# Cooling Enhancement and Stress Reduction Optimization of Disk-Shaped Electronic Components Using Nanofluids

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model

#### 2.1. The Governing Equations

_{c}” the Boltzmann constant (1.3807 $\times $ 10

^{−23}J/K), and µ was calculated as

^{7}and 10

^{8}had been used, which showed Reynolds numbers smaller than 2000 in each channel. Also, we assumed $\gamma $ = 0.33 and E* = $2\times {10}^{6}$. The thermal expansion coefficient was considered equal to 10

^{−4}.

#### 2.2. Grid-Independence Study and Validation

_{max}, Table 2), and the maximum stress (Table 3) to obtain less than 1% variation. The traditional package of simulation ANSYS CFX and ANSYS STATIC STRUCTURAL software was used for this purpose. For the velocity-pressure coupling, a SIMPLE algorithm was used. Convergence had been acquired with the error magnitudes less than 10

^{−5}. The geometry and other conditions in the current study were considered similar to Cetkin et al. [35]. As could be seen in Figure 2, there was an excellent agreement for thermal stress, mechanical load, and a combination of both loads between present modeling and findings of Cetkin et al. [35].

## 3. Result and Discussion

#### 3.1. Thermal

_{max}throughout the disk. The latter means that the best design is obtained when the average temperature is near T

_{max}.

_{max}= 10

^{7}and P*

_{max}= 10

^{8}, respectively. For P*

_{max}= 10

^{8}, the peak temperature boosted as N increased when the volume fraction was 0%, 2%, and 4%. However, for P*

_{max}= 10

^{7}, the peak temperature was obtained at N = 14. In both studied P*

_{max}, the peak temperature decreased as the volume fraction of nanoparticles increased. For the same N, the difference between maximum temperatures was larger for the range of $\xi $ between 0% and 2% compared to that between 2% and 4%. For the studied cases, by increasing the volume fraction of nanoparticle from 0% to 2%, the peak temperature decreased from 14.5% to 30% (for P*

_{max}= 10

^{7}) and 19.6% to 28.9% (for P*

_{max}= 10

^{8}). Moreover, by nanoparticle volume fraction augmentation from 0% to 4%, the peak temperature decreased from 27.3% to 44% (for P*

_{max}= 10

^{7}) and from 33.2% to 44.7% (for P*

_{max}= 10

^{8}).

^{7}and at duct numbers less than 10, the most uniformity of temperature was ascribed to the distilled water, in comparison with other concentrations of nanoparticles. The same results could be expressed for duct numbers less than ten and P* = 10

^{8}. For duct numbers less than ten, the uniformity of temperature related to the concentration of 4% was less than 2% and 0%. However, for duct numbers greater than 10, the uniformity of concentration 4% was greater than the two other volume fractions.

#### 3.2. Mechanical Strength

_{max}= 10

^{7}and P*

_{max}= 10

^{8}, by increasing the volume fraction of nanoparticle from 0% to 2%, the peak thermal stress varied from 13.6% to 29% and 27.6% to 42.9%, respectively. Moreover, by increasing the volume fraction of nanoparticle from 0% to 4%, the peak thermal stress changed from 34.3% to 51% and 38% to 54%, respectively.

^{5}Pa) for various duct numbers. Figure 6a,b shows that the use of nanofluid reduced the peak stress in the segment, and that the peak stress in the disks is decreased when the nanofluid volume fraction is increased. Besides, the greater the N, the greater the peak stress. Increasing the initial pressure diminished the peak stress. The thermal loading caused equal stress at the three orients of the coordinate system. However, the mechanical loading when considering the Poisson coefficient caused stress in opposite directions. Thus, the curve showed a non-linear behavior. When P*

_{max}= 10

^{7}and P*

_{max}= 10

^{8}, by increasing the volume fraction of nanoparticle from 0% to 2%, the peak stress changed from 9.3% to 27% and 9% to 12.9%, respectively. Moreover, by raising the volume fraction of nanoparticle from 0% to 4%, the peak stress varied from 19% to 39% and 17% to 21%, respectively.

