# Heat Transfer of Oil/MWCNT Nanofluid Jet Injection Inside a Rectangular Microchannel

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## Abstract

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## 1. Introduction

_{2}O

_{3}nanofluid with different nanoparticle volume fractions inside a rectangular microchannel and found that using rough surfaces in microchannel leads to higher heat transfer. Behnampour et al. [10] numerically investigated laminar flow and heat transfer parameters of water/AgO nanofluid with different nanoparticle volume fractions in a rectangular microchannel and showed that by increasing fluid velocity, an optimized trade-off can be obtained between heat transfer, hydrodynamic behavior of nanofluid, and the performance evaluation criteria (PEC) variations. Geravandian et al. [11] numerically simulated the laminar heat transfer of nanofluid flow in a rectangular microchannel and revealed that by increasing TiO

_{2}nanoparticles, heat transfer, friction coefficient, PEC, and pressure drop increase. Studies on the effect of using cooling fluid jet injection on heated surfaces [12] and other methods to increase heat transfer, such as using dimples, rough surfaces [13,14], and twisted tapes [15,16], have been conducted for different industrial and experimental geometries. These studies show that by creating vortexes, uniform temperature distribution can be obtained. Fluid jet plays an important role in cooling technologies and by creating better mixtures of cooling fluid flow, thermal performance can be enhanced [17,18,19]. Chen et al. [20] numerically and experimentally investigated the forced convection heat transfer inside a rectangular channel for determining fluid flow and heat transfer properties. They also compared the performance of heat sinks with solid and perforated pins and showed that by increasing the number of perforations and their diameter, pressure drop decreases and the Nusselt number increases. In their experiments, thermal performance of the heat sink with perforated pins was better than with solid pins. Nafon et al. [21] experimentally studied the effects of inlet temperature, Reynolds number, and heat flux on heat transfer properties of a water/TiO

_{2}nanofluid jet in a semi-rectangular heat sink, and showed that the average heat transfer coefficient of nanofluid is higher than base fluid, and the pressure drop increases by increasing the nanoparticle volume fraction. Jasperson et al. [22] studied the thermal and hydrodynamic performance of a copper microchannel and a pin fin microchannel and showed that by increasing the volume rate of flow, the thermal resistance of a pin fin heat sink decreases. Zhuwang et al. [23] studied heat transfer inside a microchannel with fluid jet and different coolants and showed that using fluid jet results in higher heat transfer compared with ordinary parallel flows.

## 2. Problem Definition

_{h}= 303 K. The inlet cold fluid entered from the left side of the microchannel with the temperature of T

_{c}= 293 K. Figure 1 shows the microchannel in the present study.

_{1}= 500 µm. The velocity of the inlet nanofluid jet at all studied Reynolds numbers was constant (Re = 10). Fluid flow and heat transfer inside the microchannel were separately simulated in cases with no jet and with 1, 2, and 3 jets. Nanofluids with high velocity through the lower wall were injected into the micro-channel. As the cooling fluid jet flowed on the surface, the temperature of this surface decreased. Also, in this investigation, the effect of applying slip and no-slip boundary conditions on solid walls of the microchannel in slip coefficients of B = 0.0, 0.04, and 0.08 were investigated. The flow was laminar, forced, Newtonian, single-phase, and incompressible; the nanofluid was homogeneous and uniform; and also, the radiation effects were neglected. The properties of the base fluid and nanofluid in different nanoparticle volume fractions are presented in Table 1 [24].

## 3. Governing Equations

## 4. Numerical Details

^{−6}[29,30] was used. For coupling velocity–pressure equations, the SIMPLEC [31,32] algorithm was used. Also, the effect of nanoparticle volume fraction, Reynolds number, and jet number on flow and heat transfer parameters were investigated; and flow parameters, temperature, and streamlines contours are the presented.

