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An exact method for solving unsteady convective diffusion boundary-value problems is illustrated by solving the specific case of dispersion from a prescribed axisymmetric concen tration distribution at the inlet of the system. The correspondence between the source density distribution and the concentration distribution at the inlet of the system is established rigorously. This enables one to generalize the method previously developed for initial value problems to apply to practicaldoi:10.1098/rspa.1972.0125 fatcat:pys6lpyg4zfblnihes2ung53su