# Concrete Based Jeffrey Nanofluid Containing Zinc Oxide Nanostructures: Application in Cement Industry

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## Abstract

**:**

## 1. Introduction

_{3}has added to the cement the rate of heat development enhanced rapidly. In a research article, Bahamani et al. [14] stated that when SiO

_{2}nanoparticles are added to cement-treated soil for stabilization, the compressive strength is improved by 80%. Shekari and Razzaghi [15], investigated the durability and strengths of concrete in their analysis. The results are interesting and important because, both the mechanical properties and durability are checked, and they concluded that these properties are improved by adding nanoparticles in concrete. Moreover, the aluminum nanoparticles are the most effective one amongst all the tested nanoparticles in this study. The influence of the size of silicon oxide nanoparticles on the double blended concrete was analyzed by Givi et al. [16] through an experiment. The results showed that the concrete with small size of nanoparticles (15 nm) was harder than the concrete with large size of nanoparticles (80 nm). Many scholars have studied the mechanical properties of cement mortars, including nano- $F{e}_{2}{O}_{3}$ and nano- $Si{O}_{2}$ [17,18,19,20,21]. In other sectors the applications of nanofluids are also studied by various researchers. Goodarzi et al. [22] investigated the two phase flow of nanofluid in a shallow cavity. Arasteh et al. [23] have used the nanofluids to enhance the working capacity of double-layered heat. Yousefzadeh et al. [24] have presented a numerical modelling and investigation for the flow of nanofluid with different heat transfer areas. They have used the solid silver nanoparticles having volume fraction 0%, 2%, and 4% in the base fluids to enhance the heat transfer. Ahmadi et al. [25] have used various machine learning methods including MPR (Multivariable Polynomial Regression), MARS (Multivariate Adaptive Regression Splines), ANN-MLP (Artificial Neural Network- Multilayer Perceptron), and GMDH (Group Method of Data Handling), for modeling the dynamic viscosity of CuO/water nanofluid based on the temperature, concentration, and size of nanostructures. They have concluded that the concentration of the nanoparticles has the highest importance, while the size has least importance. The heat transfer in pseudo-plastic non-Newtonian nanofluid with suction and injection was studied by Maleki et al. [26]. They have claimed that in the case of injection the heat transfer reduces in non-Newtonian nanofluids. Safaei et al. [27] numerically studied flow of nanofluid with carbon nanotubes over a forward-facing step. Their results show that heat transfer is remarkably affected by the volume fraction and Reynolds number. Gholamalizadeh et al. [28] studied the effects of forced convection on the flow of nanofluids and have mentioned that porosity does not bring any change in the velocity of nanofluid in this case. Jalali et al. [29] investigated the flow of oil based nanofluid with MWCNTs (Multiwall Carbon Nanotubes) nanoparticles. Other related studies can be found in [30,31,32,33,34,35] and the references therein.

_{2}O

_{4}nanoparticles have been taken, in their research, to analyze the compressive strength of the cement paste. This research article revealed that the strength of is attained after 42 days. After that Taylor-Lenge et al. [42], studied to improve the reactivity of metakaolin cement blends using zinc oxide. They have mentioned that ZnO nanoparticles behave like a delayed accelerator for cement slurry. To improve the biological and mechanical properties of dental cement, Nguyen et al. [43] considered the ZnO nanoparticles. They have mentioned that besides the anti-bacterial characteristics of ZnO nanoparticles also significantly, enhanced the compressive strength and tensile strength of the cement. Gowda et al. [44], studied the influence of nano-zinc and nano-silica on the compressive strength of the mortar cement. Their results show that the strength of the cement is improved when nano-zinc and nano-silica are dispersed in the cement slurry.