## 4. Conclusions

_{2}O flowing through a network of radial microchannels from the mechanical and thermal points of view was investigated. In all studied cases, the fluid volume of the cooling zone was assumed to be constant in the solid region, and the effect of using nanofluid in concentrations of 2 and 4 percent was investigated. The results indicated that CuO nanoparticles reduced the average of the maximum disk temperature, the maximum thermal stress, and the maximum stress, as well as the most significant deformation in the studied configuration. Increasing the number of microchannels would increase the maximum stress in the object, as well. Another remarkable point was that increasing the nanoparticles did not necessarily lead to a more uniform heat distribution in the disk.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Nomenclature | |

C_{p} | Specific heat capacity (J kg^{−1} K^{−1}) |

D | The thickness of the microchannel (m) |

De | Deformation (m) |

H | The height of the disk (m) |

L | Length (m) |

M | Mass flow rate (kg s^{−1}) |

N | Number of branching |

P | Pressure (N m^{−2}) |

Pr | Prandtl number |

q″ | Heat flux (W m^{−2}) |

T | Temperature (K) |

u, v, w | Velocity components (m s^{−1}) |

Greek symbols | |

A | Thermal expansion coefficient (K^{−1}) |

γ | Poisson’s ratio |

σ | Normal stress (Pa) |

µ | Dynamic viscosity (kg m^{−1} s^{−1}) |

τ | Shear stress (Pa) |

ξ | The volume fraction of nanoparticles |

ρ | Density (kg m^{−3}) |

φ | Shear strain (mm mm^{−1}) |

Subscripts | |

ave | Average |

bf | Base Fluid |

nf | Nano fluid |

s | Solid |

ref | Reference |

Superscripts | |

(*) | Dimensionless |

## References

- Bahiraei, M.; Salmi, H.K.; Safaei, M.R. Effect of employing a new biological nanofluid containing functionalized graphene nanoplatelets on thermal and hydraulic characteristics of a spiral heat exchanger. Energy Convers. Manag.
**2019**, 180, 72–82. [Google Scholar] [CrossRef] - Farzaneh, M.; Salimpour, M.R.; Tavakoli, M.R. Design of bifurcating microchannels with/without loops for cooling of square-shaped electronic components. Appl. Therm. Eng.
**2016**, 108, 581–595. [Google Scholar] [CrossRef] - Ghaedamini, H.; Salimpour, M.; Campo, A. Constructal design of reverting microchannels for convective cooling of a circular disc. Int. J. Therm. Sci.
**2011**, 50, 1051–1061. [Google Scholar] [CrossRef] - Haghighi, S.S.; Goshayeshi, H.; Safaei, M.R. Natural convection heat transfer enhancement in new designs of plate-fin based heat sinks. Int. J. Heat Mass Transf.
**2018**, 125, 640–647. [Google Scholar] [CrossRef] - Al-Rashed, A.A.A.; Hassen, W.; Kolsi, L.; Oztop, H.F.; Chamkha, A.J.; Abu-Hamdeh, N. Three-dimensional analysis of natural convection in nanofluid-filled parallelogrammic enclosure opened from top and heated with square heater. J. Cent. South Univ.
**2019**, 26, 1077–1088. [Google Scholar] [CrossRef] - Dogonchi, A.; Chamkha, A.J.; Hashemi-Tilehnoee, M.; Seyyedi, S.; Ganji, D. Effects of homogeneous-heterogeneous reactions and thermal radiation on magneto-hydrodynamic Cu-water nanofluid flow over an expanding flat plate with non-uniform heat source. J. Cent. South Univ.
**2019**, 26, 1161–1171. [Google Scholar] [CrossRef] - Dogonchi, A.S.; Chamkha, A.J.; Seyyedi, S.M.; Hashemi-Tilehnoee, M.; Ganji, D.D. Viscous Dissipation Impact on Free Convection Flow of Cu-water Nanofluid in a Circular Enclosure with Porosity Considering Internal Heat Source. J. Appl. Comput. Mech.
