ABSTRACT
In some cases relevant to engineering practice a material will be in an environment
where there is no convective transport – for example, pollutant released into a long
and narrow pipe with zero flow, or where heat may be diffusing along a metal wire
driven purely by temperature differences. In this case the equation reduces to:
(18.2)
where C is the concentration of the material or the temperature of the substance, x
is the axis, and K is the diffusion/dispersion coefficient. To solve this equation
using the finite difference method two steps are undertaken:
1. the solution space is digitised into a number of discrete points rather than a
continuum; and
2. the equation is approximated using standard approximations derived on the
basis of a Taylor expansion of the function.
