Steady Flow Of Viscous Incompressible Fluid Research Articles

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.

Numerical Solution of the Problem of Incompressible Fluid Flow in a Plane Channel with a Backward-Facing Step at High Reynolds Numbers

Numerical solutions of the problem of steady incompressible viscous fluid flow in a plane channel with a backward-facing step have been obtained by the grid method. The fluid motion is described by the Navier–Stokes equations in velocity-pressure variables. The main computations were performed on a uniform 6001 × 301 grid. The control-volume method of the second order in space was used for the difference approximation of the original equations. The results were validated for the range of Reynolds numbers (100 ≤ Re ≤ 3000) by comparing them with the experimental and theoretical data found in the literature. The stability of the computational algorithm at high Reynolds numbers was achieved by using a fine difference grid (a small grid step). The study has been carried out for a short channel at Reynolds numbers from 1000 to 10 000 with a step of 1000. A nonstandard structure of the primary vortex behind the step—the presence of numerous centers of rotation both inside the vortex and in the near-wall region under it—has been revealed. The number of centers of rotation in the primary recirculation zone is shown to grow with increasing Reynolds number. The profiles of the coefficients of friction and hydrodynamic resistance to the flow as a function of Reynolds number have also been analyzed. The results obtained can be useful for comparison and validation of the solutions of problems of such a type.

Modeling of Steady Flows in a Channel by Navier–Stokes Variational Inequalities

A mathematical model of a steady viscous incompressible fluid flow in a channel with exit conditions different from the Dirichlet conditions is considered. A variational inequality is derived for the formulated subdifferential boundary-value problem, and the structure of the set of its solutions is studied. For two-ption on the low Reynolds number is proved. In the three-dimensional case, a class of constraints on the tangential component of velocity at the exit, which guarantees solvability of the variational inequality, is found.

Asymptotic stability of higher order norms in terms of asymptotic energy stability for viscous incompressible fluid flows heated from below

We consider a steady viscous incompressible fluid flow in an infinite layer heated from below. The steady flow is assumed to be periodic with respect to the plane variables. If this flow turns out to be asymptotically energy-stable with respect to a particular disturbance then it is also asymptotically stable in higher order norms with respect to the same perturbation. No smallness of the initial values is needed.

Hall effects on temperature distribution in a rotating ionized hydromagnetic flow between parallel walls

Steady viscous incompressible fluid flow between two parallel walls has been analysed in the presence of a uniform magnetic field applied transversely to the flow and when rotated at an angular velocity about an axis perpendicular to the walls, taking Hall currents into account. It is assumed that the magnetic Reynolds number is small. The governing equations of motion accounting for the primary and secondary velocity distributions have been obtained by Raju (Ph.D. thesis, Andhra University, India). These expressions have now been made use of to calculate the temperature distribution when the temperature of the two walls have been prescribed to be the same. The behaviour of the heat transport is discussed numerically in detail for various governing parameters involved. Two cases of interest when the walls have been made up of (i) non-conducting and (ii) conducting materials have been considered. It is observed in the case of non-conducting walls that the temperature distribution is found to be independent of the partial pressure of the electron gas s (ratio of the electron pressure to the total pressure). Also it is found in the case of conducting walls that the temperature distribution decreases with increasing values of the rotation parameter for fixed Hartmann number and Hall parameter.

A Note on the Numerical Treatment of Navier-Stokes Equations. II

The steady viscous incompressible fluid flow past an arbitrary symmetric cylindrical obstacle being in the middle of two parallel walls is treated, and method to find its numerical solution is given. By an application of the theory of conformal mapping, the problem is reduced to a boundary value problem of partial differential equations on a rectangular domain. Then the difference analogue of the problem on the rectangular domain can be approximately solved on a digital computer. Some results of numerical calculations are reported for the cases where the obstacle is a circular cylinder and the distance between two walls is various, the Reynolds number being 1 and 5.

Drag of a rotating sphere

We consider the problem of steady incompressible viscous fluid flow about a rotating sphere, with the flow specified on a sphere of finite radius, which reduces to the solution of the complete Navier-Stokes equations.