Heat transfer enhancement is very important in the industry, and several techniques are employed to realize this aim. Impinging jets, whether confined or unconfined, have been widely used for efficient cooling in industrial applications as a means of providing highly localized heat transfer coefficients, representing a possible solution. Depending on the application, flow conditions can range from laminar to highly turbulent ones. Applications of impinging jets include drying of textiles, film and paper, cooling of gas turbine components and the outer walls of combustors, freezing of tissue in cryosurgery and manufacturing, material processing and electronic cooling. There are numerous articles dealing with this problem both numerically and experimentally as reported in the literature reviews on the subject 1 2 3 4 5 6 .

Several studies have been developed on impinging air jets 1 2 . Recently, a greater attention has been dedicated to the impinging liquid jet since orders of magnitude of the heat transfer rates are several times those of gas jets. Liquid jets have possible application to the cooling of heat engines 5 7 , thermal control in electronic devices 8 9 10 and in the thermal treatment of metals and material processing 11 12 13 14 .

In the application of jet impingements, circular or slot jets are the main jet configurations. For these two configurations, flow and heat transfer mechanics are significantly different. It seems that greater research activity on heat and mass transfer with circular impinging jets has been predominantly published 1 2 3 15 16 . However, investigations on heat and mass transfer with slot jet impingement have attracted more attention recently. In fact, slot jet impingements offer many more beneficial features, such as higher cooling effectiveness, greater uniformity and more controllability, as underlined in 17 . For example, these factors allow for fulfillment of the increasing heat flux and decreasing dimensions in electronics packages 17 18 19 20 21 22 23 24 . The common types of impinging jets are with or without confinement. Confined impinging jets have the advantages of smaller space design, while unconfined impinging jets have an advantage of simple design and easy fabrication. The two types of impinging jets have their own merits, and they are both commonly used as the cooling solutions, and the literature reviews on the subject have been provided in 2 3 6 . The effects of confinement on impinging jet heat transfer have been considered in 25 26 27 . Moreover, several studies show the importance of the subject and different cases have been investigated, such as confined slot-jet impingement on a moving plate 28 , impinging jet on obliquely a flat surface 29 , impinging jet on a porous medium 30 and slot jet impingement cooling on a semi-circular concave 31 .

In order to obtain a heat transfer enhancement in jet impingement, different techniques have been employed, such as the insert of foams or fins 32 . These techniques determine a modification of the cooling system whereas the use of nanofluids in a coolant seems to be simpler in realizing a heat transfer enhancement 33 . However, nanofluids are to this day controversial in many areas such as inconsistencies in published data and disagreements on the heat transfer mechanisms, as observed by Gherasim et al. 34 . Various aspects of nanofluids have been covered in several reviews and some of these are given in 35 36 37 38 39 40 41 42 43 44 45 46 47 .

The employment of nanofluids in impinging jets has been investigated recently by some researchers and, to the best of our knowledge, their investigations have been reported in 34 48 49 50 51 52 53 54 55 56 57 58 59 60 . The numerical investigation on hydrodynamic and thermal fields of Al₂O₃/water nanofluid in a radial laminar flow cooling system carried out by Roy et al. 48 can be can be considered as the first article on an impinging jet. Those authors found that considerable heat transfer enhancement was observed up to 200% in the case of a nanofluid with 10% in nanoparticle volume concentration at a Reynolds number equal to 1200. However, a significant increase in wall shear stress was noticed increasing the nanoparticle volume concentration. The laminar-forced convection flow of nanofluids between two coaxial and parallel disks with central axial injection was investigated numerically considering temperature-dependent properties by Palm et al. 51 . Results indicated a heat transfer benefit by adopting Al₂O₃/water nanofluid with a volume fraction of nanoparticles of 4%. An increase of 25% was evaluated in terms of average wall heat transfer coefficient, when referred to the water. Moreover, the use of temperature-dependent properties determined for greater heat transfer predictions with corresponding decreases in wall shear stresses when compared to evaluations employing constant properties. A numerical study on steady, laminar radial flow of a nanofluid in a simplified axi-symmetric configuration with axial coolant injection was performed by Roy et al. 52 for electronic cooling applications. Also in this investigation increases in heat removal capabilities were detected with the use of nanofluids.

