Flow Of Viscous Incompressible Fluid Research Articles

Hydromagnetic Heat and Mass Transfer on a Permeable Flat Surface Embedded in a Porous Medium

The steady boundary layer viscous incompressible fluid flow on a permeable flat plate embedded in a porous medium has been considered in the present study. The momentum transport phenomena are subjected to external magnetic field, permeability of the porous medium and cross flow due to presence of suction and injection. Moreover, the heat transfer phenomena consider the loss of thermal energy due to radiation and mass transfer phenomena accounts for the generative/destructive chemical reaction of the reactive species as well. Most importantly, the temperature dependent viscosity and thermal conductivity of the fluid makes the present study more realistic. The numerical solution presented through graphs brings out the interesting outcomes: The higher rate of suction enhances the fluid temperature. This observation is akin to the fact that the higher suction brings the molecules closure hence the heat transfer increases. The porous medium, embedding the plate, acts as a coolant by reducing the fluid temperature.

Viscous fluid flow in a microchannel with hydrodynamic traps

Simulation of creeping flows in complex three-dimensional domains is crucial for microfluidics applications, creating multipurpose microfluidic devices, which are used, for example, to study multistage chemical reactions and as analytical devices in medicine.In this work we study the features of the incompressible viscous fluid flow in a flat microchannel with a nontrivial internal structure (the hydrodynamic traps of various configurations) under the constant pressure drop.The three-dimensional boundary element method, improved by utilization high-efficient fast multipole method and heterogeneous computational workstation, was used in numerical simulation.We studied the flow pattern around C-shaped hydrodynamic traps distributed in a flat microchannel and consisting of five cylindrical elements of the same size. Such geometry is widely used in microfluidic devices for fixing particles in the flow, for example, biological objects during tests in medicine. The influence of the distance between the rows of traps on the flow pattern and distribution of the longitudinal and transverse components of the flow velocity was considered.

EFFECT OF NON-UNIFORM HEAT SOURCE AND RADIATION ON UNSTEADY MHD FREE CONVECTION FLOW PAST AN INFINITE HEATED VERTICAL PLATE IN POROUS MEDIUM

Influence of radiation and non-uniform heat source on unsteady, magneto-hydrodynamic free convection flow of viscous incompressible fluid past an infinite vertical heated plate embedded in porous medium of an optically thin environment with time dependent suction and viscous dissipation is investigated in this paper. Analytical solutions of the coupled non-linear equations are obtained for the velocity field and temperature distribution using oscillating time-dependent perturbation technique. Expressions for skin-friction and heat transfer rate are also derived. The effects of the material parameters on velocity, temperature, skin-friction, and rate of heat transfer are discussed quantitatively.

Poisson bracket and integrals of motion in the problem of viscous fluid flow around an arbitrary flat contour

The Poisson bracket is used to find the integrals of motion. A numerical and analytical method is suggested to solve Navier-Stokes equations in Helmholtz form. The approximation of the sought solution by a linear combination of basis functions lies in this method’s core. The main idea behind this method is to select basis functions and generalized independent variables. A functional series is taken as the required solution, found from the equation’s solution obtained by equating the Poisson bracket to zero. The substitution of the selected solution into the Helmholtz equation reduces it to a nonlinear algebraic system. This system is solved analytically for a range of cases due to its structure. The authors present an algorithm for solving the boundary problem of viscous incompressible fluid flow around an arbitrary flat contour. In laminar flow around the body, the geometric dimension decreases, and the boundary problem is reduced to a linear system of algebraic equations. The solutions were tested on solving viscous fluid flow around a wedge and a thin plate.

On operator semigroups arising in the study of incompressible viscous fluid flows.

This article concentrates on various operator semigroups arising in the study of viscous and incompressible flows. Of particular concern are the classical Stokes semigroup, the hydrostatic Stokes semigroup, the Oldroyd as well as the Ericksen-Leslie semigroup. Besides their intrinsic interest, the properties of these semigroups play an important role in the investigation of the associated nonlinear equations. This article is part of the theme issue 'Semigroup applications everywhere'.

