Solution of a diffusion of dust problem in terms of hypergeometric functions

Hankel transforms have been widely used in solving boundary value problems posed in cylindrical coordinates. A modified form of the Hankel transform and some of its properties are considered in connection with the problem of transport of a heavy pollutant (dust) from ground level aerial sources in a strip 0 ≤ x ≤ L within the framework of diffusion theory. Pollutant concentration for x > L is obtained using an integral representation of the solution of an analogous problem with an arbitrary initial pollutant distribution. The results are given in closed form using hypergeometric functions and some special cases are mentioned. Pollutant concentrations in the xz-plane, for different values of the parameters, are represented by some contour plots.