## 2. Mathematical Modelling

## 3. Generalization of the Classical Model

## 4. The Solution of the Heat and Mass Equations

## 5. Velocity Profile Calculations

## 6. Skin Friction, Rate of Heat Transfer, and Rate of Mass Transfer

## 7. Parametric Study

## 8. Conclusions

- ❖
- The velocity profile shows that by increasing the volume fraction of the nanoparticles, the fluid becomes more viscous and as a result, the concrete will be denser and hence will be stronger.
- ❖
- The concrete will be stronger for lesser values of $Gr$, as the lesser values of $Gr$ reduces the velocity profile, because of the higher viscous forces and weaker thermal forces.
- ❖
- Also, suspended nanoparticles in cement-concrete skin friction increase 15.26% which shows that increasing the binding strength of cement slurry and aging resistance.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${\mathrm{R}}_{\mathrm{a}}=\frac{\rho d{U}_{0}}{\mu}$ | Reynolds number | ${\lambda}_{2}$ | Jeffrey fluid parameter |

$Pe=\frac{{(\rho {c}_{p})}_{f}d{U}_{0}}{{k}_{f}}$ | Peclet number | ${\mu}_{nf}$ | dynamic viscosity |

$\lambda =\frac{{\lambda}_{2}{U}_{0}}{d}$ | Jeffrey fluid parameter | ${\sigma}_{nf}$ | electrical conductivity |

$Sc=\frac{d{U}_{0}}{{D}_{f}}$ | Schmidt number | ${B}_{0}$ | applied magnetic field |

$\mathrm{M}=\frac{\sigma {B}_{0}{}^{2}d}{\rho {U}_{0}}$ | Hartmann number | $g$ | gravitational acceleration |

$Gr=\frac{g{\beta}_{T}d({T}_{w}-{T}_{0})}{{U}_{0}{}^{2}}$ | thermal Grashof number | ${\left({\beta}_{T}\right)}_{nf}$ | thermal expansion |

$Gm=\frac{g{\beta}_{C}d({C}_{w}-{C}_{0})}{{U}_{0}{}^{2}}$ | mass Grashof number | ${\left({\beta}_{C}\right)}_{nf}$ | mass expansion |

${\rho}_{nf}$ | density |

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**Figure 2.**Variation in velocity profile for different values of $\varphi $ when $Gr=5,\alpha =0.2,\mathrm{P}e=0.2,M=0.3,\tau =1,\lambda =1.5,{\lambda}_{1}=0.5.$

**Figure 3.**Variation in temperature profile for different values of $\varphi $ when $Gr=5,\alpha =0.2,\mathrm{P}e=0.2,M=0.3,\tau =1,\lambda =1.5,{\lambda}_{1}=0.5.$

**Figure 4.**Variation in Nusselt number for different values of $\varphi $ when $Gr=5,\alpha =0.2,\mathrm{P}e=0.2,M=0.3,\tau =1,\lambda =1.5,{\lambda}_{1}=0.5.$

**Figure 5.**Variation in skin friction for different values of $\varphi $ when $Gr=5,\alpha =0.2,\mathrm{P}e=0.2,M=0.3,\tau =1,\lambda =1.5,{\lambda}_{1}=0.5.$

**Figure 6.**Variation in velocity profile for different values of $\alpha $ when $Gr=5,\varphi =0.02,\mathrm{P}e=0.2,M=0.3,\tau =1,\lambda =1.5,{\lambda}_{1}=0.5.$

**Figure 7.**Variation in temperature profile for different values of $\alpha $ when $Gr=5,\varphi =0.02,\mathrm{P}e=0.2,M=0.3,\tau =1,\lambda =1.5,{\lambda}_{1}=0.5.$

**Figure 8.**Variation in velocity profile for different values of ${\lambda}_{1}$ when $Gr=5,\alpha =0.2,\mathrm{P}e=0.2,M=0.3,\tau =1,\varphi =0.02,\lambda =1.5.$

**Figure 9.**Variation in velocity profile for different values of $\lambda $ when $Gr=5,\alpha =0.2,\mathrm{P}e=0.2,M=0.3,\tau =1,\varphi =0.02,{\lambda}_{1}=0.5.$

**Figure 10.**Variation in velocity profile for different values of $Gr$ when ${\lambda}_{1}=0.5,\alpha =0.2,\mathrm{P}e=0.2,M=0.3,\tau =1,\varphi =0.02,\lambda =1.5.$

