region of plane-parallel flow under stationary flow conditions, with an initial arbitrary distribution of velocities in the entrance section. This study was based on boundary layer equations, and a boundary problem was formed under the conditions of plane-parallel flow. The boundary conditions were chosen to reflect the pattern of arbitrary velocity distribution in the entrance section. A general solution of the approximating Navier-Stokes equations is provided, which depends on the initial conditions and the Reynolds number. The boundary conditions are established based on the nature of the motion, and the boundary value problem is described. A method for integrating the boundary value problem has been developed, and regularities for the change in velocities along the length of the inlet section have been obtained for both constant and parabolic velocity distributions in the entrance sections. Analytical solutions have been derived to obtain patterns of velocity and pressure changes in any given flow direction. Through computer analysis, velocity change patterns in various sections along the inlet transition area have been constructed, allowing for the determination of fluid velocity at any point on the section and an estimation of the length of the transition area. These proposed solutions provide a framework for accurately constructing individual units of hydromechanical equipment.

Symmetrisation of Laminar Flow of Viscous fluid in a Flat Diffuser by Periodic Influence on the Inlet Flow Velocity

The technique for symmetrisation of an asymmetric flow of a viscous incompressible fluid in a flat diffuser by means of a weak periodic vibration effect on the inlet flow is shown in the paper. The results are obtained for a viscous in-compressible fluid by modelling based on the numerical solution of the Navier-Stokes equations.

Laminar Viscous Fluid Flow with Micro-rotation Capabilities through Cylindrical Surface

Viscous fluid can micro-rotate due to collisions between particles that affect viscous fluid's velocity and temperature.This study aims to determine the effect of viscosity parameters, micro-rotation materials, and heat sources on fluid velocity and temperature. The model of the laminar flow equation for viscous fluid in this study uses the laws of physics, namely, the law of conservation of mass, Newton II, and Thermodynamics I. The formed dimensional equations are converted into non-dimensional equations by using non-dimensional variables. Then, the non-dimensional equations are converted into similarity equations using stream function and similarity variables. The formed similarity equation was solved numerically by using the Gauss-Seidel method. The results of this study indicate that the velocity and temperature of the viscous fluid flow can be influenced by the parameters of viscosity, micro-rotation material, and heat source. The presence of collisions between particles causes heat to cause an increase in the variance of viscosity parameters, micro-rotation materials, and heat sources. Therefore, the viscous fluid's velocity decreases and its temperature increases.

Laminar Flow of Viscous Fluid Around Elliptical Contours at an Angle of Attack

Laminar Flow of Viscous Fluid Around Elliptical Contours at an Angle of Attack

MHD flow study of viscous fluid through a complex wavy curved surface due to bio-mimetic propulsion under porosity and second-order slip effects

The steady laminar flow of viscous fluid from a curved porous domain under a radial magnetic field is considered. The fluid flow by a curved domain is due to peristaltic waves present at the boundary walls. The whole analysis is based on porosity (Darcy number) effects. Moreover, the effects of second-order slip on the rheology analysis are also discussed. Due to the complex nature of the flow regime, we have governed the rheological equations by using curvilinear coordinates in the fixed frame. The physical influence of magnetic (Hartmann number) and porosity (Darcy number) parameters on the rheological features of peristaltic transportation are argued in detailed (in the wave frame). Additionally, in the current study, the complex wavy pattern on both boundary walls of the channel is used. The whole rheological study is based on ancient, but medically valid, assumptions of creeping phenomena and long wavelength assumptions. Analytical solutions of the governing equations are obtained by using the simple integration technique in Mathematica software 11.0. The core motivation of the present analysis is to perceive the physical influence of embedded parameters, such as the dimensionless radius of the curvature parameter, magnetic parameter, porosity parameter, different amplitude ratios of complex peristaltic waves, first- and second-order slip parameters, on the axial velocity, pressure gradient, local wall shear stress, tangential component of the extra-stress tensor, pumping and trapping phenomena.

Effective Diffusivity for Transport with Fluctuating Drift Velocity.

