Stagnation point heat transfer under a free-surface jet

Laminar free-surface jet impingement is a crucial configuration for heat transfer processes. Focusing on the link between stagnation-point heat transfer and near-axis radial acceleration, its dependence on jet width and profile is studied. Thus, heat transfer depends on: fluid properties, flow rate, nozzle length, nozzle-to-plate spacing, surface tension and gravity (Pr, Re, L/d, H/d, We & Fr, accordingly). As existing theory is limited to specific cases, a new general description is developed from analogy to submerged jets. Validated by two-phase flow simulations, this description captures key jet dynamics evolution (centerline velocity, profile curvature). It reveals significant property changes during jet flight due to relaxation (L dependence) and contraction (Re/Fr dependence). Unlike submerged jets, contraction raises arrival Reynolds number, leading to additional dependencies Nu ∝ L and Nu ∝ H/Fr, and further deviations at low-We and -Re. The theory successfully predicts heat transfer across diverse conditions and converges to negligible gravity (horizontal jet) as expected.