Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-xbgml Total loading time: 0.325 Render date: 2022-08-17T01:50:19.138Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Marangoni convection. Part 1. A cavity with differentially heated sidewalls

Published online by Cambridge University Press:  25 February 2000

M. HAMED
Affiliation:
Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, N5A 5B9, Canada
J. M. FLORYAN
Affiliation:
Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, N5A 5B9, Canada

Abstract

Marangoni convection in a cavity with differentially heated sidewalls has been investigated. The analysis includes the complete effects of interface deformation. The results determined for large Biot and zero Marangoni (zero Prandtl) numbers show that steady convection may exist for Reynolds numbers Re larger than, and for capillary numbers Ca and cavity lengths L smaller than, certain critical values. The main factor limiting the existence of steady convection involves the interface becoming tangential to the hot wall at the contact point (tangency condition). Unsteady analysis shows that the tangency condition defines the limit point for the system; its violation is most likely to lead to the formation of a dry spot at the hot wall. The critical values of Re, Ca, and L are mutually dependent and change with the heating rate (they reach a minimum for instantaneous heating). For a certain range of parameters, multiple (i.e. steady and oscillatory) states are possible. The oscillatory state has a form consisting of the steady mode with a simple harmonic sloshing motion superposed on it. A reduction in the heating rate permits heating of the liquid without triggering the oscillatory state. Transition between the steady and the oscillatory states involves a nonlinear instability process.

Type
Research Article
Copyright
© 2000 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)
24
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Marangoni convection. Part 1. A cavity with differentially heated sidewalls
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Marangoni convection. Part 1. A cavity with differentially heated sidewalls
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Marangoni convection. Part 1. A cavity with differentially heated sidewalls
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *