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On the stability of internally heated natural convection due to the absorption of radiation in a laterally confined fluid layer with a horizontal throughflow

Authors :
Chengwang Lei
Tae Hattori
John C. Patterson
Source :
International Journal of Heat and Mass Transfer. 81:846-861
Publication Year :
2015
Publisher :
Elsevier BV, 2015.

Abstract

This study focuses on the marginal stability of the natural convection flow induced by the absorption of radiation. Non-uniform internal heating associated with the absorption of radiation following Beer’s law and the absorption and re-emission of residual radiation by the bottom boundary wall lead to a nonlinear base temperature profile that evolves with time. A horizontal throughflow and lateral confinement are incorporated in the analysis, and two forms of convective instability, i.e. longitudinal and transverse rolls, are investigated. It is shown that the formation of longitudinal rolls, with their axes parallel to the throughflow direction, is not affected by the presence of the throughflow. For transverse rolls, with their axes perpendicular to the throughflow direction, however, the throughflow is shown to have a stabilising effect, with the critical Rayleigh number increasing with the increasing throughflow Reynolds number. It follows that longitudinal rolls are the preferred form of instability in laterally unconfined domains for any nonzero Reynolds number and in confined domains if the Reynolds number is greater than a critical value. The value of the critical Reynolds number, which separates the preferred mode of instability, is found to rapidly reduce with increasing lateral extent and approaches zero for a normalised lateral extent greater than 2.0. The lateral confinement is also shown to have a stabilising effect for both longitudinal and transverse rolls, with the critical Rayleigh number increasing with the reducing lateral extent. It is shown that the lateral confinement only substantially affects the wave number of the rolls with their axes parallel to the confining walls but not the rolls with their axes perpendicular to the confining walls.

Details

ISSN :
00179310
Volume :
81
Database :
OpenAIRE
Journal :
International Journal of Heat and Mass Transfer
Accession number :
edsair.doi...........e78c11170515688909313db76c640b3a
Full Text :
https://doi.org/10.1016/j.ijheatmasstransfer.2014.11.010