Subsonic flow past localised heating elements in boundary layers

Abstract

The problem of subsonic flow past micro-electro-mechanical-type (MEMS-type) heating elements placed on a flat surface, where the MEMS devices have hump-shaped surfaces, is investigated using triple deck theory. The compressible Navier-Stokes equations supplemented by the energy equation are considered in the limit that the Reynolds number is large. The triple deck problem is formulated and the linear and non-linear analysis and results are presented. The current work is a generalisation of the problem discussed by (Koroteev & Lipatov 2012, 2013 where the MEMS devices have flat shaped surfaces. The results show the hump-shaped heating elements enhance large drops in pressure and peaks and troughs in the skin-friction over the centre of the hump as compared to the flat shaped devices which may be useful for controlling the flow.Key words: Authors should not enter keywords on the manuscript, as these must be chosen by the author during the online submission process and will then be added during the typesetting process (see http://journals.cambridge.org/data/relatedlink/jfmkeywords.pdf for the full list)

Subsonic flow past three-dimensional localised heating elements in boundary layers

“…In comparing results for the heated flat-plate with those for the heated hump, the heated hump smooths out the abrupt rise and drop in the shear and pressure distributions when the fluid enters and leaves the heated region. This is very similar to the results obtained by Aljohani and Gajjar [2017] in their investigations of the two-dimensional problem with hump-shaped elements. Also a hump shaped element promotes much larger drops and rises in the minimum and maximum pressure and shear values as compared to the heated flat plate element, or the unheated hump shaped element.…”

“…Both figures 5(a), 5(b) show that with the hump shaped heated element, the rise and drop and in the pressure and shear coinciding with the start and end locations of the heating element, is not as abrupt as seen in the flat-plate case. This was also noticed in the results of Aljohani and Gajjar [2017].…”

“…Comparison of our results for the pressure distributions of the three dimensional linear problem and the two dimensional case considered by Aljohani and Gajjar [2017], shows some differences especially in the minimum value of the pressure. For this comparison we have taken two different spanwize sizes of lengths of the element.…”

“…The results of Koroteev and Lipatov [2012] are recovered by taking the hump height to be zero. The results in Aljohani and Gajjar [2017] show that heated humps do also