Erratum: Stagnation flow and Heat Transfer Under Partially-Developed Free-surface Jets (International Journal of Heat and Mass Transfer, (S0017931025006854), (10.1016/j.ijheatmasstransfer.2025.127346))

Although laminar jet impingement is commonly used in transport processes, it's not fully understood. It is known that stagnation-point heat transfer (Nu₀) depends on the near-axis radial acceleration (A₀), which is dictated by the velocity-profile arriving at the wall. This profile varies with: nozzle length (L), nozzle-to-plate spacing (H), flow rate (Re), gravity (Fr), surface tension (We) and even dissipation (at low-Re). Other stagnation zone flow-aspects also depend on A₀, such as the wall approach and boundary layer thickness. Therefore, a new general expression is developed for A₀, which is key to predicting the stagnation flow and heat transfer. Previous (submerged) impingement analysis captured A₀ through the jet's core, while for free-surface jets it is derived from the jet's characteristic curvature. This curvature is obtained from global characteristics: centerline velocity and jet width; thereby circumventing the need for prediction of the full arriving profile. Following the analysis, an explicit, universal, prediction for Nu₀ is found in terms of nominal geometry and flow rate. It is then validated against past and present simulations, even under high surface tension and high viscosity conditions, for both horizontal and vertical jets. Resulting in a wide range of parameters (0.002≤L, 0.001≤H, 225≤Re≤2,000, N_j=Re/Fr<200, 3<We). Therein, the analysis delimited a vertical-jet regime in which heat transfer is independent of the nozzle-to-jet spacing (H) over long distances, where gravitational acceleration counteracts viscous relaxation. The present study lays the foundation for more efficient design and optimization of jet cooling applications and subsequent heat transfer distribution analysis.