Self-similarity of heat transfer characteristics in laminar submerged and free-surface slot jet impingement

Laminar slot jet impingement of free-surface and submerged jets is investigated numerically regarding self-similar behavior in local heat transfer. Two different scaling behaviors, one for the stagnation region and one for the fully developed wall-jet region are shown, and the validity of the scaling is confirmed by fully resolved numerical simulations. Within the stagnation region, self-similarity is obtained if the relaxation process of the velocity profile is considered, which is described by the dimensionless nozzle-to-plate distance as introduced in Rohlfs et al. (2014) for circular jets. Further, it is shown that the Prandtl number dependency can be well described by an analytical relationship obtained by solving the classical similarity solution of a viscous flow near stagnation point. For the wall-jet region, we first derive the scaling behavior based on the work of Watson (1964) for circular free surface jets. This analysis leads to an additional stretching of the spatial coordinate in the wall-tangential direction by the Reynolds number, e.g. .

Finally, correlations for the stagnation region heat transfer are introduced for free-surface and submerged slot jets, dependent on the dimensionless nozzle-to-plate distance and constant heat flux/wall temperature, valid over a wide range of laminar flow conditions (i.e., and ). Thereby, analytic Prandtl dependencies for stagnation point flows are employed and corresponding correlations for impinging slot jets are presented, valid in a very broad range ().