A wall plume fed by the discharge of a vertical channel

A finite-difference marching scheme was employed to obtain numerical solutions for a wall plume spawned by the discharge from a vertical, natural convection channel flow. The plume is bounded by an isothermal vertical wall that is the continuation of one of the walls of the channel. The wall-plume solutions were carried out for a range of dimensionless heights of the channel and for a Prandtl number of 0.7. Since the channel height controls the velocity and temperature profiles at the channel exit, it also plays a key role in the development of the wall plume because these profiles serve to initiate the plume. Just downstream of the channel exit, the newly exposed flank of the plume interacts with and is cooled by the ambient fluid, while the wall-adjacent portion of the plume retains its channel heritage. Subsequently, the ambient fluid penetrates deeply into the plume, effectively obliterating its channel origins. Thereafter, the plume approaches a natural convection vertical-plate boundary layer. The heat flux at the wall that bounds the plume reflects the complex stages in the plume’s development. Just downstream of the channel exit the heat flux exhibits a slight velocity-related increase, which gives way to a more significant decrease attributable to the temperature rise experienced by the fluid as it absorbs heat from the wall. This decrease is arrested and reversed as the plume is engulfed by fresh (unheated) fluid from the ambient. Then a boundary-layer-type regime is established and the heat flux decreases as the boundary layer thickens.