The unsteady magnetohydrodynamic (MHD) flow on a horizontal preamble surface with hybrid nanoparticles in the presence of the first order velocity and thermal slip conditions are investigated. Alumina (

_{2}

_{3}/

_{2}

The topic of research in various engineering and industrial fields, such as air-conditioning, microelectronic, and power generation is energy sustainability and the optimizations of thermal systems performance. For energy sustainability, an inventive variety in thermodynamics was important [

Recently, researchers introduced a new type of nanofluid, and they call it Hybrid nanofluid. Hybrid nanofluid helps the regular nanofluids to improve its thermal properties. It can be described as the hybrid nanofluid, which consists of two different kinds of nanoparticles together with new chemical and thermophysical properties that can improve the rate of heat transfer due to synergistic properties (see [_{2}O_{3}/water nanofluid. They found ranges of the existence of multiple solutions and also performed stability analysis of the solutions. Lund et al. [_{3}O_{4}/H_{2}O hybrid nanofluid over non-linear stretching and shrinking parameters in the presence of the joule heating. Two solutions were found, and an unstable solution was recognized by without doing stability analysis due to the existence of the singularity in the second solution. Further, Waini et al. [

The main objective of the current article is, therefore, to extend the works of [

Let us take the MHD unsteady flow of

The subject to boundary conditions [

where velocity of surface is

Further,

Properties | Hybrid nanofluid |
---|---|

Dynamic viscosity | |

Density | |

Thermal conductivity | |

Heat capacity |

Fluids | ^{3}) |
||
---|---|---|---|

Alumina ( |
3970 | 765 | 40 |

Copper (Cu) |
8933 |
385 |
400 |

We employ the following variable of similarity transformation to convert the

By applying

Along with the boundary conditions

The non-dimensional quantities are given as

The coefficient of skin friction

By employing

where

Merkin et al. [

By putting

Along with boundary conditions

According to Lund et al. [

where

Subject to the boundary conditions

According to Dero et al. [

The shooting method in Maple code with add of shootlib function has been employed to solve unsteady flow equations and bvp4c code in MATLAB software is used to solve the normalizing stability equations. The results of these codes are compared graphically and numerically with previously published works and found in the excellent agreements. In this study,

1st (2nd) Soln | 1st (2nd) Soln | |||

Lund et al. [ |
Present Study | Lund et al. [ |
Present | |

−1 | 1.608888 |
1.60889 |
5.22381 |
5.22382 |

−3 | 0.836978 |
0.83698 |
5.63167 |
5.63168 |

−5 | 0.775978 |
0.77598 |
7.63756 |
7.63757 |

−9 | −0.600211 |
−0.60021 |
8.24709639 |
8.24710 |

1st solution | 2nd solution | |

1 | 1.5034 | −1.3468 |

0.9 | 1.2073 | −1.1992 |

0.8 | 0.9606 | −0.9356 |

0.6 | 0.7422 | −0.7492 |

0.3 | 0.3136 | −0.4384 |

0.2 | 0.1430 | −0.1904 |

0.1718 | 0.0072 | −0.0003 |

The preparation of a hybrid nanofluid has been shown in the studies of [

We have water as a base fluid so Pr = 6.2 is kept as constant for the room temperature of 25°C. The graphical contrast with the sixth graph of [

It should be noted that at the pint of

Variations of

Effects of

It is gained that fluid velocity declines in the first solution as

In the current examination, the papers of [

_{6}H

_{9}N

_{a}O

_{7}and Ag- C

_{6}H

_{9}N

_{a}O

_{7}nanofluids flow over nonlinear shrinking surface

_{3}O

_{4}/H

_{2}O hybrid nanofluid with effect of viscous dissipation: dual similarity solutions

_{2}-Ag nanoparticles suspended in C

_{2}H

_{6}O

_{2}H

_{2}O hybrid base fluid with thermal radiation

_{2}O

_{3}/H

_{2}O nanofluid contains hybrid nanomaterials over a shrinking surface in the presence of viscous dissipation

_{2}O

_{3}/water nanofluid flow over a stretching sheet with effecting Lorentz force subject to Newtonian heating

_{6}H

_{9}NaO

_{7}and Ag− C

_{6}H

_{9}NaO

_{7}nanofluids with effect of viscous dissipation over stretching and shrinking surfaces using a single-phase model