eCite Digital Repository

The inclined Wooding problem


Rees, DAS and Bassom, AP, The inclined Wooding problem, Transport in Porous Media, 125, (3) pp. 465-482. ISSN 0169-3913 (2018) [Refereed Article]

Copyright Statement

Copyright 2018 The Authors

DOI: doi:10.1007/s11242-018-1128-9


A constant-thickness thermal boundary layer is formed by the presence of uniform suction into a constant temperature hot surface bounding a porous medium - the Wooding problem. When the hot surface lies below the porous medium, the system is susceptible to thermoconvective instability. The present paper is concerned with how the classical linear stability analysis is modified by inclining the heated surface. Analysis is confined to disturbances in the form of transverse rolls because the equivalent analysis for longitudinal rolls may be described analytically in terms of that for the horizontal layer. The linear stability analysis is made difficult by the absence of a second bounding surface, and the method of multiple shooting is needed in order to obviate the consequence of having a stiff system of disturbance equations. Therefore, the computational domain is split into 5 or 10 subdomains. It is found that all modes of instability travel up the heated surface unless the surface is horizontal. The system is found to be linearly stable for all inclinations above 31. 85473°, a value which is remarkably close to that for the inclined Darcy-Bénard problem.

Item Details

Item Type:Refereed Article
Keywords:porous media, convective instability, linear stability theory, transpiration, inclination
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Theoretical and applied mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Bassom, AP (Professor Andrew Bassom)
ID Code:129031
Year Published:2018
Web of Science® Times Cited:3
Deposited By:Mathematics and Physics
Deposited On:2018-11-02
Last Modified:2019-02-27

Repository Staff Only: item control page