**2019**, 5, 717–726. [Google Scholar] - Alkasassbeh, M.; Omar, Z.; Mebarek-Oudina, F.; Raza, J.; Chamkha, A. Heat transfer study of convective fin with temperature-dependent internal heat generation by hybrid block method. Heat Transf.—Asian Res.
**2019**, 48, 1225–1244. [Google Scholar] [CrossRef] - Kumar, P.S.; Gireesha, B.; Mahanthesh, B.; Chamkha, A.J. Thermal analysis of nanofluid flow containing gyrotactic microorganisms in bioconvection and second-order slip with convective condition. J. Therm. Anal. Calorim.
**2019**, 136, 1947–1957. [Google Scholar] [CrossRef] - Izadi, M.; Pour, S.H.; Yasuri, A.K.; Chamkha, A.J. Mixed convection of a nanofluid in a three-dimensional channel. J. Therm. Anal. Calorim.
**2019**, 136, 2461–2475. [Google Scholar] [CrossRef] - Ghalambaz, M.; Tahmasebi, A.; Chamkha, A.; Wen, D. Conjugate local thermal non-equilibrium heat transfer in a cavity filled with a porous medium: Analysis of the element location. Int. J. Heat Mass Transf.
**2019**, 138, 941–960. [Google Scholar] [CrossRef] - Bahiraei, M.; Jamshidmofid, M.; Goodarzi, M. Efficacy of a hybrid nanofluid in a new microchannel heat sink equipped with both secondary channels and ribs. J. Mol. Liq.
**2019**, 273, 88–98. [Google Scholar] [CrossRef] - Dadsetani, R.; Sheikhzadeh, G.A.; Hajmohammadi, M.R.; Safaei, M.R. Introduce a novel configuration of microchannel andhigh-conductivity insertsfor cooling of disc-shaped electronic components. Int. J. Numer. Methods Heat Fluid Flow
**2019**. [Google Scholar] [CrossRef] - Dadsetani, R.; Salimpour, M.R.; Tavakoli, M.R.; Goodarzi, M.; Bandarra Filho, E.P. Thermal and Mechanical Design of Reverting Microchannels for Cooling Disk-Shaped Electronic Parts Using Constructal Theory. Available online: https://doi.org/10.1108/HFF-06-2019-0453 (accessed on 20 March 2020).
- Tuckerman, D.B.; Pease, R.F.W. High-performance heat sinking for VLSI. IEEE Electron Device Lett.
**1981**, 2, 126–129. [Google Scholar] [CrossRef] - Bejan, A. Street network theory of organization in nature. J. Adv. Transp.
**1996**, 30, 85–107. [Google Scholar] [CrossRef] - Chol, S.; Estman, J. Enhancing thermal conductivity of fluids with nanoparticles. Asme-Publ.-Fed
**1995**, 231, 99–106. [Google Scholar] - Dadsetani, R.; Sheikhzadeh, G.A.; Safaei, M.R.; Alnaqi, A.A.; Amiriyoon, A. Exergoeconomic optimization of liquefying cycle for noble gas argon. Heat Mass Transf.
**2018**, 55, 1995–2007. [Google Scholar] [CrossRef] - Selimefendigil, F.; Chamkha, A.J. Magnetohydrodynamics mixed convection in a lid-driven cavity having a corrugated bottom wall and filled with a non-Newtonian power-law fluid under the influence of an inclined magnetic field. J. Therm. Sci. Eng. Appl.
**2016**, 8, 021023. [Google Scholar] [CrossRef] - Selimefendigil, F.; Öztop, H.F. Effects of nanoparticle shape on slot-jet impingement cooling of a corrugated surface with nanofluids. J. Therm. Sci. Eng. Appl.
**2017**, 9, 021016. [Google Scholar] [CrossRef] - Sheikhzadeh, G.; Dastmalchi, M.; Khorasanizadeh, H. Effects of walls temperature variation on double diffusive natural convection of Al
_{2}O_{3}–water nanofluid in an enclosure. Heat Mass Transf.**2013**, 49, 1689–1700. [Google Scholar] [CrossRef] - Sheikhzadeh, G.; Nikfar, M. Aspect ratio effects of an adiabatic rectangular obstacle on natural convection and entropy generation of a nanofluid in an enclosure. J. Mech. Sci. Technol.