Analysis of MHD viscous fluid flow through porous medium with novel power law fractional differential operator

The present study deals with the unsteady and incompressible viscous fluid flow with constant proportional Caputo type fractional derivative (hybrid fractional operator). We find analytical solutions of a well-known problem in fluid dynamics known as Stokes’ first problem. MHD and porosity are also considered as an additional effects. Using dimensional analysis, governing equations of motion converted into non-dimensional form and then extended with novel fractional operator of singular kernel and series solutions are obtained by Laplace transform method. As a result, we compared present result with all the existing fractional operators and found that momentum boundary layer thickness can be control by changing the value of fractional parameter. Moreover, it is also observed that constant proportional Caputo type operator is well suited in exhibiting the decay of velocity of the fluid than all the existing fractional operators with power law (C), exponential law (CF) and Mittage-Leffler law (ABC).

On Marangoni shear convective flows of inhomogeneous viscous incompressible fluids in view of the Soret effect

A new exact solution is obtained for the Oberbeck-Boussinesq equations describing the steady-state layered (shear) Marangoni convection of a binary viscous incompressible fluid with the Soret effect. When layered (shear) flows are considered, the Oberbeck-Boussinesq system is overdetermined. For it to be solvable, a class of exact solutions is constructed, which allows one to satisfy identically the “superfluous” equation (the incompressibility equation). The found exact solution allows the Oberbeck-Boussinesq system of equations to be reduced to a system of ordinary differential equations by the generalized method of separation of variables. The resulting system of ordinary differential equations has an analytical solution, which is polynomial. The polynomial velocity field describes counterflows in the case of a convective fluid flow. It is demonstrated that the components of the velocity vector can have one stagnant (zero) point inside the region under study. In this case, the corresponding component of the velocity vector can be stratified into two zones, in which the fluid flows in opposite directions. The exact solution describing the velocity field for the Marangoni convection of a binary fluid has non-zero helicity, the flow itself being almost everywhere vortex.

Weighted Stepanov-Like Pseudo Almost Automorphic Solutions for Evolution Equations and Applications

In this paper, the existence and stability of (weighted) Stepanov-like pseudo almost automorphic solutions are proved for a large class of linear and semilinear evolution equations in interpolation spaces. Our method is based on the one hand on a combination of differential inequalities and interpolations functors for the case of linearized equation, and on the other hand on the fixed point argument for the semi-linear equations to handle the case of (weighted) Stepanov-like pseudo almost automorphic functions. Finally, we apply the abstract results to various problems of incompressible viscous fluid flows.

A dual mesh control domain method for the solution of nonlinear Poisson’s equation and the Navier–Stokes equations for incompressible fluids

In this study, the dual mesh control domain method, which employs the finite element approximation of the primary variables and the finite volume idea of satisfying the governing equations over a control domain, is used for the numerical solution of the Navier–Stokes equations governing the flows of viscous incompressible fluids using the penalty function formulation for two-dimensional analysis. The primal mesh is the mesh of finite elements used to interpolate the velocity field, while the dual mesh of control domains is used to satisfy the integral form of the Navier–Stokes equations, and thus, the method shares certain desirable features of the two popular methods. Numerical examples involving nonlinear Poisson’s equation and the Navier–Stokes equations are presented to illustrate the methodology and accuracy compared to the finite element and finite volume solutions, the latter depending on the scheme used to solve the discretized equations.

Stability of an Elastically Supported Cylinder in a Circular Viscous Fluid Flow

A system consisting of two cylinders (the inner cylinder is elastically supported and the outer cylinder is rigidly fixed) and a circulation flow of viscous incompressible fluid between them is considered. In the equilibrium position the cylinders are coaxial and the inner one rotates at a constant angular velocity Ω. An expression is obtained of the force acting on the inner cylinder from the side of the fluid in the approximation of large Reynolds numbers at a small deviation of the inner cylinder from its equilibrium position. It is shown that the force has a hereditary character and depends on the entire trajectory of motion. The stability of the position of the inner elastically supported cylinder is studied in the linear approximation taking into account the hereditary force acting on the inner cylinder.

