A numerical study of the heat transfer due to an array of submerged jets impinging on a moving surface

Impingement jet heat transfer is used in numerous industrial processes due to its superior heat transfer characteristics. Cooling of electronic components and turbine blades are two such applications. Paper and textile drying as well as heat-treating of non-ferrous metal sheets also employ arrays of jets. In these instances the impingement surface is moving perpendicularly to the jet. The surface motion introduces phenomena critical to the heat transfer characteristics of the process. The jet-to-jet interaction, the geometrical parameters of the jet array, Reynolds number, and surface motion effects are investigated in a numerical study employing the finite difference technique. The SIMPLE algorithm is employed in the solution of the discretized conservation equations. The jets under consideration are submerged (jet fluid is the same as environment fluid), planar and exit the nozzle with a developed (flat) velocity profile. Laminar and turbulent regimes are considered and the impingement surface is isothermal. In the laminar range, a correlation for the average Nusselt number is derived and entrance effects are addressed. The average heat transfer coefficient on a stationary plate varies approximately as the Re0.558 and the local distribution decays with distance from the impingement point as x−0.5. Both results are consistent with experimental data. Surface motion reduces the overall heat transfer coefficient and provides a more uniform distribution. The simulations of turbulent flow (Re up to 72,300) are performed using the Lam-Bremhorst version of the low-Re k-ϵ model and verified using experimental data on stationary plates. The notorious overpredictions in the stagnation region are alleviated using the Yap correction. Transition from laminar to turbulent flow is predicted via the Schmid-Patankar Production-Term-Modification model. Good comparison with the experimental data is shown. The plate motion causes a more uniform heat transfer distribution and the average heat transfer coefficient increases when the plate velocity approaches or exceeds the jet velocity. Lower plate velocities do not alter the average heat transfer coefficient. As the plate velocity is further increased, the average heat transfer coefficient approaches that of a rotating cylinder in free air and the impact of the impinging jets is overwhelmed by the effect of plate motion.