## 5. Results and Discussion

#### 5.1. Streamlines and Isothermal Contours

#### 5.2. Local Nusselt Number

#### 5.3. Temperature along the Symmetry Plane

#### 5.4. Axial Velocity along the Symmetric Plate

#### 5.5. Average Nusselt Number on the Heated Surface

#### 5.6. Effect of Slip Coefficient on Axial Velocity

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

B | dimensionless slip velocity coefficient |

C_{p} | heat capacity, J kg^{−1} K^{−1} |

d | diameter, m |

H, L | microchannel height and length, m |

k | thermal conductivity coefficient, Wm^{−1} K^{−1} |

Nu | Nusselt number |

P | fluid pressure, Pa |

Pr = ν_{f}/f | Prandtl number |

Re = ρ_{f} u_{c} H /µ_{f} | Reynolds number |

T | temperature, K |

u, v | velocity components in the x-, y-directions, ms^{−1} |

u_{c} | inlet flow velocity, ms^{−1} |

(U, V) = (u/U_{0}, v/U_{0}) | dimensionless flow velocity in the x-, y-direction |

x, y | Cartesian coordinates, m |

(X, Y = x/H, y/H) | dimensionless coordinates |

Greek symbols | |

α | thermal diffusivity, m^{2}s^{−1} |

β * | dimensionless slip velocity coefficient |

φ | nanoparticle volume fraction |

µ | dynamic viscosity, Pa s |

θ = (T − T_{C})/(T_{H} − T_{C}) | dimensionless temperature |

ρ | density, kg m^{−3} |

ν | kinematics viscosity m^{2}s^{−1} |

Super- and Subscripts | |

c | Cold |

eff | Effective |

f | base fluid (pure water) |

h | Hot |

m | Mean |

nf | Nanofluid |

s | solid nanoparticles |

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**Figure 1.**Schematic of the studied geometry in the present numerical study. (

**A**) Case 1; (

**B**) Case 2; (

**C**) Case 3; (

**D**) Case 4.

**Figure 2.**Validation of the present numerical study with Raisi et al. [33].

**Figure 3.**Validation of the present study with Raisi et al. [33].

**Figure 6.**Local Nusselt number graphs at Re = 10 and B = 0.04 for different nanoparticle volume fractions.

**Figure 8.**Temperature distribution at Re = 10, B = 0.04, and different nanoparticle volume fractions.

**Figure 9.**Temperature distribution at R e= 50, B = 0.04, and different nanoparticle volume fractions.

**Figure 13.**Dimensionless axial velocity at Re = 10 and φ = 2% with different slip coefficients on solid walls.

**Figure 14.**Dimensionless axial velocity at Re = 50 and φ = 2% with different slip coefficients on solid walls.

Oil | MWCNT | φ = 0.02 | φ = 0.04 | |
---|---|---|---|---|

c_{p} (J/kg K) | 2032 | 1700 | 2012.9 | 1995.1 |

ρ (kg/m^{3}) | 867 | 2600 | 901.66 | 936.32 |

k (W/m K) | 0.133 | 3000 | 0.5255 | 0.7912 |

µ (Pa s) | 0.0289 | - | 0.0305 | 0.0321 |

Grid Size | 500 × 50 | 750 × 75 | 850 × 80 | 900 × 90 | 1000 × 100 |
---|---|---|---|---|---|

Re = 10 | |||||

Nu_{ave} | 0.3698 | 0.3401 | 0.3202 | 0.2922 | 0.3401 |

U_{out(Y=H/2)} | 3.806 | 3.7740 | 3.7532 | 3.6178 | 3.7740 |

Re=50 | |||||

Nu_{ave} | 0.69719 | 0.6561 | 0.6178 | 0.5541 | 0.6561 |

U_{out(Y=H/2)} | 3.972 | 3.9616 | 3.9578 | 3.9257 | 3.9616 |

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**MDPI and ACS Style**

Jalali, E.; Ali Akbari, O.; Sarafraz, M.M.; Abbas, T.; Safaei, M.R.
Heat Transfer of Oil/MWCNT Nanofluid Jet Injection Inside a Rectangular Microchannel. *Symmetry* **2019**, *11*, 757.
https://doi.org/10.3390/sym11060757

**AMA Style**

Jalali E, Ali Akbari O, Sarafraz MM, Abbas T, Safaei MR.
Heat Transfer of Oil/MWCNT Nanofluid Jet Injection Inside a Rectangular Microchannel. *Symmetry*. 2019; 11(6):757.
https://doi.org/10.3390/sym11060757

**Chicago/Turabian Style**

Jalali, Esmaeil, Omid Ali Akbari, M. M. Sarafraz, Tehseen Abbas, and Mohammad Reza Safaei.
2019. "Heat Transfer of Oil/MWCNT Nanofluid Jet Injection Inside a Rectangular Microchannel" *Symmetry* 11, no. 6: 757.
https://doi.org/10.3390/sym11060757