Dependence of submerged jet heat transfer on nozzle length

In this work the influence of nozzle length in submerged jet impingement heat transfer was studied by validated direct numerical simulations, in the laminar flow regime. With the purpose of examining the entire range of nozzle lengths and 500⩽Re⩽2000, other effects were reduced by setting a low nozzle-to-heater spacing (H/D = 3) and ideal, undisturbed inlet conditions. While developing pipe-flow is well-known, this parametric study characterized in detail short and intermediate nozzle flow regimes, affected by a separation bubble at the sharp-edged inlet. It is found that the maximal (centerline) jet velocity first decreases with increasing effective nozzle length, Z = L/(D ⋅ Re), to a minimum at Z^∗≈0.0015, beyond which it increases as in developing pipe-flow. For Z<Z^∗ two physical regimes are found: while the plane of the vena-contracta is outside the nozzle (L/D⩽0.6) the maximal centerline velocity occurs there, rather than at the nozzle exit-plane; whereas in the intermediate range, 0.6⩽L/D and Z⩽0.0015, the centerline velocity scales with the effective nozzle length, Z, and a predictive correlation could be developed for it. As a clear linear dependence of heat transfer on centerline velocity was observed, this predictive correlation could easily be converted into a new stagnation point heat transfer correlation, found to give good agreement over the entire range of nozzle lengths. This correlation provides a practical design tool, especially applicable to micro-jet cooling where constraints correspond with the new model's validity range.