Nanofluid flow in a microchannel with inclined crossflow injection
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Abstract
This paper investigates forced convection of water/Al_{2}O_{3} nanofluid flow in a microchannel with inclined crossflow injection on the lower wall. There are a number of injecting holes on its lower wall. Other walls are insulated. The effect of different parameters including injection angle and number of injections on slip flow and heat transfer is investigated. It is concluded that increasing the injection angle up to 94° lead to an enhancement of the slip velocity and the Nusselt number on the microchannel walls. The results demonstrate that maximum heat transfer corresponds to the injection angle of 94°. It is revealed that the variation of Nusselt number decreases with the number of injection. As the volume fraction of nanoparticles increases, the heat transfer rate increases.
Keywords
Forced convection Nanofluid Slip velocity Inclined injection Microchannel1 Introduction
Fluids play a vital role in cooling and heating systems in industries. Their thermal conductivity is enhanced by addition of solid nanoparticles. The first observations of the thermal conductivity of nanofluids were reported by Masuda et al. [1]. Nazari et al. [2] demonstrated that the heat transfer of the nanofluid increases compared to the base ones. Numerous studies have been carried out on the use of microchannels in heat exchangers and heat rejected systems due to the small dimensions of these channels and their high efficiency. Raisi et al. [3] demonstrated that the Nusselt number (Nu) enhances with the slip coefficient for Reynolds numbers higher than 100. Akbarinia et al. [4] revealed that at a constant Reynolds number (Re), Nu enhances with the inlet velocity and it does not change with the volume fraction of nanoparticles (φ). Anoop et al. [5] studied forced convection heat transfer of water/silica nanofluid numerically and experimentally and demonstrated that the nanofluid exhibits Newtonian behavior for the volume fractions less than 7%. Togun et al. [6] considered heat transfer of nanofluids (water/Al_{2}O_{3} and water/CuO) in a microchannel with double forwardfacing steps. They revealed that Nu is higher on the second step in comparison with the first one. It was demonstrated that the heat transfer enhances with the volume fraction of nanofluids. The results of Nemati et al. [7] revealed that the average Nusselt number increases with φ and decreases with the magnetic field intensity. Jung et al. [8] evaluated the heat transfer of a nanofluid in a rectangular microchannel and found that Nu increases by increasing φ and Re. Olawale [9] evaluated the effect of injection flow in diverging and converging microchannel on heat transfer and hydrodynamics of a nanofluid. He found that the velocity distribution is an increasing function of Reynolds number. Malvandi et al. [10] demonstrated that velocity gradient close to the walls increases with the magnetic field. Afrand et al. [11] concluded that the slip velocity on the walls increases with the magnetic field intensity and heat transfer increases in the vicinity of the walls due to the accumulation of nanoparticles in this region. Their study corresponded to water/FMWNT nanofluid. Li and Kleinstreuer [12] simulated heat transfer of water and water/CuO nanofluid in a trapezoidal microchannel and showed that thermal performance of nanofluid is higher than that of pure water. They revealed that as the volume fraction increases, heat transfer rate and pressure drop increase. Aina and Malgwi [13] investigated the combined effects of magnetic field and suction/injection on natural convection heat transfer in an inclined microchannel with porous media. They demonstrated that thermal boundary later thickness increases and decreases with the injection and suction flow rates, respectively. Hence, thermal performance decreases and increases under the influence of injection and suction, respectively. In heat channels, the fluid temperature near the hot surfaces is always higher than the central of the channel. Thus, if low temperature fluid can be mixed with the hot one adjacent to the target surface, the heat transfer rate increases significantly. For this purpose, various techniques such as injection and suction of fluids have been proposed. In most of the studies, nanofluids have been used as a cooling fluid to improve the heat transfer. Jha and Aina [14] reported that the volumetric flow rate increases by increasing injection and suction, while the heat transfer decreases. Also, the possibility of a return flow on the cold wall decreases with the Knudsen number. López et al. [15] found that Nu increases on the hot wall of a porous microchannel and decreases on its cold wall by increasing φ and injecting the flow. Jalali and Karimipour [16] reported that Nu increases with Re and φ. Convective heat transfer and entropy generation of AgMgO/water hybrid nanofluid in microchannel are discussed by Uysal and Korkmaz [17]. They found that heat transfer increases as the volume fraction of hybrid nanofluid increases. In addition, it was reported that the entropy generation decreases due to the heat transfer and increases due to fluid friction. Akinshilo [18] studied the effect of magnetic field on heat transfer of a nanofluid in a converging or diverging porous channel with injection flow. It was concluded that Nu increases with the magnetic field strength. They studied the influence of Reynolds number, volume fraction of nanoparticles and expansion angle on heat transfer and fluid friction. Evaluation of the effect of nanofluid on convective heat transfer has been considered for different geometries [19, 20, 21, 22].
Present simulations evaluate forced convection of water/Al_{2}O_{3} nanofluid in a microchannel considering inclined injection on the lower wall. The main objective of the present work is to investigate the effect of injection angle and number of injections on thermal performance of a heat microchannel. Their influence on velocity distribution, temperature profile and slip velocity is discussed.
2 Problem statement
Thermophysical properties of water/Al_{2}O_{3} nanofluid [16]
\({\varphi }\) (%)  \(\uprho_{nf}\) (kg/m^{3})  \(\mu_{nf}\) (Pa s)  \(k_{nf}\) (W/m K)  \(\left( {c_{p} } \right)_{nf}\) (J/kg K) 

0  997.1  8.91 × 10^{−4}  0.613  4179 
2  1056.5  9.37 × 10^{−4}  0.653  3922.4 
4  1116  9.87 × 10^{−4}  0.695  3693.3 
3 Governing equations
4 Results
Forced convection heat transfer of water/Al_{2}O_{3} nanofluid in a microchannel is evaluated. First, grid study and then validation are presented. The effect of the injection angle, the number of injections and different values of φ on slip velocity, temperature field and heat transfer of nanofluid will be presented in the next sections.
4.1 Grid study
Nusselt number and dimensionless velocity on the midpoint of the upper wall of the microchannel with four 60° angle injection points for different grid resolutions
40 × 400  50 × 500  60 × 600  70 × 700  80 × 800  90 × 900  

Nu  1.5173  1.5174  1.5174  1.5166  1.5161  1.5161 
U  0.5282  0.5298  0.5305  0.5323  0.5327  0.5331 
4.2 Validation
4.3 Effect of injection angle
4.4 Effect of the number of injection
4.5 Effect of the volume fraction of nanoparticles
5 Conclusions

The maximum Nu occurs at the injection angle of 94° as an optimal injection angle.

As the number of injections increases, Nu increases. Nu does not change at the microchannel output by changing the number of injections.

Increasing the injection angle to reach the optimal injection angle results in an enhancement in the slip velocity on the microchannel walls. Then, the slip velocity decreases by increasing the injection angle.

Nanofluid thermal conductivity and Nu increase with φ.
Notes
Compliance with ethical standards
Conflict of interest
The authors declare that they have no competing interests.
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