A general correlation for the stagnation point Nusselt number of an axisymmetric impinging synthetic jet Tim Persoons ⇑ , Alan McGuinn, Darina B. Murray Department of Mechanical and Manufacturing Engineering, Parsons Building, Trinity College, Dublin 2, Ireland article info Article history: Received 7 March 2011 Received in revised form 19 April 2011 Available online 14 May 2011 Keywords: Impinging jet Forced convection Synthetic jet formation Local heat transfer coefficient Hot-film anemometry abstract Whereas the heat transfer mechanisms in steady impinging jets are well understood, the available knowledge of heat transfer to impinging synthetic jets remains inconsistent. This paper provides an objective comparison of the stagnation point heat transfer performance of axisymmetric impinging syn- thetic jets versus established steady jet correlations. Furthermore, a general correlation for the stagnation point Nusselt number is proposed including the effect of all appropriate scaling parameters: Reynolds number (500 6 Re 6 1500), jet-to-surface spacing (2 6 H/D 6 16) and stroke length (2 6 L 0 /D 6 40). Based on the ratio of stroke length to jet-to-surface spacing L 0 /H, four heat transfer regimes are identified. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Impinging jets are a well established technique for achieving high local convective heat transfer rates compared to other sin- gle-phase flow configurations. Continuous jets can be used when a pressurized fluid source is readily available, e.g. to cool turbine blades or manufacturing processes. As discussed in the following sections, research has shown that beneficial heat transfer regimes are closely linked to strong fluidic perturbations. As such, the effect of flow pulsation has been studied and more recently, zero-net mass flux synthetic jets have been considered for heat transfer applications as well. These jets consist of a propagating train of vortices synthesized from the surrounding fluid by periodic ejec- tion and suction of fluid across an orifice. Synthetic jets are charac- terized by a Reynolds number, geometric parameters as well as the stroke length L 0 ¼ R 1=ð2f Þ 0 U m ðtÞdt, where U m (t) is the instantaneous mean orifice velocity. Some key heat transfer characteristics of impinging jets are reviewed in the following sections, beginning with steady jets, followed by the effect of flow pulsation and finally some estab- lished aspects of synthetic jet heat transfer, which is the frame- work for this paper. The literature review is kept quite broad to allow an objective comparison of the heat transfer performance of impinging steady and synthetic jets (see Section 3.1), which is one of the objectives of this work. 1.1. Heat transfer to a steady jet For an incompressible laminar jet with a uniform velocity pro- file impinging onto a flat surface, the Navier–Stokes equations can be simplified to analytically determine the following expres- sion for the stagnation point heat transfer coefficient [1,2]: Nu 0 ¼ h 0 D k ¼ C Db U m  1=2 Re 1=2 Pr 2=5 where b ¼ @V =@rj ðx;rÞ¼ð0;0Þ ð1Þ where C = 0.763 or 0.570 for an axisymmetric or two-dimensional jet respectively. The radial velocity gradient b at the stagnation point can be determined for particular cases. Based on a potential flow analysis, Shadlesky [3] derived Db/U m =3p/16 for an axisym- metric jet or p/4 for a two-dimensional jet, resulting in Nu 0 ¼ 0:5856Re 1=2 Pr 0:4 ðfor an axisymmetric jetÞ Nu 0 ¼ 0:5051Re 1=2 Pr 0:4 ðfor a two-dimensional jetÞ ð2Þ Throughout this paper, only single jets impinging at 90 degrees onto planar surfaces are considered. Heat transfer to steady jet arrays, oblique jets or jets impinging onto curved surfaces is reviewed elsewhere [4]. Yet even for a simple impinging jet, the heat transfer characteristics depend strongly on the boundary con- ditions (e.g. the velocity profile in the orifice, turbulence intensity, and geometric confinement) [4]. This explains the wide range of correlations reported in the literature. Table 1 gives an overview of some stagnation Nusselt number correlations for steady jets. Later in the paper (Table 2), a similar overview is given for synthetic jets. Wherever possible, correla- tions are recast in a standard formulation 0017-9310/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2011.04.037 ⇑ Corresponding author. Present address: School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907, USA. Tel.: +1 765 494 5638; fax: +1 765 494 0539. E-mail addresses: tim.persoons@tcd.ie, timpersoons@purdue.edu (T. Persoons). International Journal of Heat and Mass Transfer 54 (2011) 3900–3908 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt