OPEN ACCESS
A comprehensive review on jet impingement heat transfer is presented to consider the stateof the art in this field. Among all the singlephase heat transfer arrangements possible, it has the maximum heat transfer rate. A number of arrangements are possible to represent a practical or physical situation, such as, jet impingement on a solid flat surface or surface fitted with different kinds of turbulent promoters, inclined plane surface and cylindrical convex/concave surface, etc. A significant number of papers dealing with experimental and computational studies on different physical and computational aspects of jet impinging flows are reviewed. Several parameters were found to influence the characteristics, such as, flow confinement, nozzle shape, jet to plate spacing and Reynolds number. An extremely small number of studies dealing with application based jet impingement heat transfer configurations (e.g., ribs fitted impingement plate, moving impingement plate, etc) experimentally and numerically have been reported in the literature. Various computational approaches, such as, RANS, LES, DNS and hybrid models, that are used to study the jet impingement heat transfer, with their complexities and boundary conditions, have been reviewed. It was observed that majority of RANS based turbulence models did not predict impinging flows accurately and its complexities except a few. Many authors have reported that LES is capable of predicting the flow field and heat transfer data within the accepted accuracy limits. DNS can be applied to simple geometry with low Reynolds number. Recently some authors have employed hybrid models, such as, PANS, DES, etc., and concluded that these models provide reasonably accurate results and were found to be computationally less expensive than LES and DNS.
Jet Impingement, Ribs, Turbulence, Nusselt Number, LES
Jet impingement heat transfer is an interesting flow configuration to study because of its industrial as well as fundamental significance. Among all the singlephase heat transfer arrangements, it has the maximum heat transfer rate [1]. Due to growing demand of heat transfer enhancement in many industrial applications, jet impingements are widely used and studied. These techniques are used wherever high performance cooling, heating or drying of a surface is required. Some important industrial applications are cooling/heating of electrical equipment, drying requirements associated with textile and paper industries, cooling of turbine blades and outer combustor wall, freezing of tissues in cryosurgery, annealing of glass, rapid cooling or heating involved in glass manufacturing and shorttakeoff/vertical landing (STOVL) aircrafts, etc. Impinging jets offer an effective and flexible approach to transfer energy or mass in many industrial applications by changing the flow and geometric parameters, such as, jet Reynolds number (Re), nozzle geometry/shape, assembly of jet array, nozzletoplate spacing, angle of jet impingement, turbulence properties at the exit of the jet, ribbed surfaces and flow pulsation, etc.
Although jet impingement on a plate is geometrically simple, it involves a number of interesting complex physical flow configurations, namely, freeshear region (realization of large scale vortex structures), stagnation region (with strong streamline curvature) and a wall jet region. With escalating requirements for industrial efficiency and safety, slot and round jet impingements on a plane surface have been studied by the researchers. Several arrangements are possible to represent a physical situation involving, such as, jet impingement on a solid flat surface or surface fitted with different kinds of turbulent promoters, inclined plane surface and cylindrical convex/concave surface, etc. In the present paper we have considered a number of experimental and computational approaches used in the literature for jet impingement heat transfer to assess the stateofthe art in the field.
1.1 Flow patterns
A flow with air jet impingement orthogonally on a flat surface follows some distinct regions (Fig. 1). At the nozzle exit, the emerging jet may pass through a region where it is sufficiently faroff from the impingement plate so that it acts like a free submerged jet or free jet region. In this region, the entrainment of mass, momentum and energy occurs due to sheardriven interaction of the surroundings with existing jet. The fluid from the surroundings gets entrained in to the jet and hence there is a reduction in the jet velocity with an increase in the total mass flow rate. In the process, the jet loses kinetic energy and the velocity profile expands in the spatial direction and shrinks down in magnitude along the sides of the jet. Thus, a nonuniform radial velocity profile develops within the jet. Further the free jet can be subdivided into three regions, namely, the potential core, developing and developed regions.
The shearlayer or mixinglayer surrounds a core where the nozzle centerline fluid velocity (U_{m}) is approximately equal to the jet exit velocity and this region is called the potential core. The end of a core region may be defined as the point where U_{m} = 0.95U_{exit} [2]. The length of the potential core significantly depends on the jet exit flow conditions and geometry of the nozzle. The length of the potential core zone is found to be nearly 67 diameters and 4.7  7.7 slot widths from the nozzle exit for round and slot jets, respectively [2]. After the potential core, the axial velocity profile decays due to large shear stresses at the boundary of the jet and this region is characterized as the developing zone. After the developing zone, a fully developed velocity profile is obtained and it is designated as the developed region (Fig. 1).
Figure 1. Different regions of a jet impingement flow
A free jet region may not be present if the nozzle exit lies at a distance of two diameters or slot widths from the target plate [3]. Schlichting [4] showed that the jet half width (a distance where U = U_{m}/2 down the jet axis) and reduction in the center line velocity are directly related to the axial distance after the termination of the potential core. At the point where the jet strikes, the impingement surface is often referred to as the deflection zone/ stagnation region. In this region, the axial velocity quickly diminishes with a consequent rise in the static pressure. Thereafter the wall jet region, where the bulk flow is in the radial outward direction, becomes important (Fig. 1).
A comprehensive review of the relevant literature is presented here. It consists of different physical and computational aspects of impinging flows. Most reported studies have presented profiles of mean velocity, turbulence and heat transfer rates in different regions of the impinging flow. Heat transfer is generally expressed in terms of Nusselt number (Nu), defined as hB/k, with h, B and k representing heat transfer coefficient at the surface, hydraulic diameter (slot width, B in case of slot jets) of the nozzle and thermal conductivity of the plate material, respectively. It was observed that the stagnation point Nusselt number (Nu_{st}) and the surface distribution of Nu are the most widely reported quantities in the literature. All these quantities depend on some basic parameters discussed here.
Jet impingement heat transfer and flow features depend on various parameters, namely, jet Re, Prandtl number (Pr), heat transfer coefficient (h), turbulence at the jet exit, nozzle geometry, flow confinement, spacing between jet exit to impingement plate (H/B) and distance from the stagnation point (x/B), etc. The effect of these parameters on flow field and heat transfer characteristics of slot jet impingement has found special attention in the literature both experimentally and computationally [3, 57].