**2013**, 27, 3495–3504. [Google Scholar] [CrossRef] - Teimouri, H.; Sheikhzadeh, G.A.; Afrand, M.; Fakhari, M.M. Mixed convection in a rotating eccentric annulus containing nanofluid using bi-orthogonal grid types: A finite volume simulation. J. Mol. Liq.
**2017**, 227, 114–126. [Google Scholar] [CrossRef] - Bagherzadeh, S.A.; D’Orazio, A.; Karimipour, A.; Goodarzi, M.; Bach, Q.-V. A novel sensitivity analysis model of EANN for F-MWCNTs–Fe
_{3}O_{4}/EG nanofluid thermal conductivity: Outputs predicted analytically instead of numerically to more accuracy and less costs. Phys. A Stat. Mech. Its Appl.**2019**, 521, 406–415. [Google Scholar] [CrossRef] - Afridi, M.I.; Tlili, I.; Goodarzi, M.; Osman, M.; Khan, N.A. Irreversibility Analysis of Hybrid Nanofluid Flow over a Thin Needle with Effects of Energy Dissipation. Symmetry
**2019**, 11, 663. [Google Scholar] [CrossRef] [Green Version] - Nazari, M.A.; Ahmadi, M.H.; Sadeghzadeh, M.; Shafii, M.B.; Goodarzi, M. A review on application of nanofluid in various types of heat pipes. J. Cent. South Univ.
**2019**, 26, 1021–1041. [Google Scholar] [CrossRef] - Jiang, Y.; Bahrami, M.; Bagherzadeh, S.A.; Abdollahi, A.; Sulgani, M.T.; Karimipour, A.; Goodarzi, M.; Bach, Q.-V. Propose a new approach of fuzzy lookup table method to predict Al
_{2}O_{3}/deionized water nanofluid thermal conductivity based on achieved empirical data. Phys. A Stat. Mech. Its Appl.**2019**, 527, 121177. [Google Scholar] [CrossRef] - Nikkhah, Z.; Karimipour, A.; Safaei, M.R.; Forghani-Tehrani, P.; Goodarzi, M.; Dahari, M.; Wongwises, S. Forced convective heat transfer of water/functionalized multi-walled carbon nanotube nanofluids in a microchannel with oscillating heat flux and slip boundary condition. Int. Commun. Heat Mass Transf.
**2015**, 68, 69–77. [Google Scholar] [CrossRef] - Safaei, M.R.; Gooarzi, M.; Akbari, O.A.; Shadloo, M.S.; Dahari, M. Performance evaluation of nanofluids in an inclined ribbed microchannel for electronic cooling applications. In Electronics Cooling; IntechOpen: Zagreb, Croatia, 2016. [Google Scholar]
- Akbari, O.A.; Toghraie, D.; Karimipour, A.; Safaei, M.R.; Goodarzi, M.; Alipour, H.; Dahari, M. Investigation of rib’s height effect on heat transfer and flow parameters of laminar water–Al
_{2}O_{3}nanofluid in a rib-microchannel. Appl. Math. Comput.**2016**, 290, 135–153. [Google Scholar] - Nojoomizadeh, M.; D’Orazio, A.; Karimipour, A.; Afrand, M.; Goodarzi, M. Investigation of permeability effect on slip velocity and temperature jump boundary conditions for FMWNT/Water nanofluid flow and heat transfer inside a microchannel filled by a porous media. Phys. E Low-Dimens. Syst. Nanostruct.
**2018**, 97, 226–238. [Google Scholar] [CrossRef] - Menni, Y.; Azzi, A.; Chamkha, A. Enhancement of convective heat transfer in smooth air channels with wall-mounted obstacles in the flow path. J. Therm. Anal. Calorim.
**2019**, 135, 1951–1976. [Google Scholar] [CrossRef] - Cetkin, E.; Lorente, S.; Bejan, A. Vascularization for cooling and mechanical strength. Int. J. Heat Mass Transf.
**2011**, 54, 2774–2781. [Google Scholar] [CrossRef] - Gosselin, L.; Bejan, A. Constructal heat trees at micro and nanoscales. J. Appl. Phys.
**2004**, 96, 5852–5859. [Google Scholar] [CrossRef] - Çetkin, E.; Lorente, S.; Bejan, A. Vascularization for cooling and reduced thermal stresses. Int. J. Heat Mass Transf.
**2015**, 80, 858–864. [Google Scholar] [CrossRef] [Green Version] - Lubliner, J. Plasticity Theory; Courier Corporation: New York, NY, USA, 2008. [Google Scholar]

