Exact Solutions Corresponding to the Viscous Incompressible and Conducting Fluid Flow Due to a Porous Rotating Disk

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
Mustafa Turkyilmazoglu
Keyword(s):  
Temperature Field ◽  
Fluid Flow ◽  
Flow Field ◽  
Exact Solutions ◽  
Equations Of Motion ◽  
Rotating Disk ◽  
Conducting Fluid ◽  
Shear Stresses ◽  
Adiabatic Wall ◽  
Navier Stokes Equation

A study is pursued in this paper for the evaluation of the exact solution of the steady Navier–Stokes equation, governing the incompressible viscous Newtonian, electrically conducting fluid flow motion over a porous disk, rotating at a constant angular speed. The three-dimensional equations of motion are treated analytically yielding to the derivation of exact solutions. The effects of the magnetic pressure number on the permeable flow field are better conceived from the exact velocity and induced magnetic field obtained. Making use of this solution, analytical formulas for the angular velocity and current density components, as well as for the magnetic wall shear stresses, are extracted. Interaction of the resolved flow field with the surrounding temperature is then analyzed via energy equation. The temperature field is shown to accord with the convection, viscous dissipation, and Joule heating. As a result, exact formulas are obtained for the temperature field, which takes different forms, depending on whether isothermal and adiabatic wall conditions or suction and blowing are considered.

Effects of Partial Slip on the Analytic Heat and Mass Transfer for the Incompressible Viscous Fluid of a Porous Rotating Disk Flow

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
Mustafa Turkyilmazoglu
Keyword(s):  
Viscous Fluid ◽  
Exact Solutions ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Rotating Disk ◽  
Incompressible Viscous Fluid ◽  
Temperature Fields ◽  
Partial Slip ◽  
Shear Stresses ◽  
Rotating Disk Flow

The present paper is concerned with a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous fluid flow motion due to a porous disk rotating with a constant angular speed about its axis. The recent study (Turkyilmazoglu, 2009, “Exact Solutions for the Incompressible Viscous Fluid of a Porous Rotating Disk Flow,” Int. J. Non-Linear Mech., 44, pp. 352–357) is extended to account for the effects of partial flow slip and temperature jump imposed on the wall. The three-dimensional equations of motion are treated analytically yielding derivation of exact solutions for the flow and temperature fields. Explicit expressions representing the flow properties influenced by the slip as well as a uniform suction and injection are extracted, including the velocity, vorticity and temperature fields, shear stresses, flow and thermal layer thicknesses, and Nusselt number. The effects of variation in the slip parameters are better visualized from the formulae obtained.

The Calculation of Transport Phenomena in Electromagnetically Levitated Metal Droplets

1981 ◽  
Vol 9 ◽  
Author(s):  
N. El-Kaddah ◽  
J. Szekely
Keyword(s):  
Temperature Field ◽  
Fluid Flow ◽  
Flow Field ◽  
Force Field ◽  
Electromagnetic Force ◽  
Stokes Equations ◽  
Concentration Field ◽  
Metal Droplet ◽  
Convective Transport ◽  
Mathematical Representation

ABSTRACTA mathematical representation has been developed for the electromagnetic force field, the fluid flow field, the temperature field (and for transport controlled kinetics) in a levitation melted metal droplet. The technique of mutual inductances was employed for the calculation of the electromagnetic force field, while the turbulent Navier-Stokes equations and the turbulent convective transport equations were used to represent the fluid flow field, the temperature field and the concentration field. The governing differential equations, written in spherical coordinates, were solved numerically.The computed results were found to be in good agreement with measurements reported in the literature, regarding the lifting force and the average temperature of the specimen.

scholarly journals Effect of Draw Blank Velocity on Steel Fluid Flow Field in Blank Continuous Caster Crystallizer

2011 ◽  
Vol 2-3 ◽  
pp. 673-677
Author(s):  
Ze Ning Xu ◽  
Hong Yu Liu ◽  
Yan Ping Lu ◽  
Lei Gang Liu
Keyword(s):  
Temperature Field ◽  
Fluid Flow ◽  
Heat Conduction ◽  
Flow Field ◽  
Field Distribution ◽  
Thickness Distribution ◽  
Continuous Caster ◽  
Impurity Content ◽  
Three Dimensions ◽  
Steel Blank