Gardon et al. [8] showed that in case of impinging jets, the heat transfer properties cannot be understood with velocity and position dependent boundarylayer thickness only. These can, however, be explained by considering the influence of turbulence. Koopman and Sparrow [9] experimentally studied the effect of a row of impinging jets on plane surface on the local and average heat transfer coefficients. They showed relatively high local heat transfer coefficient in the midway between the neighboring jets due to the collision of the spreading flows from nearby jets. They also showed that at the stagnation point the maximum heat transfer occurs and it depends upon the jet to plate distance. Baines and Keffer [10] observed the shear stress to be minimum at the stagnation point with a local maxima in nearby regions. The effect of small nozzle to plate spacing on Nu_{st}and Nu was investigated by many researchers, such as, Hoogendoorn [5], Lytle and Webb [11], and AshforthFrost et al. [3].
Hoogendoorn [5] observed that the Nusselt numbers were slightly higher in the vicinity of the stagnation point than at the stagnation point for z/D < 5 and Re = 20000 to 90000. Lytle and Webb [11] experimentally investigated jet impingement heat transfer for the nozzle to plate spacing of less than one diameter. They considered nine values of Re from 3600 to 27600 and observed considerable augmentation in mean velocity and r.m.s. turbulence fluctuations with a reduction in the nozzle to plate spacing. They showed significant enhancements in heat transfer and turbulence level due to forced acceleration of impinging fluid for small spacing. AsforthFrost and Jambunathan [6] studied the effect of semiconfinement and nozzle geometry for axisymmetric air jet on the potential core at a Re of 22500. They showed that the potential core was 7% longer for fully developed condition compared to the flat jet exit condition. They also observed extended potential core by up to 20% for a semiconfinement case compared to an unconfined case, and reduced stagnation point heat transfer by 10%. The maximum stagnation point heat transfer was obtained when the impingement plate was placed at the end of the potential core. Tu and Wood [12] experimentally measured wall pressure and shear stress for 2D turbulent jet impingement on a flat plate. The uncertainties associated with the pressure measurement were +2% and +5% for the wall shear stress measurement, respectively. They performed experiments with Re from 3040 to 11000 and several H/D values and observed a Gaussian distribution of the mean static pressure independent of Re. The shape of the wall shear stress distribution depended on both Re and the nozzle to plate spacing. They showed that the half width (b) of the pressure profile increased with plate spacing. Their data may be used to validate numerical models.
AshforthFrost et al. [3] experimentally investigated velocity and turbulence characteristics of a semiconfined impinging slot jet. They considered H/B of 4 and 9.2 with Re = 20000 and showed that the length of the potential core was longer with the semiconfined arrangement than with the unconfined arrangement due to narrow entrainment and scattering of jets. For the impinging jet, turbulence characteristics and velocity were found directly in relation to heat transfer. They also observed that for a low nozzle to plate spacing a secondary peak in Nu was distinct. Maurel and Solliec [13] experimentally investigated the development of the jet impinging normally on a flat plate using LDV and PIV with variable geometry. They considered turbulence intensity at the nozzle exit between 1.6% to 2.8% and Re from 67000 to 110000. From their parametric study they concluded that the characteristic height of the impinging zone was close to 1213% of the total height (H). Zhe and Modi [7] experimentally studied velocity field near the target surface for a 2D slot jet impingement configuration with H/B from 2 – 9.2 and jet Re from 10000 – 30000. They employed a boundarylayer probe at a distance of approximately y^{+} = 2 to 4 in order to document the wall shear stress. The length in the zdirection was considered six times of its slot width. The uncertainties in their near wall measurement were 9% and mean and root mean square velocity were 4% and 3%, respectively. They carried out all the measurements in the region of x/B = +13 and y/B = 0 to 0.35 at z = 0 plane. They observed that the skin friction coefficient was independent of Re in the range of 10000 to 20000 and on the other hand it was observed to depend on H/B value. However at H/B = 2, 3 and 4 it showed slight variations. The shear at low nozzle to plate spacing showed a clear secondary peak which was absent at higher nozzle to plate spacing. Their experimental data may be used to validate numerical models.
O’Donovan and Murray [14] experimentally investigated flow field and heat transfer characteristics from a heated flat plate with H/B of 0.5 to 8 and Re from 10000 to 30000. They showed secondary peaks in heat transfer distributions in the radial direction for jet to plate spacing less than two diameters owing to a sudden growth in turbulence in the wall jet region. They also showed that high heat transfer regions are associated with the high fluid velocity and turbulence intensity regions. They observed peaks in heat transfer distribution at locations where the velocity fluctuations in normal direction to impingement plate were high. Further O’Donovan and Murray [15] experimentally investigated the temporal nature
of heat transfer and fluid flow with the values of all parameters being same as in their former study. They showed that the growth of vortices through the distance from the jet axis affected the heat transfer coefficient in the wall jet region.
Alekseenko et al. [16] experimentally studied the influence of swirl rate of an impinging jet on flow field using PIV and stereo PIV techniques. They considered H/D = 3, Re = 8900 and swirl rate from 0  1.0 and observed a decreased level of pressure diffusion with increasing swirl rates. They showed a large recirculation zone between the jet exit and the impinging surface at a swirl rate of 0.41 and vortex breakdown at swirl rates of 0.70 and 1.0 with a smaller recirculation. Strong generation of turbulence was observed due to vortex breakdown resulting in high values of TKE in the local regions. Bakirci and Bilen [17] experimentally visualized the temperature distribution on the impingement surface maintained at a constant temperature for the multichannel, swirling and conventional jet impingements by means of liquid crystal technique. They used swirl generator insert with the swirl angle fixed at 0^{0}, 22.5^{0}, 41^{0} and 50^{0} to alter the direction and strength of the swirl. The local Nusselt numbers for the multichannel impinging jet (at an angle of 0^{0}) were found much higher than those for other two configurations. The positions of the heat transfer peaks were moved sensitively from the stagnation point, when swirl angles were increased but decreased values of local and average Nusselt numbers were observed when swirl angles were increased.
Senter and Solliec [18] experimentally investigated flow field of a confined turbulent slot jet impinging orthogonally on a moving flat surface using PIV. They performed experiments for H/B = 8, Re = 5300, 8000 and 10600 and four surface to jet velocity ratios (0, 0.25, 0.5 and 1). They observed that the flow field topology was independent of Re ranging from 530010600 at a particular surface to jet velocity ratio. They observed a slightly affected flow field at a surface to jet velocity ratio of 0.25 and the most influenced flow field pattern was found at the surface to jet velocity ratio of unity. Turbulence intensity measurements in the vicinity of the stagnation zone showed enhanced values with increasing surface to jet velocity ratio.
