### Abstract

Purpose - Unsteady natural convection of water-based nanofluid within a right-angle trapezoidal cavity under the influence of a uniform inclined magnetic field using the mathematical nanofluid model proposed by Buongiorno is presented. The paper aims to discuss these issues. Design/methodology/approach - The left vertical and right inclined walls of the enclosure are kept at constant but different temperatures whereas the top and bottom horizontal walls are adiabatic. All boundaries are assumed to be impermeable to the base fluid and to nanoparticles. In order to study the behavior of the nanofluid, a non-homogeneous Buongiorno's mathematical model is taken into account. The physical problems are represented mathematically by a set of partial differential equations along with the corresponding boundary conditions. By using an implicit finite difference scheme the dimensionless governing equations are numerically solved. Findings - The governing parameters are the Rayleigh, Hartmann and Lewis numbers along with the inclination angle of the magnetic field relative to the gravity vector, the aspect ratio and the dimensionless time. The effects of these parameters on the average Nusselt number along the hot wall, as well as on the developments of streamlines, isotherms and isoconcentrations are analyzed. The results show that key parameters have substantial effects on the flow, heat and mass transfer characteristics. Originality/value - The present results are new and original for the heat transfer and fluid flow in a right-angle trapezoidal cavity under the influence of a uniform inclined magnetic field using the mathematical nanofluid model proposed by Buongiorno. The results would benefit scientists and engineers to become familiar with the flow behavior of such nanofluids, and the way to predict the properties of this flow for possibility of using nanofluids in advanced nuclear systems, in industrial sectors including transportation, power generation, chemical sectors, ventilation, air-conditioning, etc.

Original language | English |
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Pages (from-to) | 1924-1946 |

Number of pages | 23 |

Journal | International Journal of Numerical Methods for Heat and Fluid Flow |

Volume | 25 |

Issue number | 8 |

DOIs | |

Publication status | Published - 1 Jan 2015 |

### Keywords

- Brownian motion
- Magnetic field
- Nanofluid
- Natural convection
- Thermophoresis
- Trapezoidal cavity

### ASJC Scopus subject areas

- Mechanics of Materials
- Mechanical Engineering
- Computer Science Applications
- Applied Mathematics

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## Cite this

*International Journal of Numerical Methods for Heat and Fluid Flow*,

*25*(8), 1924-1946. https://doi.org/10.1108/HFF-07-2014-0236