# Electric field strength on MHD aluminum alloys (AA7075) nanofluid flow

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## Abstract

This work concerns with a numerical study on heat transfer by MHD aluminum alloys nanofluid (AA7075-water) flow over a nonlinear wall for extensible compactness of electric field. The steady governing momentum and energy equations are transformed to similarity equations for certain families of the controlling parameters. The transformed equations of momentum and thermal transport are solved by applying Runge–Kutta Fehlberg method with shooting technique. The three classical form of nanoparticle shapes are registered into report, i.e., sphere, cylinder and lamina and the heat transfer by natural convection of AA7075-water was studied. It is observed that the thermal and diffusive boundary layer thickness of AA7075-water is weaker in the presence of electric field, E1 = 0.2 as compared to E1 = 0.0. In the presence of electric field, temperature and concentration of lamina shape AA7075 particles hit a dominant role on AA7075-water nanofluid flow regime.

## Keywords

MHD AA7075-water Wall thickness Thermal radiation Similarity solution Viscous dissipation Nanoparticle shapes## 1 Introduction

Aluminum alloys are composed by melting, sintering (assemble of shaped parts utilizing metal particle that is melt together at exalted temperatures) or mechanical braiding. Durable collegial interruption to nanoparticles in distinct solvents is consistently entitled as “Nanofluids”. In this analysis the distinct attitudes to nanofluids technology are defined with an insistence on utilization in energy organization. Aluminum alloys have been very influential in aerospace manufacturing. In special, the aluminum alloys such as AA7072 and AA7075 are very fruitful in transport utilizations such as marine, aviation and automotive which are also recycled in construction of bicycle equipment, glider rock climbing equipment and aircrafts. An aluminum alloy is a chemical design where new materials are combined with pure aluminum with regard to upgrading its resources, basically to enhance its stability. Alloy desires the complete associating of aluminum with these other materials although the aluminum is in liquid-molten-form. Superficial Aluminum alloy AA7075 was cultivated over Japanese in 1942, for construction of air frame in Japanese navy [1].

The boundary layer flow of an electrical controlling nanofluid against a stretching sheet has been an alive field of analysis freshly. Nanofluid is a fluid composed by a reliable interruption of micro/nano-sized particles (nonmetallic/metallic/nanofibers) with a classic size < 100 nm in a typical base fluid (liquid). One of these advances is the inclusion of small-sized particles to the liquid. This method contributes to raise the thermal conductivity of the base fluid relatively twice and the convective heat transfer achievement. The flow due to stretching boundary has inclusive analysis in the exclusion mechanisms associates in metal and plastic industries. An aluminum alloy is a synthetic configuration where modern materials are combined with ideal aluminum with employing to improve its resources, really to boost its solidity and thermal conductivity. Aluminum alloys have been achieving a powerful issue in aerospace forming, [2, 3, 4]. Thermophoresis and Brownian motion effects on MHD bioconvection of nanofluid with nonlinear thermal radiation and quartic chemical reaction past an upper horizontal surface of a paraboloid of revolution with variable stream conditions are studied by [5, 6, 7].

Magnetohydrodynamic (MHD) nanofluid is an authentic significant in the field of engineering, science and technology. These fluids are more suitable in the optical grating, optical modulators, optical switches, tunable optical fiber filters, stretching of plastic materials, polymer industry and metallurgy. Nanotechnology investigation is repeatedly in the area of energetic scientific event due to an appreciable cast of useful utilizing in optical, medical and electrical fields and the nanoparticles thermal conductivity are more energetic as associated to the ideal fluids, as noticed in practical analysis was organized by [8, 9, 10]. The miserable of Lorentz force velocimetry is placed on appraisement of the Lorentz force that develops a convective fluid flow under the issue of an extensible magnetic field. Assigning to Faraday’s law, when a metal or convective fluid efforts over a magnetic field, eddy currents expanded there by electromotive energy in zones of controlling magnetic field gradient. Eddy current in its support admits convinced magnetic field assigning to Ampère’s law. The affiliation with eddy currents and total magnetic field allotments upgraded to Lorentz force that cracks the velocity and raises the temperature of the flow, [11, 12]. Nonlinearity in the stretching sheet surface system has been consigned to exponential and quadratic (power-law) models, [13, 14].

