 Nano Express
 Open Access
 Published:
Numerical study of a confined slot impinging jet with nanofluids
Nanoscale Research Letters volume 6, Article number: 188 (2011)
Abstract
Background
Heat transfer enhancement technology concerns with the aim of developing more efficient systems to satisfy the increasing demands of many applications in the fields of automotive, aerospace, electronic and process industry. A solution for obtaining efficient cooling systems is represented by the use of confined or unconfined impinging jets. Moreover, the possibility of increasing the thermal performances of the working fluids can be taken into account, and the introduction of nanoparticles in a base fluid can be considered.
Results
In this article, a numerical investigation on confined impinging slot jet working with a mixture of water and Al_{2}O_{3} nanoparticles is described. The flow is turbulent and a constant temperature is applied on the impinging. A singlephase model approach has been adopted. Different geometric ratios, particle volume concentrations and Reynolds number have been considered to study the behavior of the system in terms of average and local Nusselt number, convective heat transfer coefficient and required pumping power profiles, temperature fields and stream function contours.
Conclusions
The dimensionless stream function contours show that the intensity and size of the vortex structures depend on the confining effects, given by H/ W ratio, Reynolds number and particle concentrations. Furthermore, for increasing concentrations, nanofluids realize increasing fluid bulk temperature, as a result of the elevated thermal conductivity of mixtures. The local Nusselt number profiles show the highest values at the stagnation point, and the lowest at the end of the heated plate. The average Nusselt number increases for increasing particle concentrations and Reynolds numbers; moreover, the highest values are observed for H/W = 10, and a maximum increase of 18% is detected at a concentration equal to 6%. The required pumping power as well as Reynolds number increases and particle concentrations grow, which is almost 4.8 times greater than the values calculated in the case of base fluid.
List of symbols
Background
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 [1–6].
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 [8–10] and in the thermal treatment of metals and material processing [11–14].
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 [1–3, 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 [17–24]. 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 [25–27]. Moreover, several studies show the importance of the subject and different cases have been investigated, such as confined slotjet 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 semicircular 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 [35–47].
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, 48–60]. The numerical investigation on hydrodynamic and thermal fields of Al_{2}O_{3}/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 laminarforced convection flow of nanofluids between two coaxial and parallel disks with central axial injection was investigated numerically considering temperaturedependent properties by Palm et al. [51]. Results indicated a heat transfer benefit by adopting Al_{2}O_{3}/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 temperaturedependent 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 axisymmetric 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 (Al_{2}O_{3} 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 nozzletoheated 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 36nm Al_{2}O_{3}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 nozzletoplate distances and Reynolds numbers were simulated. The results showed that the use of Al_{2}O_{3} nanoparticles in laminar jets enhanced the heat transfer but for the turbulent jets Al_{2}O_{3}water nanofluid had a lower performance for heat removal compared with the base fluid. The heat transfer enhancement capabilities of Al_{2}O_{3}/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 aluminawater 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 diskspacing and larger inlet Reynolds number. The laminar forced convective heat transfer features of Al_{2}O_{3}/water nanofluid in the confined radial flow were numerically investigated by Yang and Lai [59, 60] with constant [59] and temperaturedependent 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, temperaturedependent thermophysical properties of nanofluids were found to have a marked bearing on the simulation results.
It seems that a slotconfined 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 slotconfined 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 Al_{2}O_{3}/water as the working nanofluid adopting the single phase model.
Methods
Geometrical model
A computational thermofluid dynamic analysis of a twodimensional model, Figure 1a, which regards the impinging jet on a heated wall with nanofluids, is considered in order to evaluate the thermal and fluiddynamic performances, and study the velocity and temperature fields. The twodimensional model has a length L equal to 310 mm while the height H ranges from 24.8 to 124 mm and the jet orifice width W is 6.2 mm. A constant temperature value of 343 K is applied on the impingement bottom surface. Different values of H/W ratio, equal to 4, 6, 8, 10, 15 and 20, are considered. The working fluid is water or a mixture of water and γAl_{2}O_{3} nanoparticles with a diameter of 38 nm, at different volume fractions equal to 1, 4 and 6%.
Physical properties of nanofluids
The working fluid is water or a mixture of water and γAl_{2}O_{3} nanoparticles with a diameter of 38 nm, at different volume fractions equal to 1, 4 and 6%. In Table 1, the values of density, specific heat, dynamic viscosity and thermal conductivity, given by Rohsenow et al. [61], are reported for water and γAl_{2}O_{3}. The presence of nanoparticles and their concentrations influence the mixture properties. A singlephase model was adopted, and the following equations were used for computing the thermal and physical properties of the considered nanofluids [62–65], given in Table 2. Density was evaluated using the classical formula developed for conventional solidliquid mixtures, while the specific heat values were obtained by assuming the thermal equilibrium between particles and surrounding fluid [62, 63].
