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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 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]
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 ...
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.
The upwind differencing scheme is a method used in numerical methods in computational fluid dynamics for convection–diffusion problems. This scheme is specific for Peclet number greater than 2 or less than −2
The right side of the convection-diffusion equation, which basically highlights the diffusion terms, can be represented using central difference approximation. To simplify the solution and analysis, linear interpolation can be used logically to compute the cell face values for the left side of this equation, which is nothing but the convective ...
The first well-documented use of this method was by Evans and Harlow (1957) at Los Alamos. The general equation for steady diffusion can easily be derived from the general transport equation for property Φ by deleting transient and convective terms. [1] General Transport equation can be defined as