Skip Navigation


IMA Journal of Applied Mathematics Advance Access originally published online on November 6, 2007
IMA Journal of Applied Mathematics 2007 72(6):894-911; doi:10.1093/imamat/hxm051
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
72/6/894    most recent
hxm051v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Matthews, M. T.
Right arrow Articles by Hill, J. M.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Micro/nano thermal boundary layer equations with slip–creep–jump boundary conditions

Miccal T. Matthews{dagger} and James M. Hill

Nanomechanics Group, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong NSW 2522, Australia

{dagger} Email: miccal{at}uow.edu.au

Received on November 7, 2006; Revision received June 6, 2007. Accepted on September 17, 2007

At the micro- and nanoscale, the standard continuity boundary conditions at fluid–solid interfaces of classical transport phenomena do not apply and must be replaced by boundary conditions that allow discontinuities. In this study, the classical thermal laminar boundary layer equations are studied using Lie symmetries with the no-slip boundary condition for tangential velocity and continuous temperature boundary conditions replaced by non-linear slip–creep–jump boundary conditions. These boundary conditions contain an arbitrary index parameter, denoted by n > 0, which appears in the coefficients of the coupled ordinary differential equations to be solved. As an independent check on the numerical procedure, the case of a boundary layer formed in a convergent channel with a sink, which corresponds to n = 1/2, is solved analytically for various values of the Prandtl number and zero Brinkham number. Other values of n for n > 1/2 which correspond to the thermal boundary layer formed in the flow past a wedge are solved numerically for various values of the Prandtl and Brinkham number and constant coefficients appearing in the non-linear slip–creep–jump boundary conditions. It is found that for 1/2 < n < 2, solutions may be found for all values of the constant coefficients, while for n ≥ 2 the constant coefficient for the creep term must be set to zero.

Keywords: thermal boundary layer; slip–creep–jump boundary conditions; similarity solutions; microfluidics; nanofluidics.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.