Mathematical models for flow and heat transfer combined with theoretical analysis and numerical solution are developed to predict the free surface water jet impingement heat transfer for design of water jet cooling equipment with large axles.The stagnation region

boundary layer region and similarity region are numerically solved separately by differential method.Heat transfer characteristics are obtained and validated by comparison with experimental data.Effects and contributions of key parameters on the free surface water jet heat transfer are analyzed and the arrangement for nozzles is discussed.The results show that the Reynolds number based on the nozzle diameter is a dominant parameter in local Nu-r/d distribution.The area-averaged Nusselt number increases with nozzle diameter at a constant Re and the same impinging areas

and with nozzle flow rate.At a constant flow rate

Re and nozzle diameter exhibit comparable heat transfer capacities in small impinging areas

while the combination of larger nozzle diameter and smaller Re presents a better heat transfer effect in larger impinging areas.The area-averaged Nu has a small decrease with the aspect ratio decreasing from 1∶1 to 1∶4.The staggered arrangement for nozzles is better than in-line arrangement for uniform heat transfer though the area-averaged Nu values are nearly the same.