The stagnation point heat transfer under partially-developed submerged jets

Laminar jet impingement is an efficient method for heat transfer processes, though much of its hydrodynamics and the resulting convection are still not fully understood. As previously shown, stagnation-point heat transfer (Nu₀) depends directly on the near-axis radial acceleration (A₀) varying strongly with nozzle diameter (d), normalized nozzle length (L), normalized nozzle-to-plate spacing (H) and flow rate (Re), therefore a general expression is here developed for this key parameter. Through streamline-bending analysis it was identified that A₀ can be derived from the characteristics of the velocity profile arriving at the point of transition from free jet flight to stagnation flow (at z_w). This analysis also led to the identification of the curvature of the velocity profile in the jet-core as the key factor dictating A₀, over a domain defined by a new characteristic scale R_c. Examination of this curvature, resolves the apparently contradicting trends in the literature for A₀′s dependence on flight distance. Moreover, it explains the occurrence of maximal heat transfer, when h is set around the potential core length. Building on the theoretical analysis, an explicit, yet universal, model for Nu₀ was developed in terms of nominal geometry and flow rate, rather than relying on the often-unknown arrival profile, and validated against simulations over a wide range of conditions (0.003 ≤ L, 0.001 ≤ H, 250 ≤ Re ≤ 2000). Therein, this model pin-points the location of the maximal heat transfer for any issuing profile, enabling efficient design and optimization. Finally, identifying z_w as the stagnation-flow characteristic scale instead of d, enabled extension of an existing wall-approach model to include partially-developed profiles and longer flights. Then requiring the model′s conformity to previous theory gave an explicit expression for z_w – the lower-bound of H⋅Re still permitting heat transfer analysis assuming decoupling between the nozzle and wall flows.