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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 ...
This article describes how to use a computer to calculate an approximate numerical solution of the discretized equation, in a time-dependent situation. In order to be concrete, this article focuses on heat flow, an important example where the convection–diffusion equation applies. However, the same mathematical analysis works equally well to ...
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 general equation for steady convection-diffusion can be easily derived from the general transport equation for property by deleting transient.
In addition, the Robin boundary condition is a general form of the insulating boundary condition for convection–diffusion equations. Here, the convective and diffusive fluxes at the boundary sum to zero: () = where D is the diffusive constant, u is the convective velocity at the boundary and c is the concentration. The second term is a result ...
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 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 ...
Often, the species can be considered as a passive tracer that does not modify the flow. The species can be for example a dye to be mixed. The evolution of a concentration field obeys the advection-diffusion equation, also called convection–diffusion equation:
Convection (or convective heat transfer) is the transfer of heat from one place to another due to the movement of fluid. Although often discussed as a distinct method of heat transfer, convective heat transfer involves the combined processes of conduction (heat diffusion) and advection (heat transfer by bulk fluid flow ).