Transition to an unsteady flow induced by a fin on the sidewall of a differentially heated air-filled square cavity and heat transfer

The transition from a steady to an unsteady flow induced by an adiabatic fin on the sidewall of a differentially heated air-filled cavity is numerically investigated. Numerical simulations have been performed over the range of Rayleigh numbers from Ra = 105–109. The temporal development and spatial structures of natural convection flows in the cavity with a fin are described. It has been demonstrated that the fin may induce the transition to an unsteady flow and the critical Rayleigh number for the occurrence of the transition is between 3.72 × 106 and 3.73 × 106. Furthermore, the peak frequencies of the oscillations triggered by different mechanisms are obtained through spectral analysis. It has been found that the flow rate through the cavity with a fin is larger than that without a fin under the unsteady flow, indicating that the fin may improve the unsteady flow in the cavity.

Unsteady flow and heat transfer between rotating coaxial disks

A study is made on the flow and heat transfer of a viscous fluid confined between two parallel disks. The disks are allowed to rotate with different time dependent angular velocities, and the upper disk is made to approach the lower one with a constant speed. Numerical solutions of the governing parabolic partial differential equations are obtained through a fourth-order accurate compact finite difference scheme. The normal forces and torques that the fluid exerts on the rotating surfaces are obtained at different nondimensional times for different values of the rate of squeezing and disk angular velocities. The temperature distribution and heat transfer are also investigated in the present analysis.

Unsteady-Flow Of A Viscous-Fluid Between 2 Parallel Disks With A Time-Varying Gap Width And A Magnetic-Field

The unsteady incompressible viscous fluid flow between two parallel infinite disks which are located at a distance h(t*) at time t* has been studied. The upper disk moves towards the lower disk with velocity h'(t*). The lower disk is porous and rotates with angular velocity Omega(t*). A magnetic field B(t*) is applied perpendicular to the two disks. It has been found that the governing Navier-Stokes equations reduce to a set of ordinary differential equations if h(t*), a(t*) and B(t*) vary with time t* in a particular manner, i.e. h(t*) = H(1 - alpha t*)(1/2), Omega(t*) = Omega(0)(1 - alpha t*)(-1), B(t*) = B-0(1 - alpha t*)(-1/2). These ordinary differential equations have been solved numerically using a shooting method. For small Reynolds numbers, analytical solutions have been obtained using a regular perturbation technique. The effects of squeeze Reynolds numbers, Hartmann number and rotation of the disk on the flow pattern, normal force or load and torque have been studied in detail

Unsteady flow over a stretching surface with a magnetic field in a rotating fluid

The effect of the magnetic field on the unsteady flow over a stretching surface in a rotating fluid has been studied. The unsteadiness in the flow field is due to the time-dependent variation of the velocity of the stretching surface and the angular velocity of the rotating fluid. The Navier-Stokes equations and the energy equation governing the flow and the heat transfer admit a self-similar solution if the velocity of the stretching surface and the angular velocity of the rotating fluid vary inversely as a linear function of time. The resulting system of ordinary differential equations is solved numerically using a shooting method. The rotation parameter causes flow reversal in the component of the velocity parallel to the strerching surface and the magnetic field tends to prevent or delay the flow reversal. The surface shear stresses dong the stretching surface and in the rotating direction increase with the rotation parameter, but the surface heat transfer decreases. On the other hand, the magnetic field increases the surface shear stress along the stretching surface, but reduces the surface shear stress in the rotating direction and the surface heat transfer. The effect of the unsteady parameter is more pronounced on the velocity profiles in the rotating direction and temperature profiles.

Unsteady flow with attenuation in a fluid filled elastic tube with a stenosis

An equation governing the excess pressure has been derived, for an axially tethered and stenosed elastic tube filled with viscous liquid, by introducing the elasticity of the tube through pressure-area relation. This equation is solved numerically for large Womersley parameter and the results are presented for different types of pressure-radius relations and geometries by prescribing an outgoing wave suffering attenuation at some axial point of the tube. For a locally constricted tube it is observed that the pressure oscillates more and generates sound on the down stream side of the constriction.

Unsteady flow of a dilute suspension in a semi-infinite contracting or expanding pipe

In the present paper an exact similar solution of the Navier-Stokes equation for unsteady flow of a dilute suspension in a semi-infinite contracting or expanding circular pipe is presented. The effects of the Schmidt number (Sc), Reynolds number (|ε|), the volume fraction (α) and the relaxation time (τ) of the particulate phase on the flow characteristics are examined. The presence of the solid particles has been observed to influence the flow behaviour significantly. These solutions are valid down to the state of a completely collapsed pipe, since the nonlinearity is retained fully. The results may help understanding the flow near the heart and certain forced contractions or expansions of valved veins.

