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

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

## 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 |

## References

- Gorla, R.S.R.; Chamkha, A. Natural convective boundary layer flow over a vertical plate embedded in a porous medium saturated with a non-Newtonian nanofluid. Int. J. Microscale Nanoscale Therm. Fluid Transp. Phenom.
**2011**, 3, 1–20. [Google Scholar] - Dogonchi, A.S.; Chamkha, A.J.; Seyyedi, S.M.; Ganji, D.D. Radiative nanofluid flow and heat transfer between parallel disks with penetrable and stretchable walls considering Cattaneo–Christov heat flux model. Heat Transf. Asian Res.
**2018**, 47, 735–753. [Google Scholar] [CrossRef] - Goshayeshi, H.R.; Safaei, M.R.; Goodarzi, M.; Dahari, M. Particle Size and Type Effects on Heat Transfer Enhancement of Ferro-nanofluids in a Pulsating Heat Pipe under Magnetic Field. Powder Technol.
**2016**, 301, 1218–1226. [Google Scholar] [CrossRef] - Khanafer, K.; Vafai, K. A critical synthesis of thermophysical characteristics of nanofluids. Int. J. Heat Mass Transf.
**2012**, 54, 4410–4428. [Google Scholar] [CrossRef] - Kosar, A.; Peles, Y. TCPT-2006-096. R2: Micro Scale Pin Fin Heat Sinks—Parametric Performance Evaluation Study. IEEE Trans. Compon. Packag. Technol.
**2007**, 30, 855–865. [Google Scholar] [CrossRef] - Sivasankaran, H.; Asirvatham, G.; Bose, J.; Albert, B. Experimental Analysis of Parallel Plate and Crosscut Pin Fin Heat Sinks for Electronic Cooling Applications. Therm. Sci.
**2010**, 14, 147–156. [Google Scholar] [CrossRef] - Mital, M. Analytical Analysis of Heat Transfer and Pumping Power of Laminar Nanofluid Developing Flow in Microchannels. Appl. Therm. Eng.
**2012**, 50, 429–436. [Google Scholar] [CrossRef] - Hung, T.C.; Yan, W.M.; Wang, X.D.; Chang, C.Y. Heat Transfer Enhancement in Microchannel Heat Sinks using Nanofluids. Int. J. Heat Mass Transf.
**2012**, 55, 2559–2570. [Google Scholar] [CrossRef] - Akbari, O.A.; Toghraie, D.; Karimipour, A. Impact of ribs on flow parameters and laminar heat transfer of water–aluminum oxide nanofluid with different nanoparticle volume fractions in a three-dimensional rectangular microchannel. Adv. Mech. Eng.
**2015**, 7, 1–11. [Google Scholar] [CrossRef] - Behnampour, A.; Akbari, O.A.; Safaei, M.R.; Ghavami, M.; Marzban, A.; Ahmadi Sheikh Shabani, G.R.; zarringhalam, M.; Mashayekhi, R. Analysis of heat transfer and nanofluid fluid flow in microchannels with trapezoidal, rectangular and triangular shaped ribs. Physica E
**2017**, 91, 15–31. [Google Scholar] [CrossRef] - Gravndyan, Q.; Akbari, O.A.; Toghraie, D.; Marzban, A.; Mashayekhi, R.; Karimi, R.; Pourfattah, F. The effect of aspect ratios of rib on the heat transfer and laminar water/TiO
_{2}nanofluid flow in a two-dimensional rectangular microchannel. J. Mol. Liq.**2017**, 236, 254–265. [Google Scholar] [CrossRef] - Lee, D.Y.; Vafai, K. Comparative analysis of jet impingement and microchannel cooling for high heat flux applications. Int. J. Heat Mass Transf.
**1999**, 42, 1555–1568. [Google Scholar] [CrossRef] - Chang, S.W.; Chiang, K.F.; Chou, T.C. Heat transfer and pressure drop in hexagonal ducts with surface dimples. Exp. Therm. Fluid Sci.
**2010**, 34, 1172–1181. [Google Scholar] [CrossRef] - Elyyan, M.A.; Ball, K.S.; Diller Thomas, E.; Paul Mark, R.; Ragab Saad, A. Heat Transfer Augmentation Surfaces Using Modified Dimples/Protrusions. Ph.D. Thesis, Virginia Tech, Blacksburg, VA, USA, 2008. [Google Scholar]
- Guo, J.; Fan, A.; Zhang, X.; Liu, W. A numerical study on heat transfer and friction factor characteristics of laminar flow in a circular tube fitted with centercleared twisted tap. Int. J. Therm. Sci.