Consider a particle whose drift velocity fluctuates due to transitions among discrete states or due to diffusion in a confined moving fluid. At long times, the dynamics of the particle in the direction of transport can be described in terms of the average drift velocity and an effective diffusivity. For both types of fluctuations, we show that the effective diffusivity is the sum of the average intrinsic diffusivity and the time integral of the velocity correlation function of the deviation of the fluctuating velocity from its mean value. For nearest-neighbor interstate transitions and for one-dimensional diffusion in a perpendicular direction, the time integral can be found in closed form. Our analytical expressions for the effective diffusivity recover the classic results for Taylor dispersion in the laminar flow of viscous fluid and for cargo transport along microtubules by molecular motors.

Effectiveness of Hall current and thermophysical properties in compressible flow of viscous fluid thorough spinning oscillatory disk

This study investigates the features of Hall current and thermophysical properties (viscosity, density and thermal conductivity) on unsteady, compressible, laminar flow of viscous fluid. Swirl flow is perceived by oscillatory movement of revolving disk. The well suited variables are adapted in order to achieve the non-similar system of expressions. The non-similar solutions are worked out numerically through scheme of finite differences and then utilizing Successive over Relaxation (SOR) technique. Physical parameters are discussed through one, two and three dimensional graphical forms. Tabular description of the resulting quantities is also formulated. The oscillatory thermal traces enhanced corresponding to increased magnetic parameter. An enhancement in Prandtl number contributes to lower down the thermal field but improves the rate of heat transportation.

Stokes flow and heat transfer past a circular cylinder in a square cavity with suction/injection on sidewalls

AbstractThe laminar viscous fluid flow past a circular cylinder placed in a square cavity of a uniform cross‐section is generated by applying injection/suction at the adjacent sidewalls. The temperature on the side walls without suction and on the boundary of the cylinder is kept constant, and constant heat flux is maintained on the walls with suction. The streamline flow pattern and isothermal lines are drawn. The flow is assumed to be Stokesian. Hence, the resulting biharmonic equation is solved for stream function by expressing it in two coupled equations, and a 5‐point formula is used to solve these equations. Fictitious nodes are introduced for derivative boundary conditions for stream function by using a central difference scheme, and a 3‐point backward difference formula is used for derivative boundary conditions on temperature.

Stokes flow and heat transfer past a circular cylinder in a square cavity with suction/injection on opposite-side walls

In this paper, we study laminar viscous fluid flow about a circular cylinder placed in a square cavity of uniform cross-section generated by applying injection/suction at the opposite-side walls. Constant temperature is maintained on the walls without suction and on the boundary of the cylinder and constant heat flux is maintained on the walls with suction. In the literature, the problems dealing with flow past a cylinder in a cavity are very a few. The fluid flow pattern in the form of stream lines and temperature distribution in the form of isothermal lines are studied. The flow is assumed to be Stokesian and hence the resulting coupled equations for stream function and vorticity, and the energy equation for temperature are solved numerically by using the standard 5-point formula. Fictitious nodes are introduced for derivative boundary conditions for stream function by using central-difference scheme and 3-point backward difference formula is used for derivative boundary conditions on temperature. It is observed that the temperature increases drastically when a cylinder is kept in the cavity, i.e. it makes the quick heat transfer. Similarly, when a cylinder is placed near to a corner, the heat transfer is more rapid. Suction enhances the heat transfer.

Entropy analysis for heat transfer in a rectangular channel with suction

AbstractThe purpose for this paper is to study heat transfer in a rectangular channel with suction applied at the adjacent two side walls. A two‐dimensional laminar viscous fluid flow is generated due to the application of suction/injection. The other two opposite sides are kept at a constant temperatures, and the walls with suction are maintained at a constant heat flux. The streamlines thus obtained due to the flow and isothermal lines and heat function are analyzed. The regions of high and low frictions are found by drawing contours of the entropy generation number and the Bejan number. The biharmonic equation for stream function is numerically solved by the Finite Difference Method (FDM) using a 13‐point formula, and a five‐point formula is used to solve for all other harmonic equations for temperature, heat function, and pressure. For derivative boundary conditions, the central difference formula with fictitious nodes is used. In the analysis, we note that the corner points are regions of high energy dissipation. The least dissipation of energy is near the wall, where the nondimensional temperature is 1. This paper analyzes heat transfer in the rectangular channel through the heat function and entropy generation number.

Flow Characteristics in Coaxial Channels with Three Helical Fins of Annular Gap

The helical coordinate system is used for mathematical description of laminar viscous fluid flows in channels with three helical fins of annular gap. The mathematical model in which the equations of motion are written in projection on the directions of natural basis of the helical coordinate system is suggested. The distributions of flow characteristics in channels with long triple screw inserts of various geometry are analyzed on the basis of the numerical results obtained for the Reynolds numbers up to 806.