Nanofluids may be considered as Newtonian fluids for low volume fractions, e.g., up to 10%, and for small temperature increases. In this way, for the viscosity as well as for thermal conductivity, formulas given by [64, 65] were adopted:
However, it is well known that the evaluation of these properties by various research groups differs from each other because of the numerical and experimental approaches and processes adopted [64, 65].
Mathematical description and governing equations
Steadystate, turbulent, incompressible, singlephase, and constant properties flow conditions are considered in the present analysis. The governing equations of continuity, momentum and energy are solved in rectangular coordinates:
where E is the total energy, $E={c}_{p}T\frac{P}{\rho}+\frac{{u}^{2}}{2}$ and (τ_{ij})_{eff} is the deviatoric stress tensor, defined as
The kε standard model with enhanced wall treatment is assumed. The transport equations are as follows [66]:
where G_{k} is the production of turbulent kinetic energy due to mean velocity gradients, G_{b} represents the generation of the turbulent kinetic energy due to buoyancy while Y_{ M }is referred to the fluctuation rates related to the overall dissipated turbulent thermal energy. In particular, G_{k} may be expressed by
where C_{1}_{ ε }and C_{2}_{ ε }are constants; while the term ${C}_{3\epsilon}=\mathrm{tanh}\left\frac{v}{u}\right$ defines the dependence rate of ε on buoyancy; σ_{ k }and σ_{ e }represent the turbulent Prandtl numbers based on k and ε, respectively; while S_{ k }and S_{ ε }are further generation terms. The turbulent viscosity is defined by
where C_{ μ }is a constant. The model constant values are the following:
C_{1ε}= 1.44, C_{2ε}= 1.92, C_{ μ }= 0.09, σ_{k} = 1.0 and σ_{ ε }= 1.3.
The enhanced wall treatment approach has been considered. The assigned boundary conditions are

Inlet jet section: uniform velocity and temperature profile;

Outlet section: pressure outlet;

Bottom wall: velocity components equal to zero and constant temperature;

Upper wall: velocity components equal to zero and adiabatic condition.
The dimensionless parameters considered here are
where u_{ j }is the jet velocity, W is the jet width, $\dot{q}$ is the impingement surface heat flux, T_{H} and T_{J} represent the temperature of the impingement surface and the jet temperature, respectively.
Numerical procedure
The governing equations of continuity, momentum and energy, reported in the previous section, are solved by the finite volume method by means of FLUENT code [67]. A steadystate solution and a segregated method are chosen to solve the governing equations, which are linearized implicitly with respect to dependent variables of the equation. A secondorder upwind scheme is chosen for energy and momentum equations. The SIMPLE coupling is chosen as scheme to couple pressure and velocity. The convergence criteria of 10^{5} for the residuals of the velocity components and of 10^{8} for the residuals of the energy are assumed. It is assumed that the incoming flow is turbulent at ambient temperature and pressure. Different inlet uniform velocities, corresponding to Reynolds numbers ranging from 5000 to 20000, were considered and they are reported in Table 3. Furthermore, the inlet turbulence intensity value is set to 2%.
The enhanced wall treatment functions are activated to increase the model accuracy in the nearwall region. It is a twolayer method with enhanced functions. The domain is divided into two regions, the nearwall region and the core ones, according to the turbulent Reynolds number, based on the distancetowall term y.
The core region, for Re_{ y }> 200, is solved by means of the standard kε model, while in the other region the Wolfstein model is applied [68].
Along the solid walls, no slip condition is employed, whereas a velocity inlet is given for the jet orifice and pressure conditions are set for the outlet sections.
Four different grid distributions are tested on the model with H/W ratio equal to 6 at Re = 5000, with water (ϕ = 0%) as working fluid, to ensure that the calculated results are grid independent. The four grids have 4950 (90 × 55), 19800 (180 × 110), 79200 (360 × 220), and 316800 (720 × 440) nodes, respectively. The grid mesh is structured in each case with grid adoption for y^{+} = 1 at adjacent wall region and a sketch is shown in Figure 1b. For the adiabatic wall and the bottom surface, nodes are distributed by means of an exponential relation (n = 0.9), to have a fine mesh near the impingement region, where an equispatial distribution is chosen. On the vertical ones, a biexponential (n = 0.8) distribution is considered.
