New Jet impingement flow-scale sets wall approach, Proximity limits & wall-jet heat transfer

•A new virtual origin, based on physical constraints, closes Glauert's wall-jet flow solution.•Reynolds analogy led to an analytical solution for heat transfer in the wall-jet region, for both constant wall and constant heat flux conditions.•This virtual origin found to be related to the stagnation zone height – a new profile-specific characteristic scale.•Stagnation zone height employed for a new wall-approach flow description.•Two-fifths of Stagnation zone height shown to be the constriction limit, below which an appreciable back-pressure occurs in the nozzle.•Constriction lowers heat transfer near the stagnation point and raises it farther downstream, at the cost of increased pressure drop. A new scale is here identified as dominant in laminar jet impingement flow and heat transfer, namely, the height of the stagnation zone, zw. This being the point at which the jet “senses” the approaching wall, which corresponds to the location of marginal static pressure rise above the impinged plate. It is shown that this new profile-specific scale emerges from the virtual origin concept in Glauert's wall-jet solution, and physically constrained expressions are derived for both. Reynolds analogy is then conducted for the cases of uniform-heat-flux and -wall-temperature. This leads to a new prediction of the wall-jet heat transfer, valid upon convergence to quasi-self-similarity – within a diameter or two of the stagnation point. The convergence distance depends on incoming velocity profile and flow rate, as captured by the new virtual origin expression. The analysis also reveals that the convergence to self-similarity is delayed in the uniform heat flux case, even though eventually heat transfer is about one-third higher. The new scale also led to a successful description of the deceleration during wall-approach, as an interpolation between near-wall (Homann solution) and far-field (inviscid flow) asymptotes. Consequently, the new scale is shown to give the proximity limits for nozzle-to-plate distance. This being the distance at which the incoming jet becomes distorted due to constriction and back-pressure. Here found to correspond to around 2/5 of the stagnation zone height. All these findings are confirmed and validated through simulations, experimental measurements and literature data; and simple expressions are derived for prediction and design purposes.