Search results
Results from the WOW.Com Content Network
The momentum transfer plays an important role in the evaluation of neutron, X-ray, and electron diffraction for the investigation of condensed matter. Laue-Bragg diffraction occurs on the atomic crystal lattice, conserves the wave energy and thus is called elastic scattering, where the wave numbers final and incident particles, and , respectively, are equal and just the direction changes by a ...
The various aspects of such equilibrium are directly connected to a specific transport: heat transfer is the system's attempt to achieve thermal equilibrium with its environment, just as mass and momentum transport move the system towards chemical and mechanical equilibrium.
heat transfer (advection–diffusion problems; total momentum transfer to molecular heat transfer) Péclet number: Pe = = mass transfer (advection–diffusion problems; total momentum transfer to diffusive mass transfer) Prandtl number: Pr
The basic mechanisms and mathematics of heat, mass, and momentum transport are essentially the same. Among many analogies (like Reynolds analogy, Prandtl–Taylor analogy) developed to directly relate heat transfer coefficients, mass transfer coefficients and friction factors, Chilton and Colburn J-factor analogy proved to be the most accurate.
A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity , but it can be generalized to apply to any extensive quantity .
is the momentum-transfer collision frequency, is the mass. Mobility is related to the species' diffusion coefficient through an exact (thermodynamically required) equation known as the Einstein relation: =, where
The transfer of momentum between molecules is explicitly accounted for in Revised Enskog theory, which relaxes the requirement of a gas being dilute. The viscosity equation further presupposes that there is only one type of gas molecules, and that the gas molecules are perfect elastic and hard core particles of spherical shape.
At higher Reynolds number, the analogy between mass and heat transfer and momentum transfer becomes less useful due to the nonlinearity of the Navier-Stokes equation (or more fundamentally, the general momentum conservation equation), but the analogy between heat and mass transfer remains good. A great deal of effort has been devoted to ...