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 and 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 , 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 , 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 . 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 .
Stream functions contours. (a) H/W = 10, Re = 10000 and ϕ = 0%; (b) H/W = 10, Re = 10000 and ϕ = 4%; (c) H/W = 4, Re = 10000 and ϕ = 4%; (d) H/W = 10, Re = 20000 and ϕ = 4%.
Temperature fields. (a) H/W = 10, Re = 10000 and ϕ = 0%; (b) H/W = 10, Re = 10000 and ϕ = 4%; (c) H/W = 4, Re = 10000 and ϕ = 4%; (d) H/W = 10, Re = 20000 and ϕ = 4%.
The temperature fields, depicted in Figure , 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 , respectively. It is observed that the highest values of Nux 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, Nux reaches similar values equal to about 25, as observed in Figure . In Figure , 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.
Local Nusselt number profiles along x/W: (a) H/W = 4 and 10, Re = 20000, ϕ = 6%; (b) H/W = 6, Re = 5000, ϕ = 0, 1, 4 and 6%.
In Figure , the variation of local qw/q0w ratio is shown. The qw/q0w 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, qw/q0w ratio increases. Difference in terms of qw/q0w 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 qw/q0w 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 , it is observed as the nanofluid concentration has very little influence on qw/q0w. The effects of H/W are underlined in Figure : near the stagnation point, qw/q0w ratio has almost the same value for all H/W. From x/W = 4 curves spread out and qw/q0w increases as H/W increases. This affects the results in terms of average Nusselt number, calculated at different H/W ratios.
Profiles of qw/q0w ratio along x/W: (a) H/W = 4, ϕ = 0%, Re = 5000, 10000, 15000 and 20000; (b) H/W = 4, Re = 5000, ϕ = 0, 1, 4 and 6%; (c) H/W = 4, 6, 8 and 10, ϕ = 0% and Re = 5000.
The average Nusselt number profiles as function of Re are depicted in Figure 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 Nuavg becomes higher for a fixed value of Re. Passing from ϕ = 0% to ϕ = 1%, a significant increase of Nuavg, 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.
Average Nusselt number profiles as function of Re, ϕ= 0, 1, 4 and 6%: (a) H/W = 4; (b) H/W = 6; (c) H/W = 8; (d) H/W = 10.
The heat transfer enhancement is evident, also observing the average heat transfer coefficient profiles, described in Figure . Results are given for different Re, H/W ratios and concentrations. The maximum values of havg 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 havg is equal to about 7600, 8000, 9400 and 10500 W/m2K, as depicted in Figure , while, at H/W = 4 and Re = 20000, havg are equal to about 6200, 6800, 7700, and 8600 W/m2K, for ϕ = 0, 1, 4, and 6%, respectively.
Average convective heat transfer coefficient profiles as function of Re, ϕ= 0, 1, 4 and 6%: (a) H/W = 4; (b) H/W = 6; (c) H/W = 8; (d) H/W = 10.
Figure 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 Nuavg/Nuavg, 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%.
Profiles of Nuavg/Nuavg, bf ratio as a function of Re for different values of particle concentrations, H/W = 4.
The results in terms of local Nusselt numbers, calculated for the stagnation point, are depicted in Figure . 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 Nu0 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, Nu0 values rises as H/W increases for Re > 10000, as observed in Figure .
Stagnation point values of local Nusselt number. Values of local Nusselt number in correspondence with the stagnation point, for different Re and concentrations: (a) H/W = 4; (b) H/W = 6; (c) H/W = 8; (d) H/W = 10.
In fact, Figure shows that Nu0 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 Nu0 values are about 70, 81, 86, and 87, while at Re = 20000, Nu0 = 195, 197, 200, and 205, for H/W = 4, 6, 8, and 10, respectively. The results for ϕ = 6% are depicted in Figure ; 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, Nu0 values are equal to 215, 225, 235, and 240.
Stagnation point Nusselt number values as a function of Re. Nusselt number values of stagnation point as a function of Re, for different H/W ratios: (a) ϕ = 0%; (b) ϕ = 6%.
Results in terms of average Nusselt numbers are shown in Figure , 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 Nuavg are detected for H/W = 10 while the minimum ones for H/W = 4. Moreover, average Nusselt numbers increase as ϕ increases; thus, Nuavg values are equal to 42 and 79 for water, as depicted in Figure , while for ϕ = 6%, they are equal to 48 and 92, as pointed out by Figure , at Re = 10000 and 20000, respectively.
Average Nusselt number profiles as a function of Re for different H/W ratios: (a) ϕ = 0%; (b) ϕ = 6%.
Figure 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.
Average Nusselt number profiles as a function of H/W for Re = 5000 and 20000, ϕ= 0 and 6%.
The pumping power is defined as PP = VΔP, and its profiles are shown in Figure , 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 , 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 , and 98 W for water, and 58 and 470 W for ϕ = 6%, respectively.
Profiles of the required pumping power as a function of Re, for ϕ= 0, 1, 4 and 6%: (a) H/W = 4; (b) H/W = 6; (c) H/W = 8; (d) H/W = 10.
The pumping power ratio, referred to the base fluid values, is described in Figure . It is observed that the ratio does not seem to be dependent on Re, and PP/PPbf 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.
Pumping power profile, referred to the base fluid values as a function of Re, ϕ = 1, 4 and 6%, H/W = 4.