Ozmen [19] experimentally analyzed flow characteristics of confined twin air jets impinging normally on a surface at high Re with the smoke wire technique. The uncertainties associated with axial velocity and turbulence velocity measurements in the vertical direction were +3% and +4%, respectively, and with pressure measurement it was +2%. He obtained pressure distribution on the impingement and confined surfaces with Re in the range of 30000 to 50000, H/D 0.5 to 4 and jet to jet spacing (L/D) 0.5 to 2. He observed subatmospheric region at the nozzle to plate spacing up to 1 diameter on impingement and confined plate both for the range of Re and jet to jet spacing studied and concluded that subatmospheric regions and heat transfer coefficients peaks were corelated for low spacing.
A small number of studies dealing with jet impingement heat transfer on a rib fitted surface, experimentally or numerically, exist in the literature. Jet impingement on a rib fitted target surface disrupts the wall jet and thus level of turbulence and heat transfer are expected to increase [20]. Katti and Prabhu [21] studied the effect of rib height, width, pitch, clearance of the detached ribs from the flat plate and the location of the first rib from the stagnation point on local heat transfer. They observed continuous Nu augmentation from the stagnation point up to the first detached rib for all the configurations studied, due to an accelerated fluid in the stagnation zone by the clearance of the first rib. They also observed that the addition in the rib height may lead to reduction in Nu downstream from the first rib. Likewise Gau and Lee [22] observed that the flow features with ribroughened walls were different from the flat plate configuration with a reduced heat transfer near the impingement region. Subsequently Gau and Lee [23] experimentally studied jet impingement heat transfer on a triangular ribbed surface. They showed that air bubble formation in rib cavities near the stagnation point could reduce heat transfer, which sometimes could be smaller than that on a flat plate. But they showed that for more turbulent wall jet a significant enhancement in heat transfer with ribbed surface could be achieved. However if jet flow hits the ribbed surface containing large turbulence, e.g., with high Re or large H/B value, then the wall jet may possibly infiltrate the rib cavity and can effectively impinge on the surface with a subsequent reduction in the drag force due to rib projection. Thus an enhancement in heat transfer can be achieved [23]. Recently Tan et al. [24] experimentally investigated three rib configurations, namely, orthogonal, Vshaped and inverted Vshaped ribs with H/B values of 1 to 3 and Re from 6000 to 30000. They observed 30% enhancement in heat transfer with the rib roughened wall than that with a flat plate.
Baydar and Ozmen [25] experimentally and numerically obtained the mean velocity, pressure distribution and turbulence intensity for Re ranging from 30000 to 50000 and H/D 0.2 to 6. Uncertainties involved in experimental results obtained were +2% in Re, +5% in axial velocity, +6% and +4% in turbulent velocities (u' and v'), and +1% in the pressure measurements at the impingement plate. They concluded that turbulent intensity, heat transfer coefficients and subatmospheric region were linked together and found the predictions using the standard kɛ model to be in best agreement with their experimental results for moderate H/D values. Fattah [26] experimentally and numerically studied a 2D circular jet impingement flow without any cross flow. He considered jet Re from 95000 to 224000, H/D 3 to 12, jet angle 0^{0} to 20^{0} and nozzle to nozzle centerline spacings (l/D) of 3, 5 and 8. The accuracy in wall static pressure measurement was +3% and in temperature reading of +0.5^{0}C. He observed a secondary stagnation point between the jets and a decreased pressure at this point by increasing the jet angle or decreasing Re.
Sagot et al. [27] experimentally and numerically studied the heat transfer configuration for a round jet impingement on a flat plate maintained at a constant wall temperature. They observed that the SST kω turbulence model performed well when local Nu was compared with the experimental data. Numerical results obtained with a constant wall temperature applied at the impingement wall were found to be in good agreement compared to a constant heat flux condition. Öztekin et al. [28] experimentally and numerically investigated the hydrodynamics of a slot jet impingement on concave flat surfaces. They carried out experiments for Re ranging from 3000 to 12500, H/B 1 to 14 and dimensionless curvature values (R/L) of 0.5, 0.5125, 0.566, 0.725 and 1.3 of impinging surface. They performed simulations with the kɛ model for concave plate with dimensionless curvature value (R/L) = 0.725 and flat plate with enhanced wall functions. They observed a decreased value of the pressure coefficient at the stagnation point with H/B and variation of the local pressure coefficient computed with the standard kɛ model with an enhanced wall treatment was in excellent agreement with the experimental data. Caggese et al. [29] investigated the heat transfer characteristics of fully confined jet impingement experimentally and numerically with low H/D values of 0.5 to 1.5 and Re in the range of 16500 to 41800. They observed significant effect of different separation distances on the flow field and hence it affected the distribution of heat transfer coefficient. Their numerical results showed satisfactory prediction of local and average Nusselt numbers.
4.1 RANS computations
Majority of RANS based turbulence models considered in the literature did not predict impinging flows accurately and its complexities except a few [3033]. AlSanea S [34] numerically investigated the heat transfer and flow characteristics of an impinging laminar slot jet. He observed identical results for free and semi confined jet impingements with a slight difference down the region due to entrainment effects. He also showed increased Nu with jet Re and Pr and it decreased with a reduction in the H/B value. They showed that the crossflow effect can reduce the nominal Nu by as much as 60%. Further Sharif and Banerjee [35] numerically investigated heat transfer from a moving plate due to confined slot jet impingement. They specified 2% turbulence intensity at the jet exit and a length scale equal to 2B with constant pressure outlet condition to handle such complex flow situations due to plate movement.
Arquis et al. [36] computationally studied the flow and heat transfer features for cooling of an array of multiple protruding heated blocks using laminar slot jet and studied the effect of channel height, Re, slot width, spacing between blocks and height of blocks on heat transfer and fluid flow. They categorized the flow field with the presence of impingement flow and wall jet flow with possible survival of a primary circulation cell between the jet and confinement wall. They observed secondary circulation cells between the blocks, plus a secondary recirculation cell at the top surface of the downstream blocks. The strength and size of primary and secondary circulation cells and the flow separation (formation of recirculation cells) at the top surface of downstream blocks were found to increase with Re, channel height and decreasing slot width. These flow structures significantly affected the heat transfer characteristics. They also observed that cooling efficiency of all the blocks increased with Re and through reduction in slot width and channel height. But an increase in Re and channel height and reduction in slot width decreased the heat transfer rates from the downstream blocks because of the formation of recirculation cells at the top surface of these blocks. Dutta et al. [30] observed that the inflow turbulence intensity strongly affected the heat transfer distribution on the wall and the discretization scheme did not produce any significant difference in computed results for second or higher order scheme used. Some important literature dealing with RANS computations of jet impingement heat transfer with key parameters considered and observation made are summarized in Table 1.