Comparing the third and fourthmesh configurations, in terms of average and stagnation point Nusselt number, results are very close, and the relative errors are very little, as reported in Figure 2. As a result, the third grid case has been adopted because it ensured a good compatibility between the machine computational time and the accuracy requirements.
Results are validated by comparing the obtained numerical data with the experimental and numerical ones, given in [28, 69, 70]. Figure 3 presents the comparison in terms of average Nusselt number profiles, for the cases, characterized by Re = 11000, H/W = 6, T_{J} = 373 K and T_{H} = 338 K. It is observed that the numerical results, obtained in this work, fit very well with the experimental ones given in [5, 6] both near the stagnation point region and at the side one.
Results and discussion
A computational thermofluid dynamic analysis of a twodimensional model, regarding a confined impinging jet on a heated wall with nanofluids, is considered to evaluate the thermal and fluiddynamic 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 γAl_{2}O_{3} at different volume fractions, treated by a singlephase 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 counterrotating 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/m^{2}K, 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/m^{2}K, 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 = V ΔP, 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.
Conclusions
A numerical analysis of a twodimensional model on a confined impinging jet with nanofluids has been carried out to evaluate the thermal and fluiddynamic 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 500020000. The base fluid is water and different volume concentrations of Al_{2}O_{3} nanoparticles are taken into account by adopting a singlephase 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
References
 1.
Martin H: Heat and mass transfer between impinging gas jets and solid surface. Adv Heat Transfer 1977, 13: 1–60. full_text
 2.
Downs SJ, James EH: Jet impingement heat transfera literature survey. Tech. Rep. 1987HT35, ASME
 3.
Jambunathan K, Lai E, Moss M, Button B: A review of heat transfer data for single circular jet impingement. Int J Heat Fluid Flow 1992, 13: 106–115. 10.1016/0142727X(92)900174
 4.
Viskanta R: Heat transfer to impinging isothermal gas and flame jets. Exp Thermal Fluid Sci 1993, 6: 111–134. 10.1016/08941777(93)90022B
 5.
Webb B, Ma CF: Singlephase liquid jet impingement heat transfer. Adv Heat Transfer 1995, 26: 105–117. full_text
 6.
Tesar V, Travnicek Z: Increasing heat and/or mass transfer rates in impinging jets. J Vis 2005, 8: 91–98. 10.1007/BF03181651
 7.
Ma CF, Bergles AE: Convective heat transfer on a small vertical heated surface in an impingement circular liquid jet. In Heat Transfer Science and Technology. Edited by: Wang BX. New York: Hemisphere; 1990:193–200.
 8.
Ma CF: Fundamental research on extremely small size liquid jet impingement heat transfer. Proceedings of the 3rd International Thermal Energy Congress: 28 June1 August 1997; Kitakyushu, Japan 1997, 195–202.
 9.
Jiji LM, Dagan Z: Experiment investigation of single phase multijet impingement cooling of an array of microelectronic heat sources. In Cooling Technology for Electronic Equipment. Edited by: Aung W. New York: Hemisphere; 1988:332–352.
 10.
Punch J, Walsh E, Grimes R, Jeffers N, Kearney D: Jets and rotary flows for singlephase liquid cooling: an overview of some recent experimental findings. Proceedings of the 11th International Conference on Thermal, Mechanical and MultiPhysics Simulation, and Experiments in Microelectronics and Microsystems, EuroSimE 2010: 26–28 April 2010; Bordeaux 2010, 5464505.
 11.
Kohing FC: Waterwall: water cooling system. IronSteel Eng 1985, 62: 30–36.
 12.
Ma CF, Yu J, Lei DH, Gan YP, Tsou FK, Auracher H: Transient jet impingement boiling heat transfer on hot surfaces. In Multiphase Flow and Heat TransferSecond International Symposium. Edited by: Chen XJ et al. New York: Hemisphere; 1990:349–357.
 13.
Viskanta R: Heat transfer in material processing. In Handbook of Heat Transfer. 3rd edition. Edited by: Rohsenow WM, Hartnett JP, Cho YI. New York: McGrawHill; 1998.
 14.
Schuettenberg S, Krause F, Hunkel M, Zoch HW, Fritsching U: Quenching with fluid jets. Mater Werkst 2010, 40: 408–413. 10.1002/mawe.200900468
 15.