Unsteady flow of a dilute suspension in a semi-infinite contracting or expanding pipe

In the present paper an exact similar solution of the Navier-Stokes equation for unsteady flow of a dilute suspension in a semi-infinite contracting or expanding circular pipe is presented. The effects of the Schmidt number (Sc), Reynolds number (|ε|), the volume fraction (α) and the relaxation time (τ) of the particulate phase on the flow characteristics are examined. The presence of the solid particles has been observed to influence the flow behaviour significantly. These solutions are valid down to the state of a completely collapsed pipe, since the nonlinearity is retained fully. The results may help understanding the flow near the heart and certain forced contractions or expansions of valved veins.

Magnetohydrodynamic unsteady flow in a tube of variable cross section in an axial magnetic field

Oscillatory flow in a tube of slowly varying cross section is investigated in the presence of a uniform magnetic field in the axial direction. A perturbation solution including steady streaming is presented. The pressure and shear stress on the wall for various parameters governing the flow are discussed. Physics of Fluids is copyrighted by The American Institute of Physics.

On the unsteady flow of a fairly concentrated suspension due to contracting or expanding walls of a tube

Consummating our earlier work [1], the unsteady flow of a fairly concentrated suspension due to a single contraction or expansion of the walls of a tube is studied. A comparison of the results obtained by using two different formulae for the additional drag terms in the governing equations has been made. A region of circulation in the flow field is observed when the volume fraction Z greater-or-equal, slanted 0.3, the Schmidt number Sc < 1 and the density ratio (density of the particulate phase/density of the fluid phase) > 1.

A Method of Characteristics for Solving Two-dimensional Unsteady Flow Problems

The aim of this investigation is to evolve a method of solving two-dimensional unsteady flow problems by the method of characteristics. This involves the reduction of the given system of equations to an equivalent system where only interior derivatives occur on a characteristic surface. From this system, four special bicharacteristic directional derivatives are chosen. A finite difference scheme is prescribed for solving the equations. General rectangular lattices are also considered. As an example, we investigate the propagation of an initial pressure distribution in a medium at rest.

Exact solution for the unsteady flow and heat transfer between eccentrically rotating disks

The unsteady heat transfer associated with flow due to eccentrically rotating disks considered by Ramachandra Rao and Kasiviswanathan (1987) is studied via reformulation in terms of cylindrical polar coordinates. The corresponding exact solution of the energy equation is presented when the upper and lower disks are subjected to steady and unsteady temperatures. For an unsteady flow with nonzero mean, the energy equation can be solved by prescribing the temperature on the disk as a sum of steady and oscillatory parts

Three-Dimensional Unsteady Flow With Heat and Mass Transfer Over a Continuous Stretching Surface

A numerical solution of the unsteady boundary layer equations under similarity assumptions is obtained. The solution represents the three-dimensional unsteady fluid motion caused by the time-dependent stretching of a flat boundary. It has been shown that a self-similar solution exists when either the rate of stretching is decreasing with time or it is constant. Three different numerical techniques are applied and a comparison is made among them as well as with earlier results. Analysis is made for various situations like deceleration in stretching of the boundary, mass transfer at the surface, saddle and nodal point flows, and the effect of a magnetic field. Both the constant temperature and constant heat flux conditions at the wall have been studied.

An unsteady flow due to eccentrically rotating porous disk and a fluid at infinity

An exact solution of the unsteady Navier-Stokes equations is obtained for the flow due to non-coaxial rotations of a porous disk, executing non-torsional oscillations in its own plane, and a fluid at infinity. It is shown that the infinite number of solutions existing for a flow confined between two disks reduce to a single unique solution in the case of a single disk. The adjustment of the unsteady flow near the rotating disk to the flow at infinity rotating about a different axis is explained.

Unsteady flow and heat transfer on a semi-infinite flat plate with an aligned magnetic field

The unsteady laminar boundary layer flow of an electrically conducting fluid past a semi-infinite flat plate with an aligned magnetic field has been studied when at time t > 0 the plate is impulsively moved with a constant velocity which is in the same or opposite direction to that of free stream velocity. The effect of the induced magnetic field has been included in the analysis. The non-linear partial differential equations have been solved numerically using an implicit finite-difference method. The effect of the impulsive motion of the surface is found to be more pronounced on the skin friction but its effect on the x-component of the induced magnetic field and heat transfer is small. Velocity defect occurs near the surface when the plate is impulsively moved in the same direction as that of the free stream velocity. The surface shear stress, x-component of the induced magnetic field on the surface and the surface heat transfer decrease with an increasing magnetic field, but they increase with the reciprocal of the magnetic Prandtl number. However, the effect of the reciprocal of the magnetic Prandtl number is more pronounced on the x-component of the induced magnetic field. (C) 1999 Elsevier Science Ltd. All rights reserved.