Numerical study of a confined slot impinging jet with nanofluids
 Oronzio Manca†^{1}Email author,
 Paolo Mesolella†^{1},
 Sergio Nardini†^{1} and
 Daniele Ricci†^{1}
https://doi.org/10.1186/1556276X6188
© Manca et al; licensee Springer. 2011
Received: 14 December 2010
Accepted: 1 March 2011
Published: 1 March 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
Keywords
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
Physical properties of nanofluids
Material properties at a temperature of 293 K
Material  ρ(kg/m^{3})  c_{ p }(J/kg K)  μ(Pa s)  k(W/m K) 

γAlumina (Al_{2}O_{3})  3880  773  //  36 
Water  998  4182  998 × 10^{6}  0.597 
Properties of nanofluids, singlephase model.
ϕ  ρ(kg/m^{3})  c_{ p }(J/kg K)  μ(Pa s)  k(W/m K) 

0%  998.2  4182  998 × 10^{6}  0.597 
1%  1027  4148  1083 × 10^{6}  0.614 
4%  1113  4046  1486 × 10^{6}  0.667 
6%  1171  3977  1877 × 10^{6}  0.705 
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
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.

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.
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
Inlet velocities (m/s).
Re  Water  Water/alumina 1%  Water/alumina 4%  Water/alumina 6% 

5000  0.81  0.85  1.08  1.29 
10000  1.61  1.70  2.15  2.59 
15000  2.42  2.55  3.23  3.88 
20000  3.23  3.40  4.30  5.17 
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.
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.
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.
Conclusions
List of symbols
Symbol  Quantity  SI Unit 

c _{ p }  Specific heat  J/kg K 
H  Channel height  m 
h  Heat transfer coefficient  W/m^{2} K 
k  Turbulent kinetic energy  J 
L  Channel length  m 
Nu  Nusselt number  Equation 11 
P  Pressure  Pa 
PP  Required pumping power  W 
Pr = ν/a Prandtl number  
q  Impingement surface heat flux W/m^{ 2 }  
Re  Reynolds number  Equation 10 
T  Temperature  K 
u  Velocity component  m/s 
$\dot{V}$  Volume flow rate  m^{3}/s 
W  Jet width  m 
x, y  Spatial coordinates  m 
Greek symbols  
δ  Kronecher delta function  
ε  Rate of dissipated turbulent  
thermal energy  
ϕ  Nanoparticle concentration  
λ  Thermal conductivity  W/mK 
μ  Dynamic viscosity  Pa s 
ρ  Density  kg/m^{3} 
σ  Turbulent Prandtl number  
τ  Wall shear stress  kg/m 
ν  Kinematic viscosity  m^{2}/s 
Subscripts  
0  Stagnation point  
a  Ambient  
avg  Average  
bf  Base fluid  
f  Fluid  
H  Heated  
J  Jet  
nf  Nanofluid  
p  Particle  
t  Turbulent 
Notes
Declarations
Acknowledgements
This study was supported by SUN Grant Initiative of 2008 grant and by MIUR with Articolo D.M. 593/2000 Grandi Laboratori "EliosLab".
Authors’ Affiliations
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