Сравнительный анализ сил, действующих на поглощающий элемент системы управления и защиты в потоке вязкой несжимаемой жидкости, в зависимости от геометрии наконечника стержня и диаметра направляющего канала

Сравнительный анализ сил, действующих на поглощающий элемент системы управления и защиты в потоке вязкой несжимаемой жидкости, в зависимости от геометрии наконечника стержня и диаметра направляющего канала

Free convection MHD flow of viscous fluid by means of damped shear and thermal flux in a vertical circular tube

The main concern of the article is to study the hydromagnetic, free convection, and incompressible viscous fluid flow with generalized boundary conditions. The movement of the fluid is taken into account through a vertical circular tube. We built up a fractional model with the assistance of the constitutive shear stress equation and generalized type of Fourier’s Law. We’ve received closed-form solutions of the dimensionless fractional model by the way of Laplace and finite Hankel transform approach and received results are stated relating the G–function of Lorenzo and Hartley and in the generalized form of Mittag-Leffler. Graphically, the impacts of a choice of fractional and material variables are plotted by the use of Mathcad. The velocity is expanded by expanding the values of fractional factors and The boundary layer difference increment as time is expanded. The boundary layer difference and velocity are expanding by decreasing the value of the magnetic field.

Experimental validation of computational fluid dynamics for solving isothermal and incompressible viscous fluid flow

In order to validate a computational method for solving viscous fluid flows, experiments are carried out in an eccentric cylindrical cavity showing various flow formations over a range of Reynolds numbers. Especially, in numerical solution approaches for isothermal and incompressible flows, we search for simple experimental data for evaluating accuracy as well as performance of the computational method. Verification of different computational methods is arduous, and analytic solutions are only obtained for simple geometries like a channel flow. Clearly, a method is expected to predict different flow patterns within a cavity. Thus, we propose a configuration generating different flow formations depending on the Reynolds number and make the experimental results freely available in order to be used as an assessment criterion to demonstrate the reliability of a new computational approach.

Convective heat transfer in a tube filled with homogeneous and inhomogeneous porous medium

The aim of this study is to analyze the flow and heat transfer inside a straight tube filled with porous medium analytically and numerically. Steady incompressible viscous fluid flow through the porous medium is modeled using Darcy equation as well as Brinkman equation and the results are compared. Uniform heat flux boundary condition along with homogeneous/heterogeneous porous medium is considered. Closed-form solutions for velocity profile, temperature profile, and Nusselt number as a function of shape parameter (σ) are obtained. In the limiting case of infinite permeability, the results from Brinkman model reduce to that of Hagen-Poiseuille flow and in the limiting case of zero permeability, the results approach that of Darcy model. For both homogeneous and heterogeneous porous media, Darcy model is shown to provide an upper bound for Nusselt number. The theoretical results are validated using numerical simulations on COMSOL Multiphysics.

A numerical study of boundary layer flow of viscous incompressible fluid past an inclined stretching sheet and heat transfer using nonpolynomial spline method

In the present paper, we study the boundary layer flow of viscous incompressible fluid over an inclined stretching sheet with body force and heat transfer. Considering the stream function, we convert the boundary layer equation into nonlinear third‐order ordinary differential equation together with appropriate boundary conditions in an infinite domain. The nonlinear boundary value problem has been linearized by using the quasilinearization technique. Then, we develop a nonpolynomial spline method, which is used to solve the flow problem. The convergence analysis of the method is also discussed. We study the velocity function for different angles of inclination and Froude number with the help of various graphs and tables. Then using these in heat convection flow, we obtain the expression for temperature field. Skin friction is also calculated. The various results have been given in tables. At last, we calculated the Nusselt number.

