CONSTANT PARAMETER STEADY-STATE DIFFUSION. ANALYTIC SOLUTIONS IN TWO AND THREE DIMENSIONS.

Abstract : Analytic solutions are presented for two- and three-dimensional steady-state diffusion problems with constant coefficients. Assumptions of the mathematical model used are: (1) source concentration is known in the source plane, (2) rate of absorption of material into the surface or deposit of material upon the surface is known and is proportional to concentration, (3) concentration at any point is steady state (i.e., independent of time), (4) wind velocity is constant, and (5) the coefficient of diffusion (K) is constant. A general steady-state two-dimensional solution is determined for an arbitrary source concentration function and is given in terms of convolution integrals. The solution is given for sectionally linear discontinuous source concentration functions in terms of dimensionless parameters. A method is developed to extend the two-dimensional results of parts 1 and 2 to three dimensions. Solutions are given for three-dimensional planar source concentration functions symmetric in the plane perpendicular to the wind. (Author)