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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 ...
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 ...
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 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).
Burgers' equation or Bateman–Burgers equation is a fundamental partial differential equation and convection–diffusion equation [1] occurring in various areas of applied mathematics, such as fluid mechanics, [2] nonlinear acoustics, [3] gas dynamics, and traffic flow. [4]
The methods used for solving two dimensional Diffusion problems are similar to those used for one dimensional problems. The general equation for steady diffusion can be easily derived from the general transport equation for property Φ by deleting transient and convective terms [1]
In the study of heat conduction, the Fourier number, is the ratio of time, , to a characteristic time scale for heat diffusion, .This dimensionless group is named in honor of J.B.J. Fourier, who formulated the modern understanding of heat conduction. [1]
The hybrid difference scheme [1] [2] is a method used in the numerical solution for convection–diffusion problems. It was introduced by Spalding (1970). It is a combination of central difference scheme and upwind difference scheme as it exploits the favorable properties of both of these schemes.