# Scaling for unsteady thermo-magnetic convection boundary layer of paramagnetic fluids of Pr>1 in micro-gravity conditions

Bednarz, Tomasz P., Lin, Wenxian, Patterson, John C., Lei, Chengwang, & Armfield, Steven W.
(2009)
Scaling for unsteady thermo-magnetic convection boundary layer of paramagnetic fluids of Pr>1 in micro-gravity conditions.
*International Journal of Heat and Fluid Flow*, *30*(6), pp. 1157-1170.

## Abstract

This work incorporates scaling analysis to characterise unsteady boundary-layer development for thermo-magnetic convection of paramagnetic fluids with Prandtl numbers (Pr ) greater than one. Under consideration is a square cavity with a quiescent isothermal, Newtonian fluid placed in a micro-gravity condition (g≈0g≈0), and under a uniform vertical gradient magnetic field. A distinct magnetic convection boundary layer is produced by the sudden imposition of a higher temperature on the left-hand side vertical sidewall due to the effect of the magnetic body force generated on the paramagnetic fluid. This magnetic force is proportional to the magnetic susceptibility and the gradient of the square of the magnetic induction. According to Curie’s law, the magnetic susceptibility of a paramagnetic fluid is inversely proportional to the absolute temperature. Thermal convection of a paramagnetic fluid can therefore take place even in zero-gravity environments as a direct consequence of temperature differences occurring within the fluid placed within a magnetic field gradient.

Scaling predictions presented here are verified by numerical simulations It is shown that the transient flow behaviour of the resulting boundary layer can be described by three stages: a start-up stage, a transitional stage and a steady state. Special attention in this work is paid to the dependency of the flow development upon the Prandtl number, varied over the range of 5–100, thus representing various fluids. Also, the effect of the magnetic momentum parameter, m, and the quantity γRa, upon the flow development obtained in numerical simulations confirms the accuracy of new scaling predictions for paramagnetic fluids.

Impact and interest:

**Citation counts** are sourced monthly from **Scopus** and **Web of Science®** citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the **Google Scholar™** indexing service can be viewed at the linked Google Scholar™ search.

ID Code: | 99657 |
---|---|

Item Type: | Journal Article |

Refereed: | Yes |

Keywords: | scaling analysis, magnetic convection, applied computational science |

DOI: | 10.1016/j.ijheatfluidflow.2009.08.003 |

ISSN: | 0142-727X |

Divisions: | Current > Research Centres > ARC Centre of Excellence for Mathematical & Statistical Frontiers (ACEMS) Past > QUT Faculties & Divisions > Faculty of Science and Technology Current > Institutes > Institute for Future Environments Current > Schools > School of Mathematical Sciences |

Copyright Owner: | Crown Copyright 2009 Published by Elsevier Inc. |

Deposited On: | 04 Oct 2016 04:09 |

Last Modified: | 09 Oct 2016 21:59 |

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page