On the Analysis of Laminar Flow of Viscous Fluid through a Porous Channel with Suction/Injection at Slowly Expanding or Contracting Walls

The vast biological and industrial applications of laminar flow of viscous fluid through a porous channel with contracting or expanding permeable wall have attest to the importance of studying the flow process. In this paper, two-dimensional flow of viscous fluid in a porous channel through slowly expanding or contracting walls with injection or suction is analyzed using variation parameter method. From the parametric studies using the developed approximate analytical solutions, it is shown that increase in the Reynolds number of the flow process leads to decrease in the axial velocity at the center of the channel during the expansion. The axial velocity increases slightly near the surface of the channel when the wall contracts at the same rate. Also, as the wall expansion ratio increases, the velocity at the center decreases but it increases near the wall. The results of the approximate analytical solution are verified by numerical solution using shooting method coupled with Runge-Kutta method. The results of the variation parameter method are in excellent agreement with the results obtained using numerical method.

Numerical Model for Laminar Flow in Agitated Vessel by tow Blades Impeller

A large number of chemicals, biochemical or petrochemical industry operations are performed in stirred tanks or in mechanically agitated vessels. The optimum operating mode of these equipments requires a detailed knowledge of the hydrodynamic behavior induced by the agitator. In this piece of work the characterization of the laminar viscous fluid flow fields in a cylindrical stirred tank is agitated by inclined blades anchor agitator studied. The computational fluid dynamic (CFD) model based on an implicit fractional step scheme and control volume method was developed for the spatial discretization of the Navier-Stokes, formulated in Cartesian coordinates primitives variables (u, v, p, T) on unstructured triangular mesh. Some simulations of the flow around an anchor with straights blades allowed validating the used method. We have analyzed the influence of the tilt blades degree on the hydrodynamic flow behaviors, such as the stream function, the velocity field, the velocities components, and the power consumption. The comparison between some of the obtained results with literature data, have showed a satisfactory agreement.

Aris-Taylor dispersion in tubes with dead ends.

This paper deals with transport of point Brownian particles in a cylindrical tube with dead ends in the presence of laminar flow of viscous fluid in the cylindrical part of the tube (Poiseuille flow). It is assumed that the dead ends are identical and are formed by spherical cavities connected to the cylindrical part of the tube by narrow necks. The focus is on the effective velocity and diffusivity of the particles as functions of the mean flow velocity and geometric parameter of the tube. Entering a dead end, the particle interrupts its propagation along the tube axis. Later it returns, and the axial motion continues. From the axial propagation point of view, the particle entry into a dead end and its successive return to the flow is equivalent to the particle reversible binding to the tube wall. The effect of reversible binding on the transport parameters has been previously studied assuming that the particle survival probability in the bound state decays as a single exponential. However, this is not the case when the particle enters a dead end, since escape from the dead end is a non-Markovian process. Our analysis of the problem consists of two steps: First, we derive expressions for the effective transport parameters in the general case of non-Markovian binding. Second, we find the effective velocity and diffusivity by substituting into these expressions known results for the moments of the particle lifetime in the dead end [L. Dagdug, A. M. Berezhkovskii, Yu. A. Makhnovskii, and V. Yu. Zitserman, J. Chem. Phys. 127, 224712 (2007)]. To check the accuracy of our theory, we compare its predictions with the values of the effective velocity and diffusivity obtained from Brownian dynamics simulations. The comparison shows excellent agreement between the theoretical predictions and numerical results.

Unsteady three-dimensional model of electric arc. Part 1. Mathematical model and testing results

A non-stationary three-dimensional mathematical model of the electric arc of constant current in the approximation of a partial local thermodynamic equilibrium of plasma is presented. For the purpose of testing the model and computer code a computation of the isothermal laminar viscous fluid flow past a circular cylinder (the testing of the dynamic part of the system of equations) and a computation of the axisymmetric electric arc with a reduced anode attachment have been done. A fair agreement of numerical results with experimental data points overall to the correctness of the mathematical model and the numerical solution technique.

