# Mass transfer from a sphere in an oscillating flow with zero mean velocity

by Colin K. Drummond

Publisher: NASA, Publisher: For sale by the National Technical Information Service in [Washington, D.C.], [Springfield, Va

Written in English

## Subjects:

• Mass transfer -- Mathematical models

## Edition Notes

The Physical Object ID Numbers Statement Colin K. Drummond and Frederic A. Lyman. Series NASA technical memorandum -- 102566. Contributions Lyman, Frederic A., United States. National Aeronautics and Space Administration. Pagination 19 p. : Number of Pages 19 Open Library OL17630445M OCLC/WorldCa 25035723

where is the sphere's mass. In other words, in a steady state, the weight of the sphere balances the vertical force exerted by the surrounding fluid. If the sphere is composed of material of mean density , in the frame in which the fluid a large distance from the sphere is stationary, the steady vertical velocity with which the sphere moves through the fluid is. However, if I set the cylinder oscillating, I don't think I can use just this restoring force and the cylinder's mass to find an oscillation frequency. I need to account for some sort of "effective mass" of the water. i.e. the oscillating cylinder puts kinetic energy into the water. Phenomena of the flow streaming can be found in zero-mean velocity oscillating flows in many channel geometries. Although there is no net mass flow (zero-mean velocity) passing through the channel, discrepancy in the velocity profiles between the forward and backward flows causes fluid particles near the walls to drift toward one end while Cited by: 2. 1 INTRODUCTION TO HEAT TRANSFER AND MASS TRANSFER HEAT FLOWS AND HEAT TRANSFER COEFFICIENTS HEAT FLOW A typical problem in heat transfer is the following: consider a body “A” that exchanges heat with another body, of infinite medium, “B”.

Unsteady flow over a stationary sphere with a small fluctuation in the free-stream velocity is considered at small Reynolds number, Re. A matched asymptotic solution is obtained for the frequency-dependent (or the acceleration-dependent) part of the unsteady flow at very small frequency,ω, under the restriction St Cited by: Flow Past a Spherical Obstacle , that the velocity potential is the superposition of that associated with uniform flow with velocity, parallel to the -axis, and a dipole point source of strength, located at the origin. Thus, making the fluid exerts zero net force on the sphere, in . In physics and engineering, mass flow rate is the mass of a substance which passes per unit of unit is kilogram per second in SI units, and slug per second or pound per second in US customary common symbol is ˙ (ṁ, pronounced "m-dot"), although sometimes μ (Greek lowercase mu) is used.. Sometimes, mass flow rate is termed mass flux or mass current, see for example Fluid Common symbols: m, ˙, {\displaystyle {\dot {m}}}. A particle oscillating in simple harmonic motion is: A. never in equilibrium because it is in motion B. never in equilibrium because there is always a force C. in equilibrium at the ends of its path because its velocity is zero there D. in equilibrium at the center of its path because the acceleration is zero there.

The aim of this study is to present an exact analysis of combined effects of radiation and chemical reaction on the magnetohydrodynamic (MHD) free convection flow of an electrically conducting incompressible viscous fluid over an inclined plate embedded in a porous medium. The impulsively started plate with variable temperature and mass diffusion is by:   The dimensionless drag may be related to the dimensionless mean wall heat flux, which provides a good insight into the mechanism of slip flow heat transfer past a sphere. The proposed model does provide a means to predict the Nusselt number for slip flow over a sphere in the absence of experimental by: The present chapter aims at investigating the magnetohydrodynamic (MHD) boundary layer flow and heat transfer of a non-Newtonian fluid over a stretching surface through a porous medium. Casson fluid model is utilized to describe the non-Newtonian fluid behavior. Two types of nanofluids, that is, Ag-water and Cu-water, are studied. The governing partial differential equations are transformed Author: Ayesha Siddiqui, Bandari Shankar. Chapter 1 Governing Equations of Fluid Flow and Heat Transfer is the Kronecker-Delta operator which is equal to 1 if and it is zero otherwise. Navier-Stokes equation given in Eqn () is said to be in non-conservative form. instantaneously in a flow field so that the velocity field always remains divergence free. In theFile Size: KB.

## Mass transfer from a sphere in an oscillating flow with zero mean velocity by Colin K. Drummond Download PDF EPUB FB2

A pseudospectral numerical method is used for the solution of the Navier-Stokes and mass transport equations for a sphere in a sinusoidally oscillating flow with zero mean velocity. The flow is assumed laminar and axisymmetric about the sphere's polar by: A pseudospectral numerical method is used for the solution of the Navier-Stokes and mass transport equations for a sphere in a sinusoidally oscillating flow with zero mean velocity.

The flow is assumed laminar and axisymmetric about the sphere's polar axis. Get this from a library. Mass transfer from a sphere in an oscillating flow with zero mean velocity. [Colin K Drummond; Frederic A Lyman; United States. National Aeronautics and Space Administration.].

A pseudospectral numerical method is used for the solution of the Navier-Stokes and mass transport equations for a sphere in a sinusoidally oscillating flow with zero mean velocity. The flow is assumed laminar and axisymmetric about the sphere's polar axis.

Oscillating flow results were obtained for Reynolds numbers (based on the free-stream oscillatory flow amplitude) between 1 andand. A pseudospectral numerical method is used for the solution of the Navier-Stokes and mass transport equations for a sphere in a sinusoidally oscillating flow with zero mean velocity.

The flow is assumed laminar and axisymmetric about the sphere's polar axis. Oscillating flow results were obtained for Reynolds numbers (based on the free-stream oscillatory flow amplitude) between 1 andand Author: Frederic A. Lyman and Colin K. Drummond. Heat or mass transfer from spherical particles in oscillatory flow has important applications in combustion and spray drying.

This work provides a parametric investigation of drag forces experienced by, and transport of a passive scalar from, an isolated rigid fixed sphere in Cited by:   Unsteady flow due to an oscillating sphere with a velocity U 0 cosω t ’, in which U 0 and ω are the amplitude and frequency of the oscillation and t ’ is time, is investigated at finite Reynolds number.

The methods used are: (i) Fourier mode expansion in the frequency domain; (ii) a time-dependent finite difference technique in the time domain; and (iii) a matched asymptotic expansion for Cited by: Mass Transfer Between a Sphere and an Unbounded Fluid. Shankar Subramanian.

Department of Chemical and Biomolecular Engineering. Clarkson University. When a single-component liquid drop evaporates into air, or when a solid, modeled as a single-component sphere, dissolves in a liquid or sublimes into a gas, we can construct a simple modelFile Size: 40KB.

Forced Convection Past an Oblate Spheroid at Low to Moderate Reynolds Numbers Numerical Analysis of Variable Property Heat Transfer to a Single Sphere in High Temperature Surroundings,” Mass Transfer from a Sphere in an Oscillating Flow with Zero Mean Velocity,”Cited by: mass transfer coefficients.

k ck x c= Mass transfer coefficients depend on the relevant physical properties of the fluid, the geometry used along with relevant dimensions, and the average velocity of the fluid if we are considering flow in an enclosed conduit, or the approach velocity if the flow is over an object.

Dimensional. If simple separation of the flow were to occur in each half cycle of the oscillation, a slug of fluid, at rest with respect to the sphere, would form in the wake of the sphere, this slug having length ~ a and a discontinuity ~ aω in the fluid velocity at its surface.

Heat transfer characteristics of a circular cylinder exposed to the slowly oscillating flow with zero-mean velocity were investigated.

The flow oscillation amplitude and frequency were changed in the range of 10⩽A/D⩽38 and ⩽f⩽ Hz in the experiments. Reynolds number is set small and the flow remained by: oscillating flow with zero mean velocity.

It was concluded that the mass transfer rate decreases with the decrease of the Strouhal number until reaching the value of 2 below which the rate is virtually independent of the Strouhal number. Ha and Yavuzkurt  studied heat transfer from a sphere in an oscillating free stream and showed that high.

An investigation has been made for oscillatory flow about a zero mean for different Reynolds numbers and frequencies. The simulation has been verified for steady flow conditions, and for unsteady flow there is excellent agreement with Stokes flow theory at very low Reynolds by: A pseudospectral numerical method is used for the solution of the Navier-Stokes and mass transport equations for a sphere in a sinusoidally oscillating flow with zero mean velocity.

The flow is Author: Jacob Fraden. combined heat and mass transfer in free convection flow along a vertical cylinder. Some other related studies on free convection flow in a cylinder are given in [ 26 – 30 ].

The study of the added mass and the damping of an oscillating rigid sphere in a cylindrical tube containing a viscous liquid was the particular problem under consideration.

The general objectives included the study of the effects of fluid viscosity, container boundary proximity, and ampli­ tude of oscillation on the added mass and damping. transport equations for a sphere in a sinusoidally oscillating flow with zero mean velocity.