Liu Z, Lienhard VJH, Lombara JS: Convective heat transfer by impingement of circular liquid jets. J Heat Transfer 1991, 113: 571–582. 10.1115/1.2910604
 16.
Ma CF, Zhao YH, Masuoka T, Gomi T: Analytical study on impingement heat transfer with singlephase freesurface circular liquid jets. J Thermal Sci 1996, 5: 271–277. 10.1007/BF02653234
 17.
Chen YC, Ma CF, Qin M, Li YX: Theoretical study on impingement heat transfer with singlephase freesurface slot jets. Int J Heat Mass Transfer 2005, 48: 3381–3386. 10.1016/j.ijheatmasstransfer.2005.02.027
 18.
Zhuang Y, Ma CF, Qin M: Experimental study on local heat transfer with liquid impingement flow in twodimensional microchannels. Int J Heat Mass Transfer 1997, 40: 4055–4059. 10.1016/S00179310(97)000392
 19.
Lin ZH, Chou YJ, Hung YH: Heat transfer behaviors of a confined slot jet impingement. Int J Heat Mass Transfer 1997, 40: 1095–1107. 10.1016/00179310(96)001354
 20.
Chiriac VA, Ortega A: A numerical study of the unsteady flow and heat transfer in a transitional confined slot jet impinging on an isothermal surface. Int J Heat Mass Transfer 2002, 45: 1237–1248. 10.1016/S00179310(01)002241
 21.
Park TH, Choi HG, Yoo JY, Kim SJ: Streamline upwind numerical simulation of twodimensional confined impinging slot jets. Int J Heat Mass Transfer 2003, 46: 251–262. 10.1016/S00179310(02)002703
 22.
Sahoo D, Sharif MAR: Numerical modeling of slotjet impingement cooling of a constant heat flux surface confined by a parallel wall. Int J Thermal Sci 2004, 43: 877–887. 10.1016/j.ijthermalsci.2004.01.004
 23.
Lee HG, Yoon HS, Ha MY: A numerical investigation on the fluid flow and heat transfer in the confined impinging slot jet in the low Reynolds number region for different channel heights. Int J Heat Mass Transfer 2008, 51: 4055–4059. 10.1016/j.ijheatmasstransfer.2008.01.015
 24.
Sivasamy A, Selladurai V, Kanna PR: Jet impingement cooling of a constant heat flux horizontal surface in a confined porous medium: mixed convection regime. Int J Heat Mass Transfer 2010, 53: 5847–5855. 10.1016/j.ijheatmasstransfer.2010.07.063
 25.
Lytle D, Webb B: Air jet impingement heat transfer at low nozzleplate spacings. Int J Heat Mass Transfer 1994, 37: 1687–1697. 10.1016/00179310(94)900590
 26.
Behnia M, Parneix S, Shabany Y, Durbin PA: Numerical study of turbulent heat transfer in confined and unconfined impinging jets. Int J Heat Mass Transfer 1999, 20: 1–9.
 27.
Choo KS, Kim SJ: Comparison of thermal characteristics of confined and unconfined impinging jets. Int J Heat Mass Transfer 2010, 53: 3366–3371. 10.1016/j.ijheatmasstransfer.2010.02.023
 28.
Sharif MAR, Banerjee A: Numerical analysis of heat transfer due to confined slotjet impingement on a moving plate. Appl Thermal Eng 2009, 29: 532–540. 10.1016/j.applthermaleng.2008.03.011
 29.
Ibuki K, Umeda T, Fujimoto H, Takuda H: Heat transfer characteristics of a planar water jet impinging normally or obliquely on a flat surface at relatively low Reynolds numbers. Exp Thermal Fluid Sci 2009, 33: 1226–1234. 10.1016/j.expthermflusci.2009.08.003
 30.
Dórea FT, de Lemos MJS: Simulation of laminar impinging jet on a porous medium with a thermal nonequilibrium model. Int J Heat Mass Transfer 2010, 53: 5089–5101.
 31.
Yang YT, Wei TC, Wang YH: Numerical study of turbulent slot jet impingement cooling on a semicircular concave. Int J Heat Mass Transfer 2011, 54: 482–489. 10.1016/j.ijheatmasstransfer.2010.09.021
 32.
Naphon P, Wongwises S: Investigation on the jet liquid impingement heat transfer for the central processing unit of personal computers. Int Commun Heat Mass Transfer 2010, 37: 822–826. 10.1016/j.icheatmasstransfer.2010.05.004
 33.
Choi SUS: Enhancing thermal conductivity of fluids with nanoparticles, developments and applications of nonNewtonian flows. ASME FED 1995, 231: 99–105.