An experimental investigation in a confined and submerged impinging jet on a flat, horizontal and circular heated surface with nanofluid (Al₂O₃ dispersed in water) was carried out by Nguyen et al. 56 . Experimental results were obtained for both laminar and turbulent flow regimes and they showed that, depending on the combination of nozzle-to-heated surface distance and particle volume fraction, the use of a nanofluid can determine a heat transfer enhancement in some cases, but an adverse effect on the convective heat transfer coefficient may occur in other cases. A circular confined and submerged jet impinging on a horizontal hot plate was numerically simulated by Vaziei and Abouali 57 . Water and 36-nm Al₂O₃-water nanofluid with various particle volume fractions were considered as a working fluid for cooling the hot plate. Both laminar and turbulent impinging jets in various nozzle-to-plate distances and Reynolds numbers were simulated. The results showed that the use of Al₂O₃ nanoparticles in laminar jets enhanced the heat transfer but for the turbulent jets Al₂O₃-water nanofluid had a lower performance for heat removal compared with the base fluid. The heat transfer enhancement capabilities of Al₂O₃/water inside a confined impinging jet cooling device was numerically studied by Gherasim et al. 34 . Results highlighted those limitations in the use of this nanofluid type in a radial flow configuration, due to the significant increase in the associated pumping power. Steady laminar incompressible thermal alumina-water flow between parallel disks was simulated by Feng and Kleinstreuer 58 . The results indicated that the Nusselt number increases with higher nanoparticle volume fraction, smaller nanoparticle diameter, reduced disk-spacing and larger inlet Reynolds number. The laminar forced convective heat transfer features of Al₂O₃/water nanofluid in the confined radial flow were numerically investigated by Yang and Lai 59 60 with constant 59 and temperature-dependent properties 60 . Results showed the same trend given in the previous published works: the Nusselt number increases with the increases in Reynolds number and nanoparticle volume fraction, though the increase in pressure drop is more significant with the increase of particle concentration. Furthermore, temperature-dependent thermo-physical properties of nanofluids were found to have a marked bearing on the simulation results.

It seems that a slot-confined and submerged impinging jet on a flat surface with nanofluids has not been investigated in both laminar and turbulent flow regimes in spite of its importance in engineering applications such as electronic cooling and material processing.

In this article, a numerical investigation on turbulent flow on a slot-confined and submerged impinging jet on an isothermal flat surface is carried out. The results are given to evaluate the fluid dynamic and thermal features of the considered geometry with Al₂O₃/water as the working nanofluid adopting the single phase model.

A computational thermo-fluid dynamic analysis of a two-dimensional model, regarding a confined impinging jet on a heated wall with nanofluids, is considered to evaluate the thermal and fluid-dynamic performances and study the velocity and temperature fields. Different inlet velocities are considered to ensure a turbulent regime, and the working fluids are water and mixtures of water and γ-Al₂O₃ at different volume fractions, treated by a single-phase model approach. The range of Reynolds numbers, geometric ratio and volume fractions are given below:

• Reynolds number, Re: 5000, 10000, 15000 and 20000;

• H/W ratio: 4, 6, 8, 10, 15 and 20;

• particle concentrations, ϕ: 0, 1, 4 and 6%.

Results are presented in terms of average and local Nusselt number profiles, as a function of Reynolds number, H/W ratio and particle concentrations; moreover, dimensionless temperature fields and stream function contours are provided.

Figures 4 and 5 depict the stream lines contours and the temperature fields, respectively, for the representative cases with H/W = 4 and 10, at Re = 10000 and 20000 and ϕ = 0 and 4%. According to Figure 4, two counter-rotating vortex structures are generated as the jet impinges on the bottom surface and only one stagnation point, where velocity and temperature gradients are very high, is observed. This is due to the jet entrainment and confining effects of the upper adiabatic surfaces. Vortex intensity and size depend on H/W ratio, factors such as the confining effects, Reynolds number, and particle concentrations. It can be seen in Figure 4a, b, at Re = 10000, H/W = 10 and ϕ = 0 and 4%, the introduction of particles leads to a little smoother eddies with a low intensity increase, because the nanofluid viscosity is higher than water. As H/W ratio decreases from 10 to 4, at Re = 10000 and ϕ = 4%, vortices are less strong and smaller as they extinguish at x/W values equal to about -30 and 30, as pointed out in Figure 4b, c. As Re increases, the separation area near the inlet section becomes larger while the fluid stream results to be more compressed towards the impingement surface, as observed in Figure 4d.