Table 1. A summary of important RANS computations of jet impingement heat transfer
Author(s) 
Configuration and important parameters studied 
Summary of important observations 
Craft et al. [32] 
Three different Reynoldsstress transport (RSM) models and a lowRe kε model studied for round impinging jet at Re of 23000 and 70000. 
Poor performance of the eddyviscosity model and the basic RSM model. Inaccuracy of RSM was due to the use of the eddy viscosity model near the wall which could be removed by using a lowRe version of RSM. 
Heyerichs and Pollard [37] 
Wall functions and lowRe versions of kε and kω models for impinging jet assessed. 
Observed poor performance of the wall functions approach compared to lowRe model. The kω model performed superior than the kε model. 
Hofmann et al. [33] 
Thirteen different RANS models tested for steady and pulsating impinging jets. 
Observed that SST kω model can accurately predict the pulsating jets. 
Wang and Majumdar [38] 
Compared lowRe kε models using the Yap correction in the dissipation (ε) equation for a turbulent slot jet. 
Observed that the Yap correction reduced the turbulence length scale in the near wall region and thus it was found to overpredict the turbulence kinetic energy in the stagnation region.

Behnia et al. [31] 
Studied axisymmetric isothermal fully developed turbulent jet impinging on a flat plate for fixed Re = 23000 and H/D = 0.5  14. 
Predictions of local heat transfer coefficient with v^{2}f turbulence model were in excellent agreement with the experimental data while the kɛ turbulence model overpredicted the flow features. 
Behnia et al. [39] 
Turbulent heat transfer in confined and unconfined axisymmetric impinging jets with wide range of Re and H/D. 
v^{2}f turbulence model showed an excellent agreement with experimental data. They also observed strong effect of turbulence intensity and velocity profile on Nu distribution. 
Yang and Tsai [40] 
High turbulence air jet impingement on a circular disk with lowRe kω turbulence model with Re = 16100 to 29600 and H/D = 4 to 10. 
Re has a considerable effect on the flow field and heat transfer. They observed that high value of turbulence in the jet leads to higher heat transfer coefficients in the stagnation zone. 
Draksler and Koncar [41] 
Studied local heat transfer and flow field characteristics for axissymmetric impinging jet with eddy viscosity based SST turbulence model. 
RANS computations of local and average heat transfer predictions were satisfactorily accurate. They observed that chamfering the edges of nozzle inlet resulted in a reduction in the heat transfer and pressure drop. 
Yang et al. [42] 
Flow and heat transfer features for slot jet impinging on a semicircular concave surface with kε model for Re = 5920  23700 and H/B = 0.5  12. 
Maximum Nu occurred at the stagnation point and predicted local Nu were in good agreement with the experimental data with a maximum deviation of 15%. 
Dutta et al. [30] 
Compared various RANS models for prediction of flow field and heat transfer for slot jet impinging flows with Re = 20000 and H/B = 4 and 9.2. 
Standard and SST kω models with transitional model for low H/B value and standard kε models for high H/B value were found to be in best agreement with the experimental data. 
Sharif and Banerjee [35] 
Heat transfer from a moving plate for 2D slot jet studied with standard kε turbulence model and RSM model with enhanced wall treatment for Re = 5000 to 20000, H/B = 6 to 8. 
Significant increment in average Nu with jet Re and plate velocity (normalized with jet exit velocity and varied in the range 0 to 2). The average skin friction coefficient was found comparatively unaffected with Re but it increased with the velocity of plate. 
Xu et al. [43] 
Heat transfer enhancement with turbulent impinging jet due to intermittent pulsation with 2D symmetric slot jet configuration studied with uniform velocity profile applied at the jet inlet. 
Heat transfer rate was significantly dependent on progresses of thermal and hydrodynamic boundarylayers with time. They showed considerable enhancement in heat transfer by the intermittent pulsation. Further they observed significant effect of onoff jet time ratio and H/B on heat transfer rate. 
Pakhomov and Terekhov [44] 
Fluid flow and heat transfer characteristics for an intermittent turbulent impinging round jet. They carried out simulation for steady state and intermittent cases both with Reynolds stress transport model. 
They reported reduction in heat transfer with an increase in Re such that the pulsed case turned approximately into a steady state one. They observed increased Nu with an increment in pulse frequency (f < 150 Hz) and at small frequencies (f < 30 Hz). 
Dutta et al. [45] 
Slot jet impingement heat transfer with nano fluid (Al_{2}O_{3}water). The standard kε model, SST kω model and v^{2}f model were used for computation. 
The average heat transfer coefficient at the impingement plate was observed to be approximately 27% and 22% for laminar and turbulent slot jet impingement, respectively. However the pumping power was found to increase by five times. 
4.2 LES and boundary conditions
Many authors, such as, Cziesla et al. [46], Uddin et al. [47], Dutta et al. [48], Dairay et al. [49] and Dutta et al. [50] observed that LES can predict the flow field and heat transfer data within the accepted accuracy limits. Development of LES wall functions for computation is quite important for impinging flows [1]. Cziesla et al. [46] considered periodic boundary condition along the width (equal to two slot widths), height of 8B  12B (spacing between nozzle to plate) and length 10B of the domain. Beaubert and Viazzo [51] suggested that the length of the computational domain in the horizontal direction must be large enough to capture two big recirculations on both sides of jet and showed that x/B = +40 is sufficient. Similar to Cziesla et al. [46], they also considered the periodic boundary along the width of the domain and suggested that this dimension should be large enough to capture the biggest structures of the flow in order to justify the periodic conditions.
Chattopadhyay and Saha [52] investigated the flow field and heat transfer in a rectangular slot jet, impinging on moving surface and the velocity of the impinging plate was varied two times the jet exit velocity. They considered various turbulence quantities. Icardi et al. [53] predicted turbulent flow field in a 3D confined impinging jets reactor (CJIR) with different SGS models and boundary conditions. They observed a good agreement for mean and fluctuating velocity predictions and the effect of subgrid scale model was found to be insignificant for low to moderate values of Re. They suggested that LES can be used rather than expensive DNS and micro PIV experiments to obtain fast and consistent data.
Table 2. A summary of important LES computations of jet impingement heat transfer
Author(s) 
Configuration and important parameters studied 
Summary of important observations 
Gao and Voke [54] 
Instantaneous thermal distribution with simple SGS model at Re = 6500 and with different fluid properties. 