**Figure 2.**A comparison of the dimensionless maximum Von Mises stress, based on several microchannels, compared to Cetkin et al. [35] work.

**Figure 3.**(

**a**) T*

_{max}versus N for the different volume fraction of nanoparticles under P* = 10

^{7}. (

**b**) T*

_{max}versus N for the different volume fraction of nanoparticles P* = 10

^{8}.

**Figure 4.**(

**a**) Dimensionless average temperature versus the number of ducts at different $\xi $, under P* = 10

^{7}; (

**b**) Dimensionless average temperature versus the number of ducts at different under $\xi $, P* = 10

^{8}.

**Figure 5.**(

**a**) Peak thermal stress relative to the number of cooling channels for the varying volume fraction of CuO Nanoparticle under P*

_{max}= 10

^{7}. (

**b**) Peak thermal stress relative to the number of cooling channels for the varying volume fraction of CuO Nanoparticle P*

_{max}= 10

^{8}.

**Figure 6.**(

**a**) Peak stress versus the number of cooling channels for the different volume fraction of CuO nanoparticle under P* = 10

^{7}. (

**b**) Peak stress versus the number of cooling channels for the different volume fraction of CuO nanoparticle under P* = 10

^{8}.

**Figure 7.**Dimensionless peak total deformation versus the number of cooling channels for the varying volume fraction of CuO nanoparticles.

