The rate of diffusion at point i is therefore approximately equal to D ∂2c ∂x2, ˇ D ∆x, ∂c ∂x, i+1=2, ∂c ∂x, i 1=2, ! = D (∆x)2, (ci+12ci+ci 1): Multiplying this expression by the diffusion coefficient D gives the rate of diffusion. What about the boundaries? Suppose that we have no-flux boundaries. 2-D Convection-Diffusion Program By modifying 1-D convection-diffusion program, a general 2-D convection-diffusion program can be easily obtained. This program is named "conv2d.m" which solves 2-D Cartesian (geo=1), cylindrical axisymmetric (geo=2) and polar coordinates (geo=3) problems with a known 2-dimensional velocity field. An analytical solution of the two-dimensional atmospheric diffusion equation has been developed by the method of Separation of variables. Also Fourier transform and square complement methods has of physical parameters is referred to as the thermal diffusivity , and the equation 2.4 is called the heat equation . For the remainder of this section we will use the term heat equation to refer to the equation tux,t 2u x,t 0. 3. Some Problems for the Heat Equation Various side conditions can be adjoined to the heat equation to produce a A solution of the multi-group multi-regional diffusion equation in two-dimensional cylindrical (p-z) geometry is obtained in the form of a regionwise double series com­ posed of Bessel and trigonometrical functions. The diffusion equation is multiplied by weighting functions, which satisfy the