Observed that for jets with cool edges and hot core, the cooled fluid accumulated in the recirculation regions, but the hot fluid spread over the plate as the jet impinged. 
Voke and Gau [55] 
Plane water jet impinging normally on a plate examined at Re = 6500 and with Smagorinsky SGS model. 
Proposed that the simple 1D conduction model is capable of computing the near wall thermal behavior. 
Olsson and Fuchs [56] 
LES of semiconfined circular impinging jet at Re = 10000 with both dynamic and similarity SGS models. 
Influence of SGS model on velocity field was assessed. They reported that similarity model performed better than the dynamic model at sufficient resolution. 
Cziesla et al. [46] 
Flow field and heat transfer for an impinging jet emanating from a rectangular slot nozzle at Re = 2000  10000 with dynamic SGS model. 
The model was capable of predicting the turbulent production rate. They observed negative turbulent kinetic energy production rate close to the wall and jet centerline and a better accuracy in the heat transfer predictions at the stagnation region. 
Tsubokura et al. [57] 
Compared 3D eddy structures for both plane and round impinging jets at Re = 6000 and with dynamic SGS model. 
Twin vortices were observed in the impingement region of plane jet. They also observed non organized structures in the stagnation region for round jet. 
Beaubert and Viazzo [51] 
Plane jet impingement using the dynamic Smagorinsky model at Re = 3000 to 13500. 
The wall shear stress at the impingement wall and effect of Re on the kinematic expansion of the jet were analyzed. 
Beaubert and Viazzo [58] 
Examined the influence of Re on structure of a plane jet at Re = 3000 and 7500 using dynamic SGS model. 
Counterrotating cells were observed near the impingement zone. 
Chattopadhyay and saha [52] 
Investigated the flow field and heat transfer emanating from a rectangular slot jet impinging on moving surface at Re = 5800 using dynamic SGS model. 
They observed increment in the turbulent kinetic energy with impinging surface velocity. Turbulence production rate increased primarily with the increment in the surface velocity and thereafter it came down. 
Mingzhou et al. [59] 
Flow field of a semiconfined rectangular exit turbulent impinging jet, on a flat surface at Re = 8500 and with dynamic SGS model. 
They observed that the secondary vortices generated in the wall jet region were due to the periodic advancement of the primary vortex structure. 
Hadžiabdić and Hanjalić [60] 
Studied the vortical and turbulence structures with the local heat transfer in impinging flow with Re = 20000 using dynamic SGS model. 
Their LES data provided clarifications for some of the experimentally noticed flow features, e.g., secondary peak in Nu and the negative turbulence energy production in the stagnation region. 
Rhea et al. [61] 
Investigated the single phase jet impingement with RANS and LES computations at Re = 10000 using dynamic SGS model. 
Observed some underproduction of turbulence quantities by the RANS computations in critical regions, e.g., in free and wall jet regions, the LES computations showed close agreement with the experimental data, particularly in critical zones. 
Uddin et al. [62] 
LES of an impinging jet to provide suitable data for validation of mathematical models at Re = 23000 using dynamic SGS model. 
Mean, turbulent flows and turbulent heat flux were calculated for the assessment of three turbulent heat flux models for predicting round impinging jets. 
Lodato et al. [63] 
Studied wall jet interaction with mixed similarity and WALE models at Re = 23000 and 70000. 
Compared to standard WALE, mixed similarity model showed significant improvement in the prediction of the second order moments. 
Uddin et al. [47] 
Dynamic Smagorinsky model was used to obtain the flow field and heat transfer characteristics of jet impingement at Re = 13000 and 23000 and jet to plate spacing (H/D) of 2. 
They observed that LES computations of impinging jet were extremely sensitive to the quality of the grids linked with different zones. They observed intermittent ring of vortex generation when jet struck the surface. 
Dutta et al. [48] 
Fluid flow and heat transfer of a turbulent slot jet impingement at Re = 13500 and H/B of 10 with dynamic SGS model. 
They showed that peaks of Nusselt number and turbulence kinetic energy coincided and concluded that the turbulence plays an important role in wall heat transfer. 
Dairay et al. [49] 
Computed turbulent jet impinging on a heated wall at Re of 10000 and H/D = 2. 
They concluded that in more realistic situation, increase of spatial resolution of LES resulted in capturing more correct flow feature and hence the secondary peak in Nusselt number. 
Table 2 presents review of important literature dealing with LES of jet impingement heat transfer with their key observations and numerical challenges. Uddin et al. [47] performed LES using second order accurate schemes for space and time discretizations and observed that the flow acceleration in the developing zone of the boundarylayer was linked to the secondary peak observed in the radial
distribution of Nu. Dairay et al. [49] computed turbulent jet impinging on a heated wall with LES using higher order numerical scheme and performed DNS for Re = 10000 and H/D = 2. They used DNS results as a reference to compare two LES computations, one based on the hypothesis of conventional eddy viscosity and the other on high order numerical dissipation. Both LES computations were found to be acceptable in predictions of velocity statics compared to DNS and experimental data. They observed that the conventional eddy viscosity based subgrid scale model (dynamic Smagorinsky and WALE) did not control numerical errors at small scale, which led to unrealistic predictions of heat transfer in the impingement zone. They also observed that strong nonlinearities present in the expressions for dynamic Smagorinsky and WALE models were a substantial source of error generation. Dutta et al. [48] used two inflow conditions, i.e., one with no inflow fluctuations and the other with fluctuations. They observed that LES results without any inflow fluctuations were in good agreement with the experimental data for the predictions of mean flow, turbulence intensity and heat transfer on the impingement wall.
4.3 DNS and hybrid approaches
DNS can be applied to simple geometries with low Re [64  66]. Hattori and Nagano [65] carried out DNS and observed the effects of nozzle to plate spacing. They observed a secondary peak in the local Nu in the wall jet developing region for low H/B value and showed larger wall normal turbulence intensity close to the wall in the wall jet region and hence a secondary peak in Nu occurred. They also observed a secondary peak in the skin friction coefficient in case of low H/B value similar to that of local heat transfer.
Jaramillo et al. [66] performed DNS and RANS computations in order to assess the flow field and heat transfer characteristics of plane impinging jets with Re = 20000 and H/B = 4. They used DNS results reference data to assess the performance of several RANS based models. They considered periodic boundary condition in the spanwise direction and turbulent length scale of 0.015B at the inlet and suggested that the outflow should be placed at least at 40B to capture main recirculating flow from the jet centreline. They showed that DNS produced noteworthy outcome on the local heat transfer upon changing the boundary condition at the impingement wall from a constant heat flux to a constant temperature.