The flow of electrically controlling fluids such as liquid metals is efficiently impressed by applied magnetic and electric fields. The issue has significant industrial utilizations in nuclear technology, metallurgy and other fields. The electric conductivity, which regulates the heat transit in an indirect aspect, is one of the well-designed of the transport assets because it is nearly easy to define. It has been well-defined that nanofluid flow, thus convective heat transfer, could be formed if the electrically controlling fluid is exposed to either electric or magnetic or combined fields. Electric conducting energy film nanofluid flow across a wall has been an energetic field of research freshly. This technique commits to advance conductivity of the common fluid about double and the convective heat transfer fulfillment [15, 16, 17, 18, 19]. Nanofluid placed magnetohydrodynamic hits a crucial role in technology, science and engineering [20, 21, 22, 23, 24, 25]. Synthetic reaction impact is to estimate the reactor fulfillment of flexible stream conditions is investigated by [26, 27, 28, 29, 30, 31]. Particle concentration depreciates for energetic Brownian motion although it rises for more dynamic thermophoretic of the nanofluid which rises the thermal attitude of the fluid [29, 30, 31, 32]. A few experimental based articles have been investigated with aspect of hybrid nanofluids, [33, 34, 35, 36, 37, 38, 39].

The intent at this effort is delighted by the intimate survey and strong accessible industrial and engineering applications. The instant review introduces such distinct thickness on a nonlinear wall on electric MHD boundary layer AA7075-water flow in biography. This formable thickness nonlinear stretching sheet has energetic message on mechanical, civil, marine, aeronautical structure and designs. Confirmed conditions of the current work are analyzed and authorized graphically to real amplitudes convoluted within it and the prompt attainments are associated with the suitable literature.

## 2 Mathematical formulation

Maxwell design [40] was cultivated to assign the dynamic thermal or electrical conductivity of liquid–solid suspensions. Let \(\sigma_{f}\) and \(\sigma_{s}\)—fluid and nanoparticle electrical conductivity, \(k_{nf}\)—nanofluid effective thermal conductivity. Rosseland’s dissipation for the radiative heat flux, \(q_{r} = - \frac{{4\sigma^{*} \partial T^{4} }}{{3k^{*} \partial y}}\) (Magyari and Pantokratoras [41]), \(\sigma^{*}\)—Stephen–Boltzmann constant, the thermal field by Taylor’s series, \(T^{4} + 3T_{\infty }^{4} = 4T_{\infty }^{3} T\).

It is a fundamental law of thermodynamics that the Nusselt and Shear wood number can be negative, since it is defined as the dimensionless temperature and concentration gradient at the wall. The slope may be negative or positive, depending on the direction of heat flux. The skin friction coefficient based on the wall sheat stress magnitude has to be positive.

## 3 Results and discussions

In this scheme, nanoparticle shapes (sphere, cylinder and lamina) on MHD AA7075-water flow up a nonlinear devoted stretching from the cause of electric field in thermal radiation have been analyzed numerically. The system for Eqs. (9)–(11) are not be recognized exactly and algorithmic realization acceptable to the boundary conditions (12) are approved the very appreciable conducting software Maple 18. This software networks a fourth or fifth order Runge–Kutta Fehlberg technique with shooting system as persistent to execute the boundary value problems numerically proceeding the classification model. The Prandtl number range of the nanofluid is assumed as \(6.2\;\; \le \;\;\Pr \;\; \le \;\;10\;.4\).