**Figure 9.**The contours of (

**a**) thermal strain, (

**b**) stress, and (

**c**) temperature under mechanical load.

Property | Silicon | Water |
---|---|---|

Density, ρ (kg/m^{3}) | 2330 | 997 |

Thermal conductivity, k (W/m K) | 125 | 0.6069 |

Specific heat capacity, C_{p} (J/kg K) | 700 | 4187.7 |

Dynamic viscosity, μ (Pa.s) | --- | 0.00089 |

Number of Elements | T_{max} (K) |
---|---|

879,314 | 435.9 |

2,169,346 | 429.8 |

3,256,892 | 425.6 |

5,142,765 | 424.3 |

Number of Elements | σ_{max} (Mpa) Variation |
---|---|

879,314 | 3.4281 |

2,169,346 | 3.3452 |

3,256,892 | 3.1252 |

5,142,765 | 3.1118 |

**Table 4.**Percentage change in $\Delta {T}_{max}^{*}$ by changing the number of ducts for $\xi =$ 2% and 4%.

$\mathbf{Variation}\text{}\mathbf{\Delta}{\mathit{T}}_{\mathbf{max}}^{*}$ | $\mathbf{\Delta}{\mathit{T}}_{\mathbf{max}}^{*\frac{\mathit{T}}{{\mathbf{max}}_{*|2\%-{\mathit{T}}_{\mathbf{max}}^{*|0\%}|}^{{\mathit{T}}_{\mathbf{max}}^{*|0\%}}}}$ | $\mathbf{\Delta}{\mathit{T}}_{\mathbf{max}}^{*\frac{\mathit{T}}{{\mathbf{max}}_{*|4\%-{\mathit{T}}_{\mathbf{max}}^{*|0\%}|}^{{\mathit{T}}_{\mathbf{max}}^{*|0\%}}}}$ | ||
---|---|---|---|---|

volume fraction of nanofluids | $\zeta =0\%to2\%$ | $\zeta =0\%to4\%$ | ||

N | P*_{max} = 10^{7} | P*_{max} = 10^{8} | P*_{max} = 10^{7} | P*_{max} = 10^{8} |

6 | $\Delta {T}_{\mathrm{max}}^{*}$ − 30.74% | $\Delta {T}_{\mathrm{max}}^{*}$ − 28.99% | $\Delta {T}_{\mathrm{max}}^{*}$ − 44.74% | $\Delta {T}_{\mathrm{max}}^{*}$ − 40.71% |

8 | $\Delta {T}_{\mathrm{max}}^{*}$ − 23.27% | $\Delta {T}_{\mathrm{max}}^{*}$ − 28.02% | $\Delta {T}_{\mathrm{max}}^{*}$ − 35.05% | $\Delta {T}_{\mathrm{max}}^{*}$ − 39.61% |

14 | $\Delta {T}_{\mathrm{max}}^{*}$ − 18.66% | $\Delta {T}_{\mathrm{max}}^{*}$ − 23.77% | $\Delta {T}_{\mathrm{max}}^{*}$ − 30.53% | $\Delta {T}_{\mathrm{max}}^{*}$ − 35.82% |

18 | $\Delta {T}_{\mathrm{max}}^{*}$ − 16.14% | $\Delta {T}_{\mathrm{max}}^{*}$ − 21.52% | $\Delta {T}_{\mathrm{max}}^{*}$ − 29.38% | $\Delta {T}_{\mathrm{max}}^{*}$ − 34.99% |

22 | $\Delta {T}_{\mathrm{max}}^{*}$ − 14.54% | $\Delta {T}_{\mathrm{max}}^{*}$ − 19.67% | $\Delta {T}_{\mathrm{max}}^{*}$ − 27.38% | $\Delta {T}_{\mathrm{max}}^{*}$ − 33.23% |

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**MDPI and ACS Style**

Dadsetani, R.; Sheikhzadeh, G.A.; Safaei, M.R.; Leon, A.S.; Goodarzi, M.
Cooling Enhancement and Stress Reduction Optimization of Disk-Shaped Electronic Components Using Nanofluids. *Symmetry* **2020**, *12*, 931.
https://doi.org/10.3390/sym12060931

**AMA Style**

Dadsetani R, Sheikhzadeh GA, Safaei MR, Leon AS, Goodarzi M.
Cooling Enhancement and Stress Reduction Optimization of Disk-Shaped Electronic Components Using Nanofluids. *Symmetry*. 2020; 12(6):931.
https://doi.org/10.3390/sym12060931

**Chicago/Turabian Style**

Dadsetani, Reza, Ghanbar Ali Sheikhzadeh, Mohammad Reza Safaei, Arturo S. Leon, and Marjan Goodarzi.
2020. "Cooling Enhancement and Stress Reduction Optimization of Disk-Shaped Electronic Components Using Nanofluids" *Symmetry* 12, no. 6: 931.
https://doi.org/10.3390/sym12060931