# Impacts of gold nanoparticles on MHD mixed convection Poiseuille flow of nanofluid passing through a porous medium in the presence of thermal radiation, thermal diffusion and chemical reaction

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## Abstract

Impacts of gold nanoparticles on MHD Poiseuille flow of nanofluid in a porous medium are studied. Mixed convection is induced due to external pressure gradient and buoyancy force. Additional effects of thermal radiation, chemical reaction and thermal diffusion are also considered. Gold nanoparticles of cylindrical shape are considered in kerosene oil taken as conventional base fluid. However, for comparison, four other types of nanoparticles (silver, copper, alumina and magnetite) are also considered. The problem is modeled in terms of partial differential equations with suitable boundary conditions and then computed by perturbation technique. Exact expressions for velocity and temperature are obtained. Graphical results are mapped in order to tackle the physics of the embedded parameters. This study mainly focuses on gold nanoparticles; however, for the sake of comparison, four other types of nanoparticles namely silver, copper, alumina and magnetite are analyzed for the heat transfer rate. The obtained results show that metals have higher rate of heat transfer than metal oxides. Gold nanoparticles have the highest rate of heat transfer followed by alumina and magnetite. Porosity and magnetic field have opposite effects on velocity.

## Keywords

Gold nanoparticles Mixed convection Kerosene oil Chemical reaction Heat and mass transfer MHD Porous medium Heat transfer rate## 1 Introduction

However, gold nanoparticles are rarely used for studying heat transfer rate due to mixed convection. Although mixed convection occurs in many industrial and technological processes such as chemical processing, food processing industry, nuclear reactors, electronics cooling technology and thermal insulations, the studies on gold nanoparticles in this direction are scarce. However, for other types of nanoparticles, enough literature has been developed. For example, Abu-Nada and Chamkha [16] studied mixed convection flow of a nanofluid. They considered lid-driven cavity along with wavy wall. Ajmera [17] investigated experimentally mixed convection in multiple ventilated enclosures with discrete heat source. [18, 19, 20, 21, 22, 23, 24, 25] also reported similar studies.

In nanofluids, chemical reaction of nanoparticles with base fluid is required to take place in such problems to absorb the suspended particles within the base fluid. Various authors studied heat and mass transfer problems with chemical reaction. Among them, Kandasamy [26] studied impact of chemical reaction on Cu, \({\text{Al}}_{2} {\text{O}}_{3}\) and SWCNTs-nanofluid flow under slip conditions. Pal and Biswas [27] and Odat and Azab [28] used perturbation analysis to study magneto-hydrodynamics flows with chemical reactions.

In the present work, we have chosen gold nanoparticles due to its high thermal conductivity and adjustable surface chemistry. More exactly, this work is concentrated on MHD mixed convection Poiseuille flow of fluid with gold (AuNP) nanoparticles passing taking thermal radiation, thermal diffusion and chemical reaction into account with porosity. The problem is solved analytically impacts of cylindrical shape gold nanoparticles on MHD mixed convection Poiseuille flow of nanofluid passing through a porous medium under the influence of thermal radiation, thermal diffusion and chemical reaction. This research mainly focuses on gold nanoparticles; however, for the sake of comparison, four other types of nanoparticles namely silver, copper, alumina and magnetite are analyzed for the heat transfer rate. Analytical solutions are computed using the perturbation technique and discussed in various plots and tables. Although many researchers have done experimental work on gold nanoparticles, very less work has been done on this topic analytically.

## 2 Formulation and solution of the problem

Fluid velocity is in the *x*-direction, denoted by \(u = u\left( {y,\,t} \right),\) \(T = T\left( {y,\,t} \right)\,\) is the temperature, \(\rho_{\text{nf}}\) signifies the density, the dynamic viscosity is symbolized by \(\mu_{\text{nf}}\), \(\sigma_{\text{nf}}\) is the electrical conductivity, the permeability of the porous medium is represented by \(k_{1} > 0\), \(\left( {\rho \beta } \right)_{\text{nf}}\) expresses the coefficient of thermal expansion, \(g\) is the gravitational acceleration, \(\;\left( {\rho c_{\rm p} } \right)_{\text{nf}}\) is the heat capacitance, the thermal conductivity \(k_{\text{nf}}\) of nanofluids, \(k_{\text{r}}\) is chemical reaction parameter, \(\alpha_{0}^{{}}\) is the radiation absorption coefficient and \(D_{\text{nf}}\) is thermal diffusivity. The subscript \({\text{nf}}\) corresponds to nanofluid. The pulsatile pressure gradient used by Hayat et al. [30] defined as \(- \partial p/\partial x = \lambda_{0} + \lambda_{1} \varepsilon \exp \left( {i\omega t} \right),\,\) in the flow direction is used, where \(\lambda_{0}\) and \(\lambda_{1}\) are constant and \(\omega\) signifies the frequency of oscillation.