 34.
Gherasim I, Roy G, Nguyen CT, VoNgoc D: Heat transfer enhancement and pumping power in confined radial flows using nanoparticle suspensions (nanofluids). Int J Thermal Sci 2011, 50: 369–377. 10.1016/j.ijthermalsci.2010.04.008
 35.
Das SK, Choi SUS, Patel HE: Heat transfer in nanofluidsa review. Heat Transfer Eng 2006, 27: 3–19. 10.1080/01457630600904593
 36.
Buongiorno J: Convective transport in nanofluids. J Heat Transfer 2006, 128: 240–250. 10.1115/1.2150834
 37.
Daungthongsuk W, Wongwises S: A critical review of convective heat transfer of nanofluids. Renew Sustain Energy Rev 2007, 11: 797–817. 10.1016/j.rser.2005.06.005
 38.
Trisaksri V, Wongwises S: Critical review of heat transfer characteristics of nanofluids. Renew Sustain Energy Rev 2007, 11: 512–523. 10.1016/j.rser.2005.01.010
 39.
Yu W, France DM, Routbort JL, Choi SUS: Review and comparison of nanofluid thermal conductivity and heat Transfer enhancements. Heat Transfer Eng 2008, 29: 432–460. 10.1080/01457630701850851
 40.
Keblinski P, Prasher R, Eapen J: Thermal conductance of nanofluids: is the controversy over? J Nanoparticle Res 2008, 10: 1089–1097. 10.1007/s1105100793521
 41.
Kakaç S, Pramuanjaroenkij A: Review of convective heat transfer enhancement with nanofluids. Int J Heat Mass Transfer 2009, 52: 3187–3196.
 42.
Choi SUS: Nanofluids: from vision to reality through research. J Heat Transfer 2009, 131: 1–9. 10.1115/1.3056479
 43.
Buongiorno J, et al.: A benchmark study on the thermal conductivity of nanofluids. J Appl Phys 2009, 106: 1–9. 10.1063/1.3245330
 44.
Özerinç S, Kakaç S, Yazıcıoğlu AG: Enhanced thermal conductivity of nanofluids: a stateoftheart review. Microfluid Nanofluid 2010, 8: 145–170.
 45.
Wang L, Fan J: Nanofluids research: key issues. Nanoscale Res Lett 2010, 5: 1241–1252. 10.1007/s1167101096386
 46.
Godson L, Raja B, Lal DM, Wongwises S: Enhancement of heat transfer using nanofluidsan overview. Renew Sustain Energy Rev 2010, 14: 629–641. 10.1016/j.rser.2009.10.004
 47.
Venerus D, et al.: Viscosity measurements on colloidal dispersions (nanofluids) for heat transfer applications. Appl Rheol 2010, 20: 445–462.
 48.
Roy G, Nguyen CT, Lajoie P: Numerical investigation of laminar flow and heat transfer in a radial flow cooling system with the use of nanofluids. Superlattices Microstruct 2004, 35: 497–511. 10.1016/j.spmi.2003.09.011
 49.
Maiga S, Palm SJ, Nguyen CT, Roy G, Galanis N: Heat transfer enhancement by using nanofluids in forced convection flows. Int J Heat Fluid Flow 2005, 26: 530–546. 10.1016/j.ijheatfluidflow.2005.02.004
 50.
Roy G, Palm SJ, Nguyen CT: Heat transfer and fluid flow of nanofluids in laminar radial flow cooling systems. J Thermal Sci 2005, 14: 362–367. 10.1007/s1163000500592
 51.
Palm SJ, Roy G, Nguyen CT: Heat transfer enhancement with the use of nanofluids in radial flow cooling systems considering temperaturedependent properties. Appl Thermal Eng 2006, 26: 2209–2218. 10.1016/j.applthermaleng.2006.03.014
 52.
Roy G, Nguyen CT, Comeau M: Numerical investigation of electronic component cooling enhancement using nanofluids in a radial flow cooling system. J Enhanc Heat Transfer 2006, 13: 101–115. 10.1615/JEnhHeatTransf.v13.i2.20
 53.
Schoeppler M: Correspondence address diverging inkjet technologies and applications. Proceedings of the International Conference on Digital Printing Technologies: 16–17 September 2006; Denver 2006, 1–2.
 54.
Liu ZH, Qiu YH: Boiling heat transfer characteristics of nanofluids jet impingement on a plate surface. Heat Mass Transfer 2007, 43: 699–706. 10.1007/s002310060159x
 55.
