This paper describes a finite difference experiment to simulate the transient development of the convection column above a strip of uniform high temperature source in a stratified uniform cross flow atmosphere. The k--e model of turbulence is used and an upstream weighted scheme for this vorticity-stream function formulation is employed. Some computation results for a 195 m wide source are presented. The immediate goal of the undertaking was to devise a scheme which could yield relistic flow 'boundary conditions' in the immediate vicinity of a fire to enable one to model the detailed structure of the fire region. The predictions are quite consistent with observations and this provides the link between the heat source and environmental parameters. This scheme, together with refined near zone fire model, can be used to describe the interplay between the heat source (fire) component and the environmental components of a mass fire system.