Empirical shape factors

Model | Cylinder |
---|---|

| 13.5 |

| 904.4 |

Thermophysical properties of kerosene oil and nanoparticles

Material | Symbol | \(\rho\) (kg/m | \(c_{\text{p}} ({\text{kg}}^{ - 1} \,{\text{k}}^{ - 1} )\) | \(k\,({\text{W}}/{\text{mk}})\) |
---|---|---|---|---|

Gold | Au | 19,300 | 129 | 318 |

Kerosene oil | – | 783 | 2090 | 0.145 |

Silver | Ag | 10,500 | 235 | 429 |

Magnetite | \({\text{Fe}}_{3} {\text{O}}_{4}\) | 5180 | 670 | 9.7 |

Alumina | \({\text{Al}}_{2} {\text{O}}_{3}\) | 3970 | 765 | 40 |

Copper | \({\text{Cu}}\) | 8933 | 385 | 401 |

Sphericity \(\varPsi\) for various shapes nanoparticles

Model | Cylinder |
---|---|

\(\varPsi\) | 0.62 |

## 3 Skin Friction and Nusselt Number

## 4 Graphical results and discussion

Heat and mass transfer flow of nanofluids inside a channel is analyzed with radiation impact. Mixed convection MHD, chemical reaction, thermal diffusion with saturated porous medium is taken into account. Cylindrical shaped \({\text{AuNPs}}\) were chosen with kerosene oil as conventional base fluid. Rate of heat transfer is evaluated for various types of nanoparticles, and comparison is made among them. This study mainly focuses on cylindrical shape gold nanoparticles; however, for the sake of comparison, four other types of nanoparticles namely silver, copper, alumina and magnetite are analyzed for the heat transfer rate. Analytical solutions are computed using the perturbation technique and discussed in various plots and tables. The graphical results for velocity (magnetic parameter \(M\), permeability parameter \(k\), volume fraction \(\phi\) and radiation parameter \(N\)), temperature (for \(\phi\) and \(N\)) and concentration profile (for \(\phi\), \(N\), Soret number \(Sr\) and Reynolds number \(Re\)) are plotted.

Influence of volume fraction on heat transfer rate for various kinds of nanoparticles at *N* = 1.5

Volume fraction \(\phi\) | Gold (Au) | Copper (Cu) | Silver (Ag) | Magnetite \(({\text{Fe}}_{3} {\text{O}}_{4} )\) | Alumina \(({\text{Al}}_{2} {\text{O}}_{3} )\) |
---|---|---|---|---|---|

0 | 0.106 | 0.106 | 0.106 | 0.106 | 0.106 |

0.01 | 0.156 | 0.156 | 0.156 | 0.153 | 0.155 |

0.02 | 0.201 | 0.201 | 0.201 | 0.195 | 0.2 |

0.03 | 0.243 | 0.243 | 0.243 | 0.235 | 0.241 |

0.04 | 0.28 | 0.28 | 0.28 | 0.271 | 0.278 |

## 5 Conclusions

- 1.
Velocity of nanofluid minimizes with maximization of volume fraction of \({\text{AuNP}}\) owing to amplifying viscosity and thermal conductivity.

- 2.
The drag force increases with increase in magnetic parameter, which slows down velocity of \({\text{AuNP}}\) nanofluid.

- 3.
The velocity of \({\text{AuNP}}\) nanofluid also suppresses with maximizing of Reynolds number.

- 4.
Concentration decreases with maximizing chemical reaction parameter due to emission of heat during chemical reaction.

- 5.
Concentration profile increases with maximizing volume fraction of \({\text{AuNP}}\) and decreases with increase in radiation parameter.

- 6.
Nanofluids with gold nanoparticles have higher rate of heat transfer as compared to metal oxides (alumina and magnetite) due to its high thermal conductivity.

- 7.
Alumina nanofluid has higher heat transfer rate as compared to magnetite-based nanofluid.

- 8.
Heat transfer rate of different types of nanoparticles increases with maximizing volume fraction due to an increase in their thermal conductivities.

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