As the heart of continuous caster, crystallizer is the cradle of most surface deficiencies and inside quality problems in steel blank. Steel blank surface quality, nonmetal impurity content and relevant distribution rely on the steel fluid solidification behavior namely steel fluid flow field distribution on great extent. For the high temperature steel fluid has big kinetic energy, so, the immixture dregs, solidification heat conduction, temperature field distribution in crystallizer, solidification blank shell thickness distribution and continuous caster blank quality were influenced by steel fluid flow. The numerical simulation analysis on flow field and temperature field in crystallizer were conducted in this paper. Three dimensions turbulent flow model was adopted to computate flow field. The heat conduction was ignored on draw blank direction in temperature field. The conjugate heat conduction model of ANSYS CFX was adopted to analyze temperature field, which can consider heat conduction in solid layer and convection heat conduction between solid shell face and fluid simultaneity. The draw blank velocity was found by setting crystallizer water gap insertion depth and crystallizer water gap angle, which can obtain reasonable flow field in blank crystallizer.

Heat and Mass Transfer on the MHD Fluid Flow Due to a Porous Rotating Disk With Hall Current and Variable Properties

2010 ◽  
Vol 133 (2) ◽  
Author(s):  
Mustafa Turkyilmazoglu
Keyword(s):  
Viscous Dissipation ◽  
Joule Heating ◽  
Hall Current ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Rotating Disk ◽  
Integration Scheme ◽  
Shear Stresses ◽  
Similarity Transformations ◽  
Fluid Properties

The steady magnetohydrodynamics (MHD) laminar compressible flow of an electrically conducting fluid on a porous rotating disk is considered in the present paper. The governing equations of motion are reduced to a set of nonlinear differential equations by means of similarity transformations. The fluid properties are taken to be strong functions of temperature and Hall current that also readily accounts for the viscous dissipation and Joule heating terms. Employing a highly accurate spectral numerical integration scheme, the effects of viscosity, thermal conductivity, Hall current, magnetic field, suction/injection, viscous dissipation, and Joule heating on the considered flow are examined. The quantities of particular physical interest, such as the torque, the wall shear stresses, the vertical suction velocity, and the rate of heat transfer are calculated and discussed.

CFD MODELING OF THE STEADY-STATE MOMENTUM AND OXYGEN TRANSPORT IN A BIOREACTOR THAT IS DRIVEN BY AN AERIAL ROTATING DISK

2009 ◽  
Vol 23 (02) ◽  
pp. 121-127 ◽  
Author(s):  
K. Y. S. LIOW ◽  
B. T. TAN ◽  
G. A. THOUAS ◽  
M. C. THOMPSON
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Aqueous Phase ◽  
Gaseous Phase ◽  
Oxygen Transfer ◽  
Culture Medium ◽  
Rotating Disk ◽  
Recirculation Region ◽  
Shear Stresses ◽  
Cylinder Wall

This work considers the momentum transport and mass transfer of O 2 in a novel aerial rotating disk bioreactor (RDB) for animal cell or tissue culture. Specifically, this design uses a rotating lid placed above the surface of the culture medium to provide a stirring mechanism, which has potential benefits of enhanced gas transfer, reducing possible contamination, and better access to the culture medium below. The aim of this study is to use CFD to characterize the flow field, shear stresses, and oxygen profiles at a range of Reynolds number that lies within the laminar flow regime. Ultimately, such data will aid the development of an aerial RDB for tumor progression. Numerical simulation is used whereby the two-phase flow, comprising air as the gaseous phase, and water as the aqueous phase, is obtained by solving the unsteady, axisymmetric, incompressible Navier Stokes equation. Having obtained an accurate flow field, a species transport equation is then used to predict the oxygen transfer from the gaseous phase to the aqueous phase. Results are presented for a rotation Reynolds number (Re) range that corresponds to the impeller speed range of 60 to 240 rpm. While the flow is primarily swirl-dominant, it is found that the secondary flow in the aqueous region consists of a single recirculation pattern. As the oxygen transfer in the aqueous phase is mainly driven by convection, there is a clear depletion of oxygen at the center of the recirculation region. Shear stress distributions along the bottom stationary wall indicate a shift in the peak towards the external cylinder wall with increasing Re.