Analytical solutions for some unsteady flows of fluids with linear dependence of viscosity on the pressure

New exact solutions for unidirectional unsteady flows of incompressible viscous fluids with linear dependence of viscosity on the pressure between two infinite horizontal parallel plates are established when the lower plate is moving in its plane with an arbitrary time-dependent velocity. In addition to being useful solutions to idealizations of technologically relevant problems such exact solutions also serve to test the validity and the efficacy of numerical schemes that have been developed for much more complicated three-dimensional flows. The flows considered herein correspond to important solutions in the study of the classical Navier-Stokes fluid model. General results which are obtained can generate exact solutions for any motion of this type of the respective fluids. For illustration, three special cases with technical relevance are considered, and the variations of the fluid velocity and the non-trivial shear stress are graphically presented and discussed in some situations. The exact solutions corresponding to some motions generated by an accelerated plate are connected to the adequate solutions of the simple Couette flow.

Numerical Simulation of the Water Surface Movement with Macroscopic Particles of Dam Break Flow for Various Obstacles

In this paper, the movement of the water surface with macroscopic particles during a dam break flow using the volume of fluid (VOF) methods and the DPM and MPM models were numerically simulated. The numerical simulation is based on the averaged Navier-Stokes equations, and was closed by the LES turbulent model, representing by the incompressible viscous fluid flow, equations for the phase and particle motion. The PISO numerical algorithm was chosen to solve this equation system numerically. The accuracy of the mathematical model and the selected numerical scheme were compared with experimental measurements on the destruction of the dam break problem. In test problem, the values were matched with measurement values and simulation data of other authors, as well as the improved model illustrated values close to the measured values. A matching was also made of the computational data with measured values using different turbulent models. One problem has been considered, the problem is water movement with macroscopic particles, through a heterogeneous terrain and a dam that has a hole. With the help of the problems, it was determined the flooding zones and the time of flooding evacuating people from dangerous areas.

Incompressible Viscous Flow Simulation Using the Quasi-Hydrodynamic Equations’ System

In this paper, we consider the problem of modeling viscous incompressible fluid flow using the quasi-hydrodynamic (QHD) system of equations. The use of this approach makes it possible to avoid instability in the pressure calculation when using the classical formulation of the Navier–Stokes equations, which is manifested when using cellular numerical schemes. For the numerical implementation of QHD equations, the finite volume method is used with cell-center approximation. In the case of a two-dimensional problem a square mesh is used. A cubic mesh is used in the case of a three-dimensional problem. Two series of calculations are performed for testing in areas of complex geometry for several Reynolds numbers. The results are compared with the ANSYS CFX software package. The comparison shows the high quality of the numerical simulation results using the QHD system of equations.

Numerical Simulation of Laminar Taylor–Couette Flow

The problem of the viscous incompressible fluid flow between two coaxial cylinders is considered in the case when the inner cylinder is rotates and the outer cylinder is stationary. The process of fluid flow is simulated by solving the three-dimensional Navier–Stokes equations. The computational algorithm is based on the finite volume method. The dependences of the dimensionless viscous torque from the Reynolds number and the radius ratio are established.

Structure-Preserving Numerical Approximations to a Non-isothermal Hydrodynamic Model of Binary Fluid Flows

We present two second order, structure-preserving numerical schemes for a newly derived thermodynamically consistent, non-isothermal hydrodynamical phase field model for incompressible binary viscous fluid flows. The schemes preserve the volume of each fluid phase, the total energy and the positive entropy production rate. The entropy quadratization approach is employed to devise the two semi-discrete numerical schemes in time, preserving both the total energy and the positive entropy production rate. The first scheme is weakly nonlinear, which is solved using iterative methods aided by fast Fourier algorithms. The second scheme is linear, in which a time-dependent supplementary variable is added to preserve the positive entropy production rate. The semi-discrete schemes are discretized in space by a finite difference method on staggered grids subsequently to yield two fully discrete schemes. Mesh refinement is carried out to confirm the order of the schemes and several numerical examples are provided to show hydrodynamic as well as thermal effects in resolving thermocapillary convection near the fluid interface in the incompressible binary viscous fluid flow.