**2011**, 50, 1263–1270. [Google Scholar] [CrossRef] - Zhang, X.; Liu, Z.; Liu, W. Numerical studies on heat transfer and flow characteristics for laminar flow in a tube with multiple regularly spaced twisted tapes. Int. J. Therm. Sci.
**2012**, 58, 157–167. [Google Scholar] [CrossRef] - Zheng, N.; Liu, W.; Liu, Z.; Liu, P.; Shan, F. A numerical study on heat transfer enhancement and the flow structure in a heat exchanger tube with discrete double inclined ribs. Appl. Therm. Eng.
**2015**, 90, 232–241. [Google Scholar] [CrossRef] - Shan, F.; Liu, Z.; Liu, W.; Tsuji, Y. Effects of the orifice to pipe diameter ratio on orifice flows. Chem. Eng. Sci.
**2016**, 152, 497–506. [Google Scholar] [CrossRef] - Zheng, N.; Liu, P.; Shan, F.; Liu, Z.; Liu, W. Effects of rib arrangements on the flow pattern and heat transfer in an internally ribbed heat exchanger tube. Int. J. Therm. Sci.
**2016**, 101, 93–105. [Google Scholar] [CrossRef] - Chin, S.B.; Foo, J.J.; Lai, Y.L.; Yong, T.K.K. Forced Convective Heat Transfer Enhancement with Perforated Pin Fins. Heat Mass Transf.
**2013**, 49, 1447–1458. [Google Scholar] [CrossRef] - Naphon, P.; Nakharintr, L. Heat Transfer of Nanofluids in the Mini-rectangular Fin Heat Sinks. Int. Commun. Heat Mass Transf.
**2012**, 40, 25–31. [Google Scholar] [CrossRef] - Jasperson, B.A.; Jeon, Y.; Turner, K.T.; Pfefferkorn, F.E.; Qu, W. Comparison of Micro-pin-fin and Microchannel Heat Sinks Considering Thermal-hydraulic Performance and Manufacturability. IEEE Trans. Compon. Packag. Technol.
**2010**, 33, 148–160. [Google Scholar] [CrossRef] - Zhuang, Y.; Ma, C.F.; Qin, M. Experimental study on local heat transfer with liquid impingement flow in two-dimensional micro-channels. Int. J. Heat Mass Transf.
**1997**, 40, 4055–4059. [Google Scholar] [CrossRef] - Gholami, M.R.; Akbari, O.A.; Marzban, A.; Toghraie, D.; Ahmadi Sheikh Shabani, G.H.R.; Zarringhalam, M. The effect of rib shape on the behavior of laminar flow of Oil/MWCNT nanofluid in a rectangular microchannel. J. Therm. Anal. Calorim.
**2017**, 1–18. [Google Scholar] [CrossRef] - Raisi, A.; Aminossadati, S.M.; Ghasemi, B. An innovative nanofluid-based cooling using separated natural and forced convection in low Reynolds flows. J. Taiwan Inst. Chem. Eng.
**2016**, 1–5. [Google Scholar] [CrossRef] - Aminossadati, S.M.; Raisi, A.; Ghasemi, B. Effects of magnetic field on nanofluid forced convection in a partially heated microchannel. Int. J. Non-Linear Mech.
**2011**, 46, 1373–1382. [Google Scholar] [CrossRef] - Bahmani, M.H.; Sheikhzadeh, G.; Zarringhalam, M.; Akbari, O.A.; Alrashed, A.A.A.A.; Ahmadi Sheikh Shabani, G.; Goodarzi, M. Investigation of turbulent heat transfer and nanofluid flow in a double pipe heat exchanger. Adv. Powder Technol.
**2018**, 29, 273–282. [Google Scholar] [CrossRef] - Arani, A.A.A.; Akbari, O.A.; Safaei, M.R.; Marzban, A.; Alrashed, A.A.A.A.; Ahmadi, G.R.; Nguyen, T.K. Heat transfer improvement of water/single-wall carbon nanotubes (SWCNT) nanofluid in a novel design of a truncated double layered microchannel heat sink. Int. J. Heat Mass Transf.
**2017**, 113, 780–795. [Google Scholar] [CrossRef] - Khodabandeh, E.; Rahbari, A.; Rosen, M.A.; Najafian Ashrafi, Z.; Akbari, O.A.; Anvari, A.M. Experimental and numerical investigations on heat transfer of a water-cooled lance for blowing oxidizing gas in an electrical arc furnace. Energy Conversat. Manag.
**2017**, 148, 43–56. [Google Scholar] [CrossRef] - Safaiy, M.R.; Saleh, S.R.; Goudarzi, M. Numerical studies of laminar natural convection in a square cavity with orthogonal grid mesh by finite volume method. Int. J. Adv. Des. Manuf. Technol.
**2011**, 1, 13–21. [Google Scholar] - Akbari, O.A.; Goodarzi, M.; Safaei, M.R.; Zarringhalam, M.; Ahmadi Sheikh Shabani, G.R.; Dahari, M. A modified two-phase mixture model of nanofluid flow and heat transfer in 3-D curved microtube. Adv. Powd. Technol.
**2016**, 27, 2175–2185. [Google Scholar] [CrossRef] - Safaei, M.R.; Goodarzi, M.; Akbari, O.A.; Safdari Shadloo, M.; Dahari, M. Performance Evaluation of Nanofluids in an Inclined Ribbed Microchannel for Electronic Cooling Applications. Electron. Cool.
**2016**. [Google Scholar] [CrossRef] [Green Version] - Raisi, A.; Ghasemi, B.; Aminossadati, S.M. A Numerical Study on the Forced Convection of Laminar Nanofluid in a Microchannel with Both Slip and No-Slip Conditions. Numer. Heat Transf. Part A
**2011**, 59, 114–129. [Google Scholar] [CrossRef]

**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 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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