A general, numerical, marching procedure is presented for the calculation of the transport processes in three-dimensional flows characterised by the presence of one coordinate in which physical influences are exerted in only one direction. Such flows give rise to parabolic differential equations and so can be called three-dimensional parabolic flows. The procedure can be regarded as a boundary-layer method, provided it is recognised that, unlike earlier published methods with this name, it takes full account of the cross-stream diffusion of momentum, etc., and of the pressure variation in the cross-stream plane. The pressure field is determined by: first calculating an intermediate velocity field based on an estimated pressure field; and then obtaining appropriate correction so as to satisfy the continuity equation. To illustrate the procedure, calculations are presented for the developing laminar flow and heat transfer in a square duct with a laterally-moving wall.
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