Kubacki and Dick [67] simulated plane impinging jets using the kω based hybrid RANS/LES and kω RANS models with H/B = 10, 9.2 and 4 and Re from 13500 – 20000. They set πB as the size of the domain in the spanwise direction and applied periodic boundary and turbulent length scale at the inlet was set as 0.015B and observed that the hybrid models predicted the wall shear stress and heat transfer rate on the impingement plate in much better way than by the kω RANS model. They also observed that the hybrid model was capable of resolving the evolution of the large scale structures originating at the jet exit and its destruction in to smaller scales. Further Kubacki and Dick [68] simulated the flow and convective heat transfer characteristics of round impinging jets for different set of H/D of 2, 6 and 13.5 and Re of 5000, 23000 and 70000. They tested the kω model with three hybrid RANS/LES models and observed that the turbulence kinetic energy was overpredicted at low value of H/D computed by RANS model. For high H/D value the turbulence mixing was underpredicted by RANS model in the shear layer and thus length of the potential core became too large and therefore heat transfer results were also overpredicted. They observed that all hybrid RANS/LES models produced better result by improving over and underpredictions of RANS model.
Kubacki et al. [69] studied the capability of hybrid RANS/LES computations of jet impingement with Detached Eddy Simulation (DES) and PartiallyAveraged Naiver Stokes (PANS) model for two configurations, i.e., H/B = 10, Re = 13500 and H/B = 4, Re = 20000. They considered the outflow boundary condition at X = +40B, periodic boundary condition in the spanwise direction (width equal to π) and turbulent length scale as 0.1667B. For DES the turbulent length scale was substituted by the grid size in the eddy viscosity formulation and in the destruction term of kequation and for PANS it was substituted from the subfilter dissipation rate and total turbulence kinetic energy. They observed that the hybrid models in contrast to RANS models were capable of replicating the turbulent flow dynamics of the impinging jet in the shear layer. They observed that the prediction of the skin friction was better with DES than with PANS. Taghinia et al. [70] performed CFD study of twin jet impingement using hybrid RANSLES model. They applied the SSTSAS kω (shear stress transport with scaleadapted simulation) model with hybrid (RANS/LES) feature for turbulence modeling. They observed that the SSTSAS model can predict reasonably accurate results particularly for low H/B value and showed accurate prediction of the peak value of Nu by the SSTSAS model.
Zuckerman and Lior [20] described the physics, correlations and numerical simulation techniques for jet impingement heat transfer. They studied various turbulence models, namely, kɛ, kω, RSM, algebraic stress, SST and v^{2}f, to identify methods to predict with their drawbacks and suitability. They observed that the SST and v^{2}f models provided the best result in small computation times. Jambunathan et al. [71] reviewed the experimental data of heat transfer available for single circular impinging turbulent jets and considered Re in range of 5000 to 124000 and H/D 1.2 to 16. Based on the assessment of the empirical results they showed Nu as a function of Re, axial distance, H/D and Pr. They also showed that Nu in the wall jet region was independent of H/D in the range of 1 to 12 for circular jets.
Viskanta [72] considered both slot and circular jets and effect of cross flow on jet impingement heat transfer. He emphasized on physical phenomenon involved in impingement heat transfer for all the cases considered. He summarized the effect of various factors for single and multiple gas jets, such as, turbulence in jet, geometric effects, jet outlet conditions, angle of incidence, curvature surfaces and various other external factors on impingement heat transfer enhancement. He observed that for single impinging jet the maximum heat transfer occurred at the end of the potential core (nearly 6 diameters downstream). Zukerman and Lior [73] carried out a concise review of accuracy and shortcomings associated with numerical methods used to predict flow field and heat transfer characteristics of jet impingement and showed that kε, kω, ASM and RSM models provided poor results compared to experimental data even with high resolution grids. The SST and v^{2}f RANS models produced better prediction of flow field and heat transfer characteristics. Dewan et al. [1] presented a review of computational status of turbulent jet impingement heat transfer. They reviewed SGS models, inflow and other boundary conditions associated with different LES studies and concluded that the accuracy of different LES computations cannot be judged because of a lack of the generalization in the reported LES data.
Some key conclusions that can be drawn from the literature review presented here are as follows. Jet impingement heat transfer configuration is widely studied by many researchers, both experimentally and computationally. Several parameters were found to affect its flow features and heat transfer characteristics, such as, flow confinement, nozzle shape, jet to plate spacing and Re. These parameters have found special attention in the literature either experimentally or numerically. Low nozzle to plate spacing configuration was less studied computationally with LES or hybrid models. Some authors, such as, Chung et al. [64] and Jaramillo et al. [66], showed that DNS can be applied to simple geometries with low Re but its result can be used as a reference as the use of DNS is much more expensive than LES. Further, some hybrid models are needed that can predict the fluid flow and heat transfer characteristics within the acceptable accuracy limits [73]. Recently some authors [6769] have used hybrid models, such as, PANS, DES, etc., and concluded that these models provide reasonably accurate result and were found to be less computationally expensive than LES and DNS. Hence some of hybrid models, such as, PANS and DES, may be used to obtain a suitable compromise between the accuracy and cost of solution.
A small number of studies dealing with application based jet impingement heat transfer configuration, e.g., ribs fitted impingement plate, moving impingement plate, etc., experimentally or numerically have been reported in the literature. Pulsating inlet flow jets produce large scale eddies in the vicinity of jet exit, which cause unsteady boundarylayers on the impingement plate. This behavior may change the heat transfer and flow features of jet impingement on a surface and it depends on the frequency of flow pulsation, Re and other dimensions [20]. Jet impingement on a rib fitted target surface disrupts the wall jet. Hence level of turbulence is expected to increase and consequently the heat transfer. But the use of ribs increases the drag force and the wall jet decelerates and disappears rapidly. This effect needs to be analyzed in details [20].
Fig. 2 shows details of the computational domain that can be considered to study jet impingement on flat and ribbed surfaces [30, 46, 67, and 69]. The no slip boundary condition can be applied at all walls (confined wall, impingement wall and ribs). A constant heat flux or constant temperature can be applied at the impingement plate. Fully developed flow or velocity profile observed in experiments can be applied at the nozzle exit with the specification of the nozzle exit velocity U based on Re with turbulence intensity (I) and turbulent length scale. The outflow boundary conditions were applied in the reported studies at sufficiently large distance to avoid a reversed flow. Periodic boundary conditions were applied at Z = 0, W (W = πB) [67]. It is quite important to design a grid that offers an appropriate compromise between accuracy and computational cost. Grid should be finer at critical regions, such as, near the impingement and ribbed surfaces (at separation and reattachments), etc. Various initial and boundary conditions used by different researchers are as follows.
