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Transonic flow over localised heating elements in boundary layers

Published online by Cambridge University Press:  12 April 2018

A. F. Aljohani Open the ORCID record for A. F. Aljohani [Opens in a new window]  and
J. S. B. Gajjar Open the ORCID record for J. S. B. Gajjar [Opens in a new window]
A. F. Aljohani
Affiliation:
Department of Mathematics, Faculty of Science, University of Tabuk, Saudi Arabia School of Mathematics, University of Manchester, Manchester M13 9PL, UK
J. S. B. Gajjar*
Affiliation:
School of Mathematics, University of Manchester, Manchester M13 9PL, UK
*
†Email address for correspondence: [email protected]
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Abstract

The problem of transonic flow past an array of micro-electro-mechanical-type (MEMS-type) heating elements placed on a flat surface is investigated using the triple-deck theory. The compressible Navier–Stokes equations supplemented by the energy equation are considered for large Reynolds numbers. The triple-deck problem is formulated with the aid of the method of matched expansions. The resulting nonlinear viscous lower deck problem, coupled with the upper deck problem governed by the nonlinear Kármán–Guderley equation, is solved using a numerical method based on Chebyshev collocation and finite differences. Our results show the differences in subsonic and supersonic flow behaviour over heated elements. The results indicate the possibility of using the elements to favourably control the transonic flow field.

JFM classification

Boundary Layers: Boundary Layers Compressible Flows: Compressible Flows Flow Control: Flow Control
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 844 , 10 June 2018 , pp. 746 - 765
Copyright
© 2018 Cambridge University Press 

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References

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