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The unsteady convection–diffusion problem is considered, at first the known temperature T is expanded into a Taylor series with respect to time taking into account its three components. Next, using the convection diffusion equation an equation is obtained from the differentiation of this equation.
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 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]
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 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 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. [3] [4]
The power-law scheme [1] [2] interpolates the face value of a variable, , using the exact solution to a one-dimensional convection-diffusion equation given below: =In the above equation Diffusion Coefficient, and both the density and velocity remains constant u across the interval of integration.
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 ).