Search results
Results from the WOW.Com Content Network
The convection–diffusion equation can be derived in a straightforward way [4] from the continuity equation, which states that the rate of change for a scalar quantity in a differential control volume is given by flow and diffusion into and out of that part of the system along with any generation or consumption inside the control volume: + =, where j is the total flux and R is a net ...
The Maxwell–Stefan diffusion (or Stefan–Maxwell diffusion) is a model for describing diffusion in multicomponent systems. The equations that describe these transport processes have been developed independently and in parallel by James Clerk Maxwell [ 1 ] for dilute gases and Josef Stefan [ 2 ] for liquids.
Naively, this could be done using a particular coordinate system. However, unless proper care is applied, the parallel transport defined in one system of coordinates will not agree with that of another coordinate system. A more appropriate parallel transportation system exploits the symmetry of the sphere under rotation.
The diffusion equation is a parabolic partial differential equation.In physics, it describes the macroscopic behavior of many micro-particles in Brownian motion, resulting from the random movements and collisions of the particles (see Fick's laws of diffusion).
As mentioned above, chemical molar flux of a component A in an isothermal, isobaric system is defined in Fick's law of diffusion as: = where the nabla symbol ∇ denotes the gradient operator, D AB is the diffusion coefficient (m 2 ·s −1) of component A diffusing through component B, c A is the concentration (mol/m 3) of component A. [9]
Reaction–diffusion systems are naturally applied in chemistry. However, the system can also describe dynamical processes of non-chemical nature. Examples are found in biology, geology and physics (neutron diffusion theory) and ecology. Mathematically, reaction–diffusion systems take the form of semi-linear parabolic partial differential ...
The transient flow of groundwater is described by a form of the diffusion equation, similar to that used in heat transfer to describe the flow of heat in a solid (heat conduction). The steady-state flow of groundwater is described by a form of the Laplace equation, which is a form of potential flow and has analogs in numerous fields.
The flow graph is associated with a number of simple rules which enable every possible solution [related to the equations] to be obtained." [ 1 ] Although this definition uses the terms "signal-flow graph" and "flow graph" interchangeably, the term "signal-flow graph" is most often used to designate the Mason signal-flow graph , Mason being the ...