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Fluid Modelling: Foundations and First Applications
Published in Robert E. Robson, Ronald D. White, Malte Hildebrandt, Fundamentals of Charged Particle Transport in Gases and Condensed Matter, 2017
Robert E. Robson, Ronald D. White, Malte Hildebrandt
A transport coefficient is a material coefficient and is generally defined as the constant of proportionality in the relation linking the flow of some property with the “force” which causes it. The mobility coefficient is an example. Equation 7.33 can be rewritten in terms of the electric current density (current per unit area) J=nevd, to give Ohm's law, J=σcondE, where σcond=neK is the electrical conductivity coefficient.
Basic Concepts
Published in Ron Darby, Raj P. Chhabra, Chemical Engineering Fluid Mechanics, 2016
This expression can be applied to the transport of any conserved (extensive) quantity “Q,” for example, mass, energy, momentum, electric charge, etc. The rate of transport of Q per unit area normal to the direction of transport is called the flux of Q, with dimensions of “Q”/(time × area). This transport equation can be applied on a microscopic scale in a stationary medium or to a fluid in motion. The moving fluid can be in laminar flow in which the mechanism for the transport of Q is the intermolecular forces of attraction between molecules or groups of molecules, or in turbulent flow in which the transport mechanism is the result of the motion of turbulent eddies which move in three dimensions and carry Q along with them. The resistance or conductance term in Equation 1.1 is also called the transport coefficient. For laminar or stationary media, the transport coefficient is a fluid or material property, but for turbulent flows it also depends upon the degree of turbulence in the medium.
Modeling of the HCPB Helium Coolant Purification System for EU-DEMO: Process Simulations of Molecular Sieves and NEG Sorbents
Published in Fusion Science and Technology, 2023
Jonas C. Schwenzer, Alessia Santucci, Christian Day
where = fluid side transport coefficient (m‧s−1)= diffusion coefficient of species in the bulk fluid= Schmidt number and Reynolds number, respectively, with the kinematic viscosity of the fluid and the superficial bulk fluid velocity.
The effect of temperature-dependent viscosity and thermal conductivity on the onset of compressible convection
Published in Geophysical & Astrophysical Fluid Dynamics, 2021
The form of transport coefficients, dynamic viscosity and thermal conductivity, are often simplified to be constant in stellar modelling. To explore the impact of non-constant transport coefficients in the modelling of convective instabilities, a general form of the equations governing thermal convection in a compressible polytropic atmosphere, using the Spitzer relations for temperature-varying thermal conductivity and viscosity, were derived for the first time and the stability of the system was examined using linear stability analysis for each non-constant transport coefficient separately. The linear equations were solved numerically to determine the nature of the unstable modes, together with the structure of the eigenfunctions.
Application of molasses as draw solution in forward osmosis desalination for fertigation purposes
Published in Environmental Technology, 2021
Bizhan Bagheri, Ayoub Karimi-Jashni, Mohammad Mahdi Zerafat
Equation (2) is the general equation describing water transport in osmosis-based processes [17].where Jw is the permeate water flux (L/m2.h, referenced to as LMH) through a semipermeable membrane, A is the pure water permeability constant of the membrane, P is the applied pressure, and σ is the reflection coefficient which describes the ability of a membrane active layer to preferentially allow solvent permeation over solute permeation [41]. In RO, ΔP > Δπ and in FO, ΔP = 0. Pressure retarded osmosis is defined as the region between osmosis and osmotic equilibrium, where ΔP < Δπ. In FO applications (in the absence of applied pressure) Jw is directly proportional to the osmotic pressure difference across the membrane and can be expressed by the classical solution-diffusion model (Equation (3)) [17].where πD and πF are osmotic pressures of DS and FS, respectively, and assuming that salt does not cross the membrane (or σ has a value of 1). To include the effect of ECP at high fluxes, Equation (3) is modified as Equation (4) [10].where kD and kF are the mass transfer coefficients of the draw and the feed side respectively. The first and second terms in the equation refer to the effect of dilutive and concentrative ECP on the flux, respectively. Equation (5) is used for taking into consideration ICP effect on water flux [42].where B is the transport coefficient for solute, and Km is the mass transfer coefficient, which is given by the ratio of the solute diffusion coefficient (D) over the membrane structural parameter (S).