A transmission line model of the human foetal circulatory system

A transmission line model of the human foetal circulatory system is presented. The model has been developed in the frequency domain with the cardiac input modeled as a flow rather than as a pressure pulse and is structured upon electrical transmission line analogies. The model is formed by cascading solutions to the two-dimensional Navier–Stokes equations for both oscillatory and steady, laminar viscous fluid flow in isotropic visco-elastic tubes with thick walls, which are constrained by surrounding tissues. Simulations allow for representation of both forward and retrograde travelling flow and pressure waves in all of the main foetal arterial vessels. The solution is verified by a comparison of model generated Doppler indices in the thoracic aorta, abdominal aorta, iliac artery and both ends of the umbilical arteries with previously published indices obtained by clinical measurements in these arteries. For simulations of blood flow in a healthy foetus, the model generated Pulsatility and Resistance indices were on average within 8% of the corresponding clinical measurements. The model results also demonstrates that placental resistance must increase by a factor of three, corresponding to a 60% decrease in flow to the placenta, before umbilical arterial absent end diastolic flow is observed. Differences between indices obtained from simulations at opposite ends of the umbilical arteries increase with increasing placental resistance.

Motion of a nonrectilinear fiber in a viscous fluid flow

The plane problem of dynamic interaction of a laminar viscous fluid flow and an inextensible pliable fiber of finite length is solved using the perturbation method. Two types of rheological two‐dimensional flows — pure shear and simple shear — are considered. Formulas are obtained for the evolution of the tensile force and the shape of the fiber. Results of asymptotic and numerical calculations are compared.

Pressure correction DRBEM solution for heat transfer and fluid flow in incompressible viscous fluids

The Dual Reciprocity Boundary Element Method (DRBEM) is used to solve incompressible laminar viscous fluid flows and heat transfer. The DRBEM is extended to develop a pressure correction scheme to solve the incompressible Navier-Stokes equations. The velocity field is then used as input to the DRBEM solution of the energy transport equation, thereby retaining the boundary only discretization feature of the BEM for the solution of this problem. Numerical results for the proposed DRBEM solution for laminar flow and heat transfer in a channel are obtained for several Reynolds numbers and compare well with previously published data.

Control of Temperature Distribution at Cylinder Surface by Magnetic Fluid

The present study deals with the influence of a magnetic fluid coating, held onto a circular cylinder surface by a magnetic field, on the temperature distribution at the surface of a cylinder heated by a constant heat flux. The temperature distribution over the cylinder surface in the fluid is determined by the heating power of the cylinder and the incoming flow structure. The flow structure near the cylinder can be changed by applying a magnetic fluid coating over its surface and by holding it with a magnetic field. In this case, heat from its surface to the external flow is removed by two modes. First, the heat is transferred to the external flow due to heat conduction of the magnetic fluid. Second, the heated layers of the magnetic fluid are entrained due to circulation and give up their heat to the external flow at the interface. Thus, there are two mechanisms of removing the heat inside the magnetic-fluid coating: conductive and convective. The balance of these two mechanisms is determined by the circulation intensity inside the coating and by the value of magnetic fluid thermal conductivity. A steady laminar flow of viscous fluid past a circular cylinder with magnetic fluid kept on its sur-face under a magnetic field is investigated numerically by finite-element method. A grid of 5751 nodes is used. The cases of Reynolds number Re = 10, 30, 100 are considered. The role of heat conduction ratio is determined for the meanings A = 0.1, 1, 10. The great influence of magnetic fluid coating on surface temperature distribution is discovered in the paper. The distribution can be profitably varied by the magnetic fluid properties and flow velocity: it can be nonmonotonic, and the temperature of a solid can increase in the direction opposite to the direction of fluid flow.

Laminar forced convection heat transfer in rectangular ducts rotating about an axis parallel to duct axis.

Fully developed steady laminar flow of viscous fluid in straight rectangular ducts rotating about a parallel axis is analyzed numerically. Thermal boundary condition of axially uniform wall heat flux is considered. Numerical results of flow and temperature field in ducts with aspect ratio from 0.2 to 5 are obtained for ReRaΩ number upto 6.725×106 (for Re numbers upto 1346) and Prandtl number from 0.3 to 400. At low to moderate ReRa numbers, a double-vortex secondary flow is exist under the influence of buoyancy due to centrifugal force field. It is found that a pair of additional vortices appear and disappear for higher range of ReRaΩ numbers. It is shown that tritical number of ReRaΩ for onset of additional vortices is affected by Prandtl number and aspect ratio. The friction factor and Nusselt number are pressented. The solution is compared with other analyses.