Liu ZH, Qiu YH: The boiling heat transfer of water based nanofluid jet impingement on a plate surface. J Shanghai Jiaotong Univ 2007, 41: 1658–1661.
 56.
Nguyen CT, Galanis N, Polidori G, Fohanno S, Popa CV, Le Bechec A: An experimental study of a confined and submerged impinging jet heat transfer using Al_{2}O_{3}water nanofluid. Int J Thermal Sci 2009, 48: 401–411. 10.1016/j.ijthermalsci.2008.10.007
 57.
Vaziei P, Abouali O: Numerical study of fluid flow and heat transfer for Al_{2}O_{3}water nanofluid impinging jet. Proceedings of the 7th International Conference on Nanochannels, Microchannels and Minichannels 2009: 22–24 June 2009; Pohang 2009, 977–984.
 58.
Feng Y, Kleinstreuer C: Nanofluid convective heat transfer in a paralleldisk system. Int J Heat Mass Transfer 2010, 53: 4619–4628. 10.1016/j.ijheatmasstransfer.2010.06.031
 59.
Yang YT, Lai FH: Numerical study of heat transfer enhancement with the use of nanofluids in radial flow cooling system. Int J Heat Mass Transfer 2010, 53: 5895–5904. 10.1016/j.ijheatmasstransfer.2010.07.045
 60.
Yang YT, Lai FH: Numerical investigation of cooling performance with the use of Al_{2}O_{3}/water nanofluids in a radial flow system. Int J Thermal Sci 2011, 50: 61–72. 10.1016/j.ijthermalsci.2010.08.017
 61.
Rohsenow WM, Hartnett JP, Cho YI: Handbook of Heat Transfer. 3rd edition. New York: McGrawHill; 1998.
 62.
Pak BC, Cho YI: Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp Heat Transfer 1998, 11: 151–170. 10.1080/08916159808946559
 63.
Maiga SEB, Nguyen CT, Galanis N, Roy G: Heat transfer behaviours of nanofluids in a uniformly heated tube. Superlattices Microstruct 2004, 35: 543–557. 10.1016/j.spmi.2003.09.012
 64.
Maiga SEB, Cong Tam N, Galanis N, Roy G, Mare T, Coqueux M: Heat transfer enhancement in turbulent tube flow using Al_{2}O_{3}nanoparticle suspension. Int J Numer Methods Heat Fluid Flow 2006, 16: 275–292. 10.1108/09615530610649717
 65.
Palm SJ, Roy G, Nguyen CT: Heat transfer enhancement with the use of nanofluids in radial flow cooling systems considering temperature dependent properties. Appl Thermal Eng 2006, 26: 2209–2218. 10.1016/j.applthermaleng.2006.03.014
 66.
Launder BE, Spalding DB: The numerical computation of turbulent flows. Comput Methods Appl Mech Eng 1974, 3: 269–289. 10.1016/00457825(74)900292
 67.
FLUENT Computational Fluid Dynamic Code Version 6.3 User Guide, Fluent, Inc[http://www.fluent.com]
 68.
Wolfstein M: The velocity and temperature distribution of onedimensional flow with turbulence augmentation and pressure gradient. Int J Heat Mass Transfer 1969, 12: 301–318. 10.1016/00179310(69)90012X
 69.
Cadek FFA: Fundamental investigation of jet Impingement heat transfer. In Ph.D Thesis. University of Cincinnati; 1968.
 70.
Gordon R, Akfirat JC: Heat transfer characteristics of impinging twodimensional air jets. J Heat Transfer 1966, 88: 101–108.
Acknowledgements
This study was supported by SUN Grant Initiative of 2008 grant and by MIUR with Articolo D.M. 593/2000 Grandi Laboratori "EliosLab".
Author information
Affiliations
Corresponding author
Additional information
Competing interests
The authors declare that they have no competing interests.
Authors' contributions
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.
Oronzio Manca, Paolo Mesolella, Sergio Nardini and Daniele Ricci contributed equally to this work.
Authors’ original submitted files for images
Below are the links to the authors’ original submitted files for images.
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Manca, O., Mesolella, P., Nardini, S. et al. Numerical study of a confined slot impinging jet with nanofluids. Nanoscale Res Lett 6, 188 (2011). https://doi.org/10.1186/1556276X6188
Received:
Accepted:
Published:
Keywords
 Nusselt Number
 Stagnation Point
 Base Fluid
 Heat Transfer Enhancement
 Local Nusselt Number