Figure 2. Details of (a) 2D computational domain and (b, c) 3D computational domain of jet impingement over flat and ribbed surfaces
An extremely small number of studies dealing with jet impingement heat transfer on a ribbed surface either experimentally or numerically have been reported. Different kinds of turbulent promoter surfaces and arrangements have been used in the literature for convective heat transfer enhancement [2123, 7477]. Two arrangements for rib roughened impingement surface are possible, e.g., ribs may be attached with the impingement surface [22, 23, 74, 78] (attached ribs) or these may be detached from the impingement surface with a small spacing between rib and impingement wall [21] (Fig. 3). Jet impingement on a ribbed surface disrupts the wall jet and flow separation and reattachment takes place due to rib projection. Thus level of turbulence and hence the heat transfer are expected to increase on a ribbed surface [Fig. 3 (c)]. Some application may be found in agriculture field for water jets. Understanding of thermal and fluid dynamic performance of a water droplet travelling from the nozzle outlet is quite important for its application area, such as, sprinkler used for irrigation in agriculture field to save water [79]. Such application of sprinkler jet can also be seen in [80] for classic quantum description used for single and multidroplets. However we have not considered this topic in detail as here our focus is on jet impingement heat transfer.
Figure 3. (a, b and c) Different arrangements of ribs on impingement surface
The NavierStokes (NS) equations for instantaneous incompressible flow and without body forces can be written as:
$∂u_i/∂t+u_j ∂u_i/∂x_j=∂p/∂x_i+ν∂^2 u_i/x_j x_j$ (1)
$∂u_i/∂x_i=0$ (2)
Table 3 shows various techniques that can be used for computation of turbulent flows. For RANS computations, the timeaveraged governing equations are solved. In DNS, unsteady, 3D NavierStokes equations for instantaneous flow are solved numerically and all temporal and spatial scales need to be resolved. In LES, unsteady, filtered governing equations are solved and the effect of small scales are considered using suitable subgrid scale (SGS) models.
Table 3. Various techniques used for computation of turbulent flows
DNS 
LES 
RANS 

Governing Equations 
Original NavierStokes (NS) equations 
Filtered NS equations 
Time averaged NS equations 
Velocity field 
Threedimensional and unsteady 
Threedimensional and unsteady 
Steady/unsteady 
Modeling 
No modeling 
Only small scales are modeled 
All scales are modeled 
Cost of computations for flow over an airliner (Spalart [81]) in terms of number of grid points x number of time steps 
Most expensive, 10^{24 } 
Between DNS and RANS, 10^{18} 
Least expensive 10^{7 }(3D, steady) 
Application 
Simple geometries at low Re 
High potential for practical as well as fundamental use. 
Widely used in practice. 
The instantaneous velocity component can be decomposed as follows (with different meanings for RANS, PANS and LES)
${{u}_{i}}(x,t)\text{ }=\text{ }{{\overline{U}}_{i}}(x,t)+{{u}^{/}}_{i}(x,t)$ (3)
Similarly temperature can also be decomposed into its resolved and unresolved components
$T(x,t)=\overline{T}(x,t)+{{T}^{/}}(x,t)$ (4)
7.1 Reynoldsaveraged NavierStokes (RANS) equations
Many researchers have used RANS approach for impinging jet computation [3033, 37, 82]. In the Reynoldsaveraged NavierStokes (RANS) equations, the timeaveraged NavierStokes equations are numerically solved. The instantaneous velocity field can be decomposed into its mean (timeaveraged) ${{\overline{U}}_{i}}$ and fluctuating components ( ${{u}^{/}}_{i}$ ) (Eq. 3), such that $\overline{{{u}^{/}}_{i}}=0$ . Thus, the time averaging of the NavierStokes equations leads to extra terms, known as the Reynolds stresses, which need to be modelled. This results in a closure problem which require some approximation. The timeaveraged governing equations for the conservations of mass, momentum and energy can be written as:
$\frac{\partial \rho }{\partial t}+\rho \frac{\partial {{{\bar{u}}}_{i}}}{\partial {{x}_{i}}}=0$ (5)
$\frac{\partial {{{\bar{u}}}_{i}}}{\partial t}+{{\bar{u}}_{j}}\frac{\partial {{{\bar{u}}}_{i}}}{\partial {{x}_{j}}}=1/\rho \frac{\partial \bar{\rho }}{\partial {{x}_{i}}}+1/\rho \frac{\partial }{\partial {{x}_{j}}}(2\mu {{\bar{S}}_{ij}}\rho \overline{u_{i}^{'}u_{j}^{'}})$ (6)
$\frac{\partial \bar{T}}{\partial t}+{{\bar{u}}_{j}}\frac{\partial \bar{T}}{\partial {{x}_{j}}}=1/\rho \frac{\partial }{\partial {{x}_{j}}}(\frac{k}{{{c}_{p}}}\frac{\partial \bar{T}}{\partial {{x}_{j}}}\rho \overline{u_{i}^{'}{{T}^{'}}})$ (7)
where, ${{\bar{S}}_{ij}}\text{=}\frac{1}{2}\left( \frac{\partial {{{\bar{u}}}_{i}}}{\partial {{x}_{j}}}+\frac{\partial {{{\bar{u}}}_{i}}}{\partial {{x}_{i}}} \right)$ .
Here the term ($\rho \overline{u_{i}^{'}u_{j}^{'}}$) in equation (6) is the Reynolds stress. Various turbulence models can be used. Most of the models are based on the Boussinesq approximation, which relates the Reynolds stresses to the mean velocity gradients as:
$\rho \overline{u_{i}^{'}u_{j}^{'}}\text{=}2{{\mu }_{t}}{{\bar{S}}_{ij}}\frac{2}{3}\rho k{{\delta }_{ij}}$ (8)
where k denotes the turbulence kinetic energy defined as $1/2\overline{u_{i}^{'}u_{j}^{'}}$, $\delta_{ij}$ denotes the Kronecker delta where $δ_ij=1$ if $i=j$ and $δ_ij=0$ if $i≠j$ and $µ_t$ the turbulent or eddy viscosity. Turbulent transport of heat is modeled in the same way as that for momentum
$\rho \overline{u_{i}^{'}{{T}^{'}}}=\frac{{{\mu }_{t}}}{{{p}_{rt}}}\frac{\partial \bar{T}}{\partial {{x}_{i}}}$ (9)
The turbulent Prandtl number (Pr_{t}) is defined as the ratio of the turbulent viscosity (µ_{t}) and turbulent thermal diffusivity (Г_{t}) and is given as: $Pr_t=µ_t/ɼ_t$ .
