### Abstract

The onset of Marangoni convection in a horizontal fluid layer with a free surface overlying a solid layer heated from below is studied. Problem is focused on the effect of the solid layer depth or its conductivity. The viscosity group, R_{v}, Biot number, Bi, depth ratio, d_{r} and conductivity ratio, k_{r}, are significant on deterniming the critical Marangoni number M_{c} with the corresponding critical wavenumber α_{c}. The characteristics problem is solved numerically. Results show that the temperature-dependent viscosity destabilizes the fluid system but it behaves oppositely when a higher relative thermal conductivity ratio or higher depth ratio is taken.

Original language | English |
---|---|

Pages (from-to) | 1-8 |

Number of pages | 8 |

Journal | Journal of Mathematics and Statistics |

Volume | 4 |

Issue number | 1 |

Publication status | Published - 2008 |

### Fingerprint

### Keywords

- Marangoni convection
- Temperature-dependent viscosity

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*Journal of Mathematics and Statistics*,

*4*(1), 1-8.

**Boundary effect on Marangoni convection in a variable viscosity fluid layer.** / Abidin, N. Z.; Arifin, Norihan M.; Md. Noorani, Mohd. Salmi.

Research output: Contribution to journal › Article

*Journal of Mathematics and Statistics*, vol. 4, no. 1, pp. 1-8.

}

TY - JOUR

T1 - Boundary effect on Marangoni convection in a variable viscosity fluid layer

AU - Abidin, N. Z.

AU - Arifin, Norihan M.

AU - Md. Noorani, Mohd. Salmi

PY - 2008

Y1 - 2008

N2 - The onset of Marangoni convection in a horizontal fluid layer with a free surface overlying a solid layer heated from below is studied. Problem is focused on the effect of the solid layer depth or its conductivity. The viscosity group, Rv, Biot number, Bi, depth ratio, dr and conductivity ratio, kr, are significant on deterniming the critical Marangoni number Mc with the corresponding critical wavenumber αc. The characteristics problem is solved numerically. Results show that the temperature-dependent viscosity destabilizes the fluid system but it behaves oppositely when a higher relative thermal conductivity ratio or higher depth ratio is taken.

AB - The onset of Marangoni convection in a horizontal fluid layer with a free surface overlying a solid layer heated from below is studied. Problem is focused on the effect of the solid layer depth or its conductivity. The viscosity group, Rv, Biot number, Bi, depth ratio, dr and conductivity ratio, kr, are significant on deterniming the critical Marangoni number Mc with the corresponding critical wavenumber αc. The characteristics problem is solved numerically. Results show that the temperature-dependent viscosity destabilizes the fluid system but it behaves oppositely when a higher relative thermal conductivity ratio or higher depth ratio is taken.

KW - Marangoni convection

KW - Temperature-dependent viscosity

UR - http://www.scopus.com/inward/record.url?scp=49249117097&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49249117097&partnerID=8YFLogxK

M3 - Article

VL - 4

SP - 1

EP - 8

JO - Journal of Mathematics and Statistics

JF - Journal of Mathematics and Statistics

SN - 1549-3644

IS - 1

ER -