The flow is assumed laminar and axisymmetric about the sphere's polar axis. Oscillating flow results were obtained for Reynolds numbers (based on the free-stream oscillatory flow amplitude) between 1 andand Strouhal numbers between 1 and Mass transfer correlations for single sphere: ℎ=2+ à C and m are constants and their values depend on the type of fluid, the range of Re and the range of Sc.

The characteristic length in Sh and Re is the sphere diameter. Ex: For mass transfer from a single sphere into gas streams: ℎ=2+ For a binary mixture of A and B, the mass flux, nA,z, of species A relative to the z axis is nA,z = − ρDAB A d dz ω + ωA(nA,z + nB,z) () The molar flux of species i can be expressed as Ni = civi () In this equation, is the absolute velocity of species i relative to the stationary coordinate Size: 58KB.

velocity be zero everywhere at the surface of the sphere; this implies the existence of gradients (that is, spatial rates of change) of velocity, very sharp under some conditions, at and near the surface of the sphere.

These velocity gradients produce a shear stress on the surface of the sphere File Size: KB. oscillations, at low but non-zero Re.

In both cases, the sphere was assumed to be free and either in an in nite domain or rotating inside a larger concentric sphere, and the uid was shown to move around the oscillating sphere in concentric shells, the centres of which lie on the axis of Size: 5MB.

Cross flow Sh D = 2 + ( Re D 1/2 + Re D 2/3)Sc ×(µ/µs)1/4 Sphere Average, T∞, mass transfer or low mass transfer rate where the mole fraction of species A is less than about For higher mass transfer rate theFile Size: 51KB.

Their combined citations are counted only for the first article. Mass transfer from a sphere in an oscillating flow with zero mean velocity.

CK Drummond, FA Lyman. Computational mechanics 6 (4),Mass Transfer from a Napthalene Sphere Under Oscillatory Flow.

CK Drummond. Syracuse University, 6. flow of a viscous fluid past a sphere by restricting consideration to low Reynolds numbers ρUD/μ (where, as before, U is the uniform approach velocity and D is the diameter of the sphere).

Figure Steady flow of a viscous fluid at very low Reynolds numbers (“creeping flow”) past a sphere. The flow lines are shown in a planar section. A certain oscillating mass-spring system has a period of s with a kg mass. What will the period be when a kg mass is substituted for the kg mass.

velocity of the °uid in contact with a solid surface typically equals the velocity of that surface|zero if the surface is stationary.1 And, for the few cases in which one °uid (A, say) is in contact with another immiscible °uid (B), the velocity in °uid A equals the velocity in °uid B at the common Size: KB.

2. Formulation. Consider a sphere of radius a 0 undergoing small oscillations with frequency ω in an incompressible viscous fluid with density ρ and viscosity goal is to calculate the hydrodynamic force acting on the sphere when the minimum clearance between the sphere surface and the rigid wall is is assumed that the amplitude A s of the sphere oscillation is small compared to h Cited by: 6.

Therefore deriving more accurate drag formulas for constantly moving sphere in liquid does not help. Acceleration is too high, not the velocity: Next step in approximation is to derive drag force on single oscillating sphere in fluid.

The question is, what is the drag force on the sphere which is moving with velocity \$\mathbf{v} = \mathbf{ v}_0. I am trying to find out the maximum speed of a mass in oscillation. I know the mass (g), frequency (2Hz), Amplitude (cm), and that "At one instant, the mass is at x = cm and has v = cm/s." Not matter what I try, it ends up having the speed be 0, or Any hints on what formula to use / how to use it would help me out a lot.

Read "Dissolution of a colloidal particle in an oscillatory flow, International Journal of Heat and Mass Transfer" on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.

Mass transfer from a sphere in an oscillating flow with zero mean velocity. Drummond, C.Reversible and Irreversible Tracer Dispersion in an mass transfer.

To our knowledge, relatively little attention has been paid to the effect of oscillating ﬂows on the dynamics of the spreading of concentration fronts.

Apart from references Scotter et al. (), Scot- Dispersion measurements in oscillating gas ﬂows of zero mean.The °uid medium surrounding the sphere is air with sound speed c = m=s and mean density ‰o = kg=m3. The characteristic impedance of air Zo = ‰oc = Rayl. The wavenumber at a frequency!

is given as k =!=c. The sphere is oscillating with unit velocity in the z direction, that is vz = 1m=s. The BE mesh of the sphere is shown in File Size: KB.