A typical value of the turbulent Prandtl number used in engineering computations is approximately equal to 1 [83]. Readers are referred to any book or paper for details on turbulence model used in the literatures, such as [30, 83, 84].
Turbulent models are categorized on the basis of the number of differential transport equations employed to determine the turbulent viscosity (µ_{t}) and these can be broadly classified as
7.2 Large eddy simulation
Many researchers have used LES for impinging jet computation [4650]. Large eddy simulation (LES) is a computation in which the large eddies are computed and the effect of the smaller eddies, termed as the subgridscale (SGS), are modeled. This approach is used because the largest eddies are directly affected by the boundary conditions and flow domain, carry most energy, and must be computed. On the other hand, the smallscale eddies are isotropic in nature, contribute less to Reynolds stresses, carry small energy and therefore are less critical. Also, small eddies have nearlyuniversal characteristics and therefore are easy to model (Wilcox [84]). Thus, a coarser grid and much larger time steps can be used in a LES compared to DNS.
In LES, a filtering operation is performed over the governing equations, in which velocity u(x,t) is decomposed into resolved ${{\overline{U}}_{i}}$ (x,t) and unresolved u^{/}(x,t) components (Eq. 1). The filtered velocity is defined as:
${{\bar{U}}_{i}}(x,t)=\int{G(x,x'){{u}_{i}}(x\text{ }\!\!'\!\!\text{ },t)d{x}'}$
where the function $G\left( x,{x}' \right)$ denotes the filter kernel.
The filtering operation of the continuity and NavierStokes equations provides almost similar forms as Eqs. (5) and (6). The resulting momentum equation is closed by modeling the viscous tensor, $τ_ij$ which can be defined using the Smagorinsky model as:
${\tau _{ij}} =  2{\mu _t}\overline {{S_{ij}}} {\rm{ }}$
where $\overline {{S_{ij}}} $ denotes the rate of stress tensor for the resolved scale. The turbulent viscosity (µ_{t}) is a function of density (ρ), filter width (∆) and characteristic filtered rate of strain ( $\overline S$ ). It is defined as:
$µ_t=C_s^2 ρ∆^2 \overline S $
where C_{s }is an empirical constant.
Subgrid stress model (SGS) is used in LES to consider the interactions between the resolved and unresolved scales. More specifically SGS models are used to consider the subgrid stress term ($τ_ij$) in the filtered governing equations. Although, SGS models are often compared with RANS based turbulence models, the way in which the Reynolds averaging is defined is different from the filtering approach in LES. Moreover, since small scales are generally assumed to be isotropic and universal, SGS models are fairly easy to model and are accurate as compared to RANS based turbulence models. SGS models are of two types, i.e., similarity and eddyviscosity models. The eddy viscosity models are more popular than similarity models.
7.3 Partiallyaveraged NavierStokes (PANS) Modeling
Some researchers have used the PANS approach for impinging jet computations [68, 69] which employs unsteady, filtered governing equations. The PANS equations [85] vary smoothly from RANS equations to NavierStokes equations (direct numerical simulation), depending on the values of the filterwidth control parameters, $f_k$ and $f_ε$. Here $f_k$ is the ratio of the unresolved turbulence kinetic energy ($k_u$) to total kinetic energy (k) and $f_ε$ is the ratio of unresolved dissipation rate ($ε_u$) to total dissipation rate ($ε$).
$f_k=k_u/k$; $f_ε=ε_u/ε $
In the PANS approach, the extent of filtering is quantified by specifying the values of f_{k} and f_{ε}. It is well known that much of the kinetic energy is contained in large scales and most of the dissipation occurs in the smallest scales due to which 0 ≤ f_{k} ≤ f_{ε} ≤ 1. Smaller the value of f_{k}higher the physical resolution: f_{k}= 1 represents RANS and f_{k}= 0 indicates DNS. Authors may find detailed formulation of PANS in [85].
A comprehensive review of jet impingement heat transfer has been presented. The review includes different physical and computational aspects of impinging flows. Studies dealing with application based jet impingement heat transfer configuration have also been reviewed. Jet impingement heat transfer is widely studied experimentally by many researchers. Although it is also extensively studied computationally by many researchers, it is clear that majority of RANS turbulence models did not predict impinging flows accurately and its complexities. Several parameters affect the flow and heat transfer characteristics of jet impingement and these have found special attention in the literature experimentally and numerically. It can be observed that for low nozzle to plate spacing reason for appearance of secondary peak in Nusselt number still needs to be addressed. Many authors have observed that LES is capable of predicting the flow and heat transfer characteristics within the accepted accuracy limits. DNS can be applied to simple geometries with low values of Re. Recently some researchers have used hybrid models, such as, PANS, DES, etc., and concluded that these models provide reasonably accurate results and were less computationally expensive than LES and DNS. Some studies dealing with application based jet impingement heat transfer configuration (e.g., ribs fitted impingement plate, moving impingement plate, etc.) have been reported in the literature. It has been observed that jet impingement on a rib fitted target surface disrupts the wall jet and boosts the turbulence level through better mixing of fluid and hence heat transfer enhancement can be achieved through it.
The work reported here forms a part of the Department of Science and Technology (DST), Government of India, New Delhi, sponsored project (SR/S3/MERC/0114/2012). Authors acknowledge the financial support received from DST.
B (W) 
slot width 
c 
rib clearance 
c/e D 
nondimensional rib clearance nozzle exit diameter 
e H H/B or H/D h k_{f} Nu P p/e Re T U x,y,z 
rib height height between nozzle to plate normalized nozzle to plate spacing heat transfer coefficient (W/m^{2}K) thermal conductivity (W/mK) Nusselt number (hB/k) mean pressure normalized rib pitch Reynolds number (ρUB/µ) mean temperature mean velocity coordinate directions 
Greek symbols 

a 
thermal diffusivity, m^{2}/s 
µ 
dynamic viscosity, kg./m.s 
Subscripts 

f 
fluid 
t 
turbulent 
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