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A singularity in thermal boundary-layer flow on a horizontal surface

Published online by Cambridge University Press:  26 April 2006

P. G. Daniels
P. G. Daniels
Affiliation:
Department of Mathematics. City University, Northampton Square, London, EC1V 0HB, UK
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Abstract

A thermal boundary layer, in which the temperature and velocity fields are coupled by buoyancy, flows along a horizontal, insulated wall. For sufficiently low local Froude number the solution terminates in a singularity with rising skin friction and falling pressure. The structure of the singularity is obtained and the results are compared with numerical solutions of the horizontal boundary-layer equations. A novel feature of the analysis is that the powers of the streamwise coordinate involved in the structure of the singularity do not appear to be simple rational numbers and are determined from the solution of a pair of ordinary differential equations which govern the flow in an inner viscous region close to the wall. Modifications of the theory are noted for cases where either the temperature or a non-zero heat transfer are specified at the wall.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 242 , September 1992 , pp. 419 - 440
Copyright
© 1992 Cambridge University Press

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