### 3.1 Affirmation

Thermal and physical asserts of fluid and particles

Thermophysical properties | H | AA7075 |
---|---|---|

\(\rho\) | 997.1 | 2810 |

\(c_{p}\) | 4179 | 960 |

\(k\) | 0.6129 | 173 |

\(\sigma\) | 0.05 | 26.77 \(\times 10^{6}\) |

Comparison of \(- f^{\prime\prime}(0)\) when \(E1 = M = 0\)

Parameter | Fang et al. [42] | Daniel et al. [43] | Present result | Error |
---|---|---|---|---|

\(n,\alpha = 0.25\) | ||||

10.0 | 1.1433 | 1.143316 | 1.143308 | 8.1E−06 |

9.0 | 1.1404 | 1.140388 | 1.140372 | 3.2E−06 |

7.0 | 1.1323 | 1.132281 | 1.132268 | 1.3E−06 |

5.0 | 1.1186 | 1.118587 | 1.118575 | 1.2E−06 |

3.0 | 1.0905 | 1.090490 | 1.090479 | 1.1E−06 |

1.0 | 1.0000 | 1.000001 | 1.000000 | 1.0E−06 |

### 3.2 Magnetic effects on temperature and concentration profiles, Fig. 3

### 3.3 Thermal radiation energy effects on temperature and concentration profiles, Fig. 4

### 3.4 Non-linear wall strength on temperature and concentration profiles, Fig. 5

### 3.5 Nanoparticle volume fraction on temperature and concentration profiles, Fig. 6

### 3.6 Thermophoresis particle deposition on temperature and concentration profiles, Fig. 7

### 3.7 Nanoparticle volume fraction on skin friction, rate of heat and mass transfer, Table 3

Nanoparticle volume fraction and shape on \(f^{\prime\prime}(0)\), \(- \theta^{\prime}(0)\) and \(- \phi^{\prime}(0)\) with or without electric field (E1 = 0.2) in the presence of AA7075-water

\(\zeta\) | \(f^{\prime\prime}(0)\) | \(- \theta^{\prime}(0)\) | \(- \phi^{\prime}(0)\) | AA7075 shapes |
---|---|---|---|---|

0.05 | − 1.572663 | | 2.408874 | Sphere shape |

0.1 | − 1.511998 | 0.460948 | 2.534099 | |

0.2 | − 1.361190 | 0.360827 | 2.817025 | |

0.05 | − 1.572663 | 0.474963 | 2.423611 | Cylindrical shape |

0.1 | − 1.511998 | 0.390063 | 2.555679 | |

0.2 | − 1.361190 | 0.276281 | | |

0.05 | − 1.572663 | 0.383708 | | Lamina shape |

0.1 | − 1.511998 | 0.281016 | 2.584528 | |

0.2 | − 1.361190 | | 2.838250 |

## 4 Conclusion

Impact of electric field strength on AA7075-water convective flow through a non-linear stretching wall is presented using Runge–Kutta Felhberg method with shooting technique, MAPLE 18. Effects of magnetic strength, thermal radiation energy, thermophoresis particle deposition, particle shapes and volume fraction on AA7075-water nanofluid behaviour are taken into account in the subsistence of electric field. It is interesting to note that the thermal and diffusive thermal boundary layer thickness of lamina shaped AA7075-water, \(E_{1} = 0.2\) is more significant as compared to \(E_{1} = 0.0\) because of the combined effects of electric and magnetic strength with increase of all parameters strength. In the presence of electric field, it is noted that the temperature and concentration of AA7075-water increase with increase of all parameters strength while it decreases with rise of magnetic strength. Heat/mass transfer rate of sphere/cylindrical shaped particles on AA7075–water is stronger whereas the lamina shaped particles on AA7075-water is weaker as related to other shapes with rise of nanoparticle volume fraction.

## Notes

### Acknowledgement

Authors thanks to UTHM and Higher Education Ministry, Malaysia for their monetary assistance, (Geran Penyelidikan Kontrak/U687/2016-2018).

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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