Channel flow transport equation

With the exception of a spatially dependent body force f, there is no source or sink term in the vorticity transport equation. Therefore the source of vorticity is usually at boundaries, with the shear at solid walls being the most common means to produce vorticity. To illustrate the behavior of vorticity generation at a wall, consider the axisymmetric flow in a circular channel as illustrated in Fig. 3.12. 

While an understanding of the molecular processes at the fuel cell electrodes requires a quantum mechanical description, the flows through the inlet channels, the gas diffusion layer and across the electrolyte can be described by classical physical theories such as fluid mechanics and diffusion theory. The equivalent of Newton s equations for continuous media is an Eulerian transport equation of the form... 

Chemical reaction and mass transfer are two unique phenomena that help define chemical engineering. Chapter 8 described problems involving chemical reaction and mass transfer in a porous catalyst, and how to model chemical reactors when the flow was well defined, as in a plug-flow reactor. Those models, however, did not account for the complicated flow situations sometimes seen in practice, where flow equations must be solved along with the transport equation. Microfluidics is the chemical analog to microelectro-mechanical systems (MEMS), which are small devices with tiny gears, valves, and pumps. The generally accepted definition of microfluidics is flow in channels of size 1 mm or less, and it is essential to include both distributed flow and mass transfer in such devices. 

We consider a steady-state version of the GDL model described in Section 7.2, coupled to the membrane model and to the channel flow model developed in [3]. This a class of 1 + ID models, which consider the lateral transport of reactants to occur only within the flow fields with the MEA supporting only through-plane transport. A ID model for the molar fractions in the flow fields is coupled to a ID model for through-plane transport in the MEA. The MEA model dictates the local current density and hence the consumption of reactants and production of water in liquid and vapor forms these serve as forcing terms for the flow field equations. In turn, the flow field equations provide the boundary conditions for the MEA model, as described in Section 7.2. 

Yotsukura, N. (1977). Derivation of solute-transport equations for a turbulent natural-channel flow. J. Res. U.S. Geol. Surv. 5, 277-284. 

For a free-surface slurry flow in an open conduit inclined to the horizontal, the transport of the suspended load is similar to that of a closed conduit. However, for the case of free-surface flow, there is no pressure differential across the length of the conduit, and direct application of Equation 27 is not meaningful. For sediment transport in open-channel flow, Yalin [57] and Novak and Nalhuri [58] showed that the Froude number is an important parameter that describes sediment transport, and is given as... 

In spite of all the difficulties caused by the two-phase effects, channel flows in fuel cells are understood better than the flows in porous layers. Channel flows are subject to fluid dynamics equations with known transport coefficients. Modern commercially available CFD packages... 

The total volumetric flow in the accessible region, is not available experimentally, and an assumption must be made before Equation 7.27 can be applied meaningfully to macroscopic experimental observations in the laboratory. Probably the most sensible of these assumptions is to recognise that, in either of the models discussed above, the vast majority of the flow will take place in the so-called accessible region, since this is associated either with the larger pores or with the central parts of all flow channels (where the flows are faster). Therefore, the best practical approximation is to assume that is almost equal to Qj. This then leads to an approximate transport equation of the form ... 

Mass Species Transport Equation in Gas Flow Channels... 

The computer simulation model for studying the hydro-dynamically developing flow-field and developing heat and mass transport phenomena in the gas flow channel is given based on the incompressible Navier-Stokes equation for fluid flow and heat and mass transport equations as described below. 

The velocity and pressure fields for the gas mixtures are solved first in the coupled gas channel-gas diffuser domains disregarding the changes in composition of the gas mixtures. This enables one to solve the flow and pressure fields for the gas mixtures first, and once these fields are found, the equations for the other dependent variables may be solved. The gas species concentrations are dependent on the transfer current densities therefore, the transport equations for the gas components are solved iteratively, together with the Butler-Volmer equations for anode and cathode catalyst layers. After convergence is achieved, one proceeds to solve for the transport equations related to the liquid water flow, for the membrane phase potential and current densities. Because the source terms of the energy equations are functions of the current density, a new level of iterations is needed, except for the velocity and pressure fields of the gas mixtures. 

Isothermal Gas Flow in Pipes and Channels Isothermal compressible flow is often encountered in long transport lines, where there is sufficient heat transfer to maintain constant temperature. Velocities and Mach numbers are usually small, yet compressibihty effects are important when the total pressure drop is a large fraction of the absolute pressure. For an ideal gas with p = pM. JKT, integration of the differential form of the momentum or mechanical energy balance equations, assuming a constant fric tion factor/over a length L of a channel of constant cross section and hydraulic diameter D, yields,... 

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