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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 ...
There are some notable similarities in equations for momentum, energy, and mass transfer [7] which can all be transported by diffusion, as illustrated by the following examples: Mass: the spreading and dissipation of odors in air is an example of mass diffusion. Energy: the conduction of heat in a solid material is an example of heat diffusion.
The convection–diffusion equation describes the flow of heat, particles, or other physical quantities in situations where there is both diffusion and convection or advection. For information about the equation, its derivation, and its conceptual importance and consequences, see the main article convection–diffusion equation. This article ...
Many other convection–diffusion equations describe the conservation and flow of mass and matter in a given system. In chemistry, the calculation of the amount of reactant and products in a chemical reaction, or stoichiometry, is founded on the principle of conservation of mass. The principle implies that during a chemical reaction the total ...
is the Diffusion coefficient [2] and is the Source term. [3] A portion of the two dimensional grid used for Discretization is shown below: Graph of 2 dimensional plot. In addition to the east (E) and west (W) neighbors, a general grid node P, now also has north (N) and south (S) neighbors.
Fick's first law relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative), or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low ...
Convection is always followed by diffusion and hence where convection is considered we have to consider combine effect of convection and diffusion. But in places where fluid flow plays a non-considerable role we can neglect the convective effect of the flow. In this case we have to consider more simplistic case of only diffusion.
The molecules in a drop of food coloring added to water will eventually disperse throughout the entire medium, where the effects of molecular diffusion are more evident. However, stirring the mixture with a spoon will create turbulent flows in the water that accelerate the process of dispersion through convection-dominated dispersion.
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