Journal of Mathematics and Statistics

Boundary Effect on Marangoni Convection in a Variable Viscosity Fluid Layer

N.Z. Abidin, N.M. Arifin and M.S.M. Noorani

DOI : 10.3844/jmssp.2008.1.8

Journal of Mathematics and Statistics

Volume 4, Issue 1

Pages 1-8

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, Rv, Biot number, Bi, depth ratio, dr and conductivity ratio, kr, are significant on determining 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.

Copyright

© 2008 N.Z. Abidin, N.M. Arifin and M.S.M. Noorani. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.