MOLECULAR DYNAMICS SIMULATION OF A MICROVILLUS IN A CROSS FLOW

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1643-1646 ◽  
Author(s):  
X. Y. CHEN ◽  
Y. LIU ◽  
R. M. C. SO ◽  
J. M. YANG
Keyword(s):  
Molecular Dynamics ◽  
Fluid Flow ◽  
Flow Field ◽  
Cross Flow ◽  
Dynamics Simulation ◽  
Endothelial Glycocalyx ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Nanoscale Structures ◽  
Drag Forces

One of the functions of microvilli in the microvessel endothelial glycocalyx is molecular filtering. The microvillus behaves as a mechanosensory system which may sense the fluid shear and drag forces. The permeability of small particles in microvessel is crucial for drug design and drug delivery. Therefore a better understanding of flow field around microvillus is important to simulate accurately the particle penetration in microvessel. Since the dimension of the microvilli is about ~10 nm , the conventional Navier-Stokes equation may not be good enough to simulate the fluid flow in such microscale and nanoscale structures. Molecular dynamics (MD) simulation is a powerful method to simulate the fluid flow at the molecular level. As a first attempt, the microvillus is reduced as a two-dimensional cylinder which is in a cross flow. The detailed drag and lift together with flow field are obtained and compared with available data.

Inertia Effects in Fully Developed Axisymmetric Laminar Flow

1971 ◽  
Vol 93 (3) ◽  
pp. 408-414 ◽  
Author(s):  
E. Makay ◽  
P. R. Trumpler
Keyword(s):  
Integral Equations ◽  
High Speed ◽  
Equations Of Motion ◽  
Rotating Disk ◽  
Navier Stokes ◽  
Centrifugal Impeller ◽  
Navier Stokes Equation ◽  
Inertia Effects ◽  
Nonlinear Form ◽  
Clearance Face

The three components of the Navier-Stokes equation are solved here simultaneously in their nonlinear form for axisymmetric radial inward and outward flow cases between two parallel rotating walls. Examples of application in rotating machinery are close clearance face seals, thrust bearings, high speed thrust device, rotating disk, narrow gap between centrifugal impeller and housing, etc. The differential equations of motion with the proper boundary conditions were converted into integral equations of the “Fredholm second kind” type and solutions have been obtained for the nonlinear cases. The use of integral equations greatly enhanced the advantage of the numerical solution developed here. The results are compared to simplified solutions and to solutions considering some of the nonlinear members. The effects of the inertia forces are especially emphasized and discussed in detail. The inclusion of these terms significantly affected the velocity field in the area discussed here. It is shown here that for low inward or outward flows the centrifugal force, and for high flows the convective acceleration terms have the main controlling influence on the radical velocity component.

An Analysis on the Flow in a Casing Induced by a Rotating Disk Using a Four-Layer Flow Model

1976 ◽  
Vol 98 (2) ◽  
pp. 192-198 ◽  
Author(s):  
Y. Senoo ◽  
H. Hayami
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Analytical Study ◽  
Flow Model ◽  
Equations Of Motion ◽  
Side Wall ◽  
Rotating Disk ◽  
Wall Boundary Layer ◽  
Through Flow ◽  
Layer Flow

An analytical study has been made to clarify the details of the flow between a rotating disk and a stationary casing side-wall with and without an axisymmetric inward through-flow. The flow field between the casing side-wall and the surface of the rotating disk is divided into four layers instead of three in earlier analyses. Proceeding from the casing side-wall to the disk, they are a wall boundary layer, an outward-flow layer, a core and a disk boundary layer. The flow field is determined so that the integrated equations of motion as well as the continuity equation are satisfied for each of the four layers. In the present analysis, least empirical informations relative to a rotating disk are used compared with the theories in the literature. The mechanics of the flow field is explained by the flow model without contradiction, and the predicted radial and axial distributions of velocity and the pressure distribution in the casing agree well with experimental results.

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