The temperature fields, depicted in Figure 5, follow the stream line patterns. For increasing concentrations, nanoparticles produce an increase of fluid bulk temperature, because of the elevated thermal conductivity of mixtures. Near the impingement surface, temperature grows and tends to decrease for increasing x/W values. For larger Reynolds numbers, the efficiency of heat transfer increases.

The variation of local Nusselt number along the impingement plate for Re = 20000, H/W = 4 and ϕ = 6% and for Re = 5000, H/W = 6 and different concentrations, is shown in Figure 6a, b, respectively. It is observed that the highest values of Nu _x are evaluated at the stagnation point for all the considered cases; their values are 214 and 239 for H/W = 4 and H/W = 10, respectively. For low H/W values, local Nusselt number decreases more quickly than high H/W ratios. At the end of the plate, for any considered H/W, Nu _x reaches similar values equal to about 25, as observed in Figure 6a. In Figure 6b, it is shown how the variation of nanofluid concentration affects the heat transfer. Higher heat transfer enhancements are observed for ϕ = 4, 6%, especially, near the impingement location. This does not happen only for H/W = 4 as can be understood from the average Nusselt number value trends, reported later, in comparison with other H/W ratios.

In Figure 7, the variation of local q _w /q _{0 w} ratio is shown. The q _w /q _{0 w} value represents the local ratio between the local total heat flux and total heat flux at stagnation point for any case. The maximum value is reached at the stagnation point of any considered case. As Re increases, q _w /q _{0 w} ratio increases. Difference in terms of q _w /q _{0 w} is more significant passing from Re = 5000 to 10000 than the other considered Re. In fact, at x/W = 4, there is a difference of 0.12 in terms of q _w /q _{0 w} while in the other cases, the largest difference is 0.9. The heat transfer augmentation is more significant near the stagnation point than in correspondence with the end of the impinged plate. In Figure 7b, it is observed as the nanofluid concentration has very little influence on q _w /q _{0 w} . The effects of H/W are underlined in Figure 7c: near the stagnation point, q _w /q _{0 w} ratio has almost the same value for all H/W. From x/W = 4 curves spread out and q _w /q _{0 w} increases as H/W increases. This affects the results in terms of average Nusselt number, calculated at different H/W ratios.

The average Nusselt number profiles as function of Re are depicted in Figure 8 for H/W = 4, 6, 8, and 10. Profiles increase as Re increases for all the considered cases. It is observed that as ϕ increases Nu _avg becomes higher for a fixed value of Re. Passing from ϕ = 0% to ϕ = 1%, a significant increase of Nu _avg, only for H/W = 4 configuration is noted, where it passes from 35 to 37 at Re = 15000 or 65 to 69 for Re = 20000. For the other cases, a significant heat transfer enhancement is found for the highest ϕ values; in fact in these cases, passing from ϕ = 0% to ϕ = 1%, the maximum enhancement is found to be equal to 1.22 times for H/W = 10 at Re = 20000.

The heat transfer enhancement is evident, also observing the average heat transfer coefficient profiles, described in Figure 9. Results are given for different Re, H/W ratios and concentrations. The maximum values of h _avg are calculated for the highest values of Re, H/W and concentrations considered. In fact, for H/W = 10 and Re = 20000, it results that h _avg is equal to about 7600, 8000, 9400 and 10500 W/m²K, as depicted in Figure 9d, while, at H/W = 4 and Re = 20000, h _avg are equal to about 6200, 6800, 7700, and 8600 W/m²K, for ϕ = 0, 1, 4, and 6%, respectively.

Figure 10 shows the average Nusselt number profiles, referred to the values calculated for the base fluid, as a function of Reynolds number for particle concentrations equal to 1, 4 and 6% at H/W ratio of 4. It is observed that the ratio Nu _avg /Nu _{avg, bf} is greater than one for all the configurations analyzed and rises slightly for increasing Reynolds numbers and concentrations; in fact, the highest value of 1.18 is detected at Re = 20000 and ϕ = 6%.