**Figure 11.**Variation in velocity profile for different values of $Gm$ when ${\lambda}_{1}=0.5,\alpha =0.2,\mathrm{P}e=0.2,M=0.3,\tau =1,\varphi =0.02,\lambda =1.5.$

**Figure 12.**Variation in velocity profile for different values of $M$ when ${\lambda}_{1}=0.5,\alpha =0.2,\mathrm{P}e=0.2,Gr=Gm=5,\tau =1,\varphi =0.02,\lambda =1.5.$

**Table 1.**The values of involved terms in the Zakian method for Laplace inverse [65].

$\mathit{j}$ | ${\mathit{K}}_{\mathit{j}}$ | ${\mathit{\alpha}}_{\mathit{j}}$ |
---|---|---|

1 | $12.83767675+i1.666063445$ | $-36902.0821+i196990.4257$ |

2 | $12.22613209+i5.012718792$ | $61277.02524-i95408.62551$ |

3 | $10.93430308+i8.409673116$ | $-28916.56288+i18169.18531$ |

4 | $8.776434715+i11.92185389$ | $4655.361138-i1.901528642$ |

5 | $5.225453361+i15.72952905$ | $-118.7414011-i141.3036911$ |

Properties | Concrete | $\mathit{Z}\mathit{n}\mathit{O}$ |
---|---|---|

$\rho (\mathrm{kg}{\mathrm{m}}^{-3})$ | 2300 | 5.61 × 10^{3} |

$k({\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1})$ | 1.160 | 1.046 |

${C}_{p}({\mathrm{kg}}^{-1}{\mathrm{K}}^{-1})$ | 41.086 | 0.880 |

$\beta \times {10}^{-5}({\mathrm{K}}^{-1})$ | 1.57 | 1.25 |

$\mathit{\varphi}$ | $\mathit{\alpha}$ | $\mathit{\lambda}$ | ${\mathit{\lambda}}_{\mathbf{1}}$ | $\mathit{\tau}$ | ${\mathit{C}}_{\mathit{f}}$ | Enhancement (%) |
---|---|---|---|---|---|---|

0.00 | 0.2 | 0.5 | 0.5 | 2 | 0.596 | |

0.01 | 0.2 | 0.5 | 0.5 | 2 | 0.645 | 8.221% |

0.02 | 0.2 | 0.5 | 0.5 | 2 | 0.669 | 12.24% |

0.03 | 0.2 | 0.5 | 0.5 | 2 | 0.681 | 14.26% |

0.04 | 0.2 | 0.5 | 0.5 | 2 | 0.687 | 15.26% |

$\mathit{\varphi}$ | $\mathit{\tau}$ | $\mathit{\alpha}$ | $\mathit{N}\mathit{u}$ | Enhancement (%) |
---|---|---|---|---|

0.00 | 2 | 0.2 | 0.603 | |

0.01 | 2 | 0.2 | 0.675 | 11.94% |

0.02 | 2 | 0.2 | 0.758 | 25.70% |

0.03 | 2 | 0.2 | 0.854 | 41.62% |

0.04 | 2 | 0.2 | 0.969 | 60.69% |

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**MDPI and ACS Style**

Sheikh, N.A.; Chuan Ching, D.L.; Khan, I.; Ahmad, A.; Ammad, S.
Concrete Based Jeffrey Nanofluid Containing Zinc Oxide Nanostructures: Application in Cement Industry. *Symmetry* **2020**, *12*, 1037.
https://doi.org/10.3390/sym12061037

**AMA Style**

Sheikh NA, Chuan Ching DL, Khan I, Ahmad A, Ammad S.
Concrete Based Jeffrey Nanofluid Containing Zinc Oxide Nanostructures: Application in Cement Industry. *Symmetry*. 2020; 12(6):1037.
https://doi.org/10.3390/sym12061037

**Chicago/Turabian Style**

Sheikh, Nadeem Ahmad, Dennis Ling Chuan Ching, Ilyas Khan, Afnan Ahmad, and Syed Ammad.
2020. "Concrete Based Jeffrey Nanofluid Containing Zinc Oxide Nanostructures: Application in Cement Industry" *Symmetry* 12, no. 6: 1037.
https://doi.org/10.3390/sym12061037