Transient Flow in a Wall Plume and its Application to Solve an Inverse Problem

The transient buoyancy-induced flow generated by a line heat source on a vertical surface is investigated. The transient characteristics of this wall plume are of particular interest in wall fires and electronic systems. The nature of the flow as the leading edge effects move downstream and the flow gradually approaches steady flow is studied in detail. These results are then applied to solve an inverse problem, where the temperature variation downstream is known but the boundary conditions, in terms of heat input and source location, are not. The method presented here is a search and optimization algorithm developed to approach the inverse two-dimensional wall plume flow using only transient data. The data are taken at particular locations on the wall rather than at arbitrary locations. In the forward problem, downstream locations experience a peak in the temperature before attaining the steady state temperature. Here, the time when the peak temperature is achieved is determined at selected points. Then, an interpolation function is presented to relate these peak times with source strength and location. A system of equations is solved to find these. Particle swarm optimization is then applied to solve for the unknown source strength and location with minimum uncertainty.