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Thermal-ignition analysis in boundary-layer flows

Published online by Cambridge University Press:  19 April 2006

C. K. Law  and
H. K. Law
C. K. Law
Affiliation:
Department of Mechanical Engineering and Astronautical Sciences, Northwestern University, Evanston, Illinois 60201
H. K. Law
Affiliation:
Department of Mechanical Engineering and Astronautical Sciences, Northwestern University, Evanston, Illinois 60201
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Abstract

The weakly reactive state leading to the ignition of a steady laminar boundary-layer flow of a combustible mixture over a hot, isothermal, non-permeable, non-catalytic flat plate is studied both numerically and using matched asymptotic analysis in the realistic limit of large activation energy. It is shown that the flow consists of a locally similar diffusive-reactive region next to the plate and a non-similar diffusive-convective region outside it; that the analytic solution obtained reproduces the lower half of the S-shaped ignition-extinction response curve such that ignition is expected to occur when a suitably defined Damköhler number, which increases with the streamwise distance, reaches unity; and that at the point of ignition the heat transfer from the wall vanishes identically. An explicit expression for the minimum distance for ignition to occur is also derived.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 92 , Issue 1 , 15 May 1979 , pp. 97 - 108
Copyright
© 1979 Cambridge University Press

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