The results in terms of local Nusselt numbers, calculated for the stagnation point, are depicted in Figure 11. They are provided as a function of Reynolds numbers and given for different concentrations for different H/W ratios, equal to 4, 6, 8, and 10. It is shown that profiles increase almost linearly with increasing Reynolds numbers for all the considered concentrations and H/W ratios. Moreover, the Nu ₀ values are the highest for ϕ = 6% for all the considered Reynolds numbers. For example, comparing the results for ϕ = 1, 4, and 6%, with the base fluid ones, an increase in values of 2.7, 10.8, and 16.2% are detected for H/W = 4 at Re = 20000, respectively. Moreover, Nu ₀ values rises as H/W increases for Re > 10000, as observed in Figure 11b, c, d.

In fact, Figure 12 shows that Nu ₀ is maximum in correspondence with H/W = 4 for Re < 10000 and H/W = 10 for higher Reynolds numbers for all the concentrations. For ϕ = 0%, at Re = 5000 Nu ₀ values are about 70, 81, 86, and 87, while at Re = 20000, Nu ₀ = 195, 197, 200, and 205, for H/W = 4, 6, 8, and 10, respectively. The results for ϕ = 6% are depicted in Figure 12b; it is shown that at Re = 5000 the maximum value of the stagnation point Nusselt number is about 102, 100, 93, and 82, for H/W = 4, 6, 8, and 10, respectively. For the same geometrical configurations, at Re = 20000, Nu ₀ values are equal to 215, 225, 235, and 240.

Results in terms of average Nusselt numbers are shown in Figure 13, for different H/W ratios and ϕ = 0, 6%. The profiles increase linearly as Re increases as well as H/W ratio. In fact, the highest values of Nu _avg are detected for H/W = 10 while the minimum ones for H/W = 4. Moreover, average Nusselt numbers increase as ϕ increases; thus, Nu _avg values are equal to 42 and 79 for water, as depicted in Figure 13a, while for ϕ = 6%, they are equal to 48 and 92, as pointed out by Figure 12b, at Re = 10000 and 20000, respectively.

Figure 14 confirms that the configurations with H/W = 10 exhibit the maximum values of the average Nusselt numbers for all the considered Reynolds numbers and concentrations. In fact, at Re = 5000 and 20000, the profiles increase as H/W rises until H/W = 10, and then they decrease for H/W = 15 and 20.

The pumping power is defined as PP = VΔP, and its profiles are shown in Figure 15, for all the considered H/W values, concentrations and as a function of Reynolds number. The required power has a square dependence on Re. It increases as H/W and particle concentration increase. For example, as observed in Figure 15a, at H/W = 4, for water PP = 15 and 90 W at Re = 10000 and 20000, respectively, while for ϕ = 6% PP = 50 and 410 W. At the same Re, for H/W = 10, PP is equal to 18 W, as underlined in Figure 15d, and 98 W for water, and 58 and 470 W for ϕ = 6%, respectively.

The pumping power ratio, referred to the base fluid values, is described in Figure 16. It is observed that the ratio does not seem to be dependent on Re, and PP/PP_bf ratio increases as concentration increases, as expected. In fact, at Re = 15000, the required pumping power is 1.2, 2.6 and 4.8 times greater than the values calculated in case of water.

A numerical analysis of a two-dimensional model on a confined impinging jet with nanofluids has been carried out to evaluate the thermal and fluid-dynamic performances and study the velocity and temperature fields. The bottom impinged wall is heated at a constant temperature and different fluid velocities are considered in the range 5000-20000. The base fluid is water and different volume concentrations of Al₂O₃ nanoparticles are taken into account by adopting a single-phase model approach. Furthermore, different H/W ratios have been studied. The dimensionless stream function contours showed that the vortex intensity and size depend on H/W ratio, such as on the confining effects, Reynolds number and particle concentrations. Furthermore, for increasing concentrations, nanofluids produce an increase of fluid bulk temperature, because of the elevated thermal conductivity of mixtures. The local Nusselt number profiles present the highest values at the stagnation point and the lowest at the end of the heated plate. The highest values of the average Nusselt numbers increase as the particle concentrations and Reynolds numbers increase and the highest values are observed for H/W = 10. A maximum increase of 18% is detected at ϕ = 6%. The required pumping power increases as well as Reynolds number, and particle concentrations grow, which is almost 4.8 times greater than the values calculated in the case of water. For list of symbols please see Table 4

All the authors have made substantial contributions in order to write this work. PM and DR developed the numerical model, ran the simulation and acquired data. The analysis and the interpretation of data have been carried out together with OM and SN. All the authors have been involved in drafting the manuscript and revising it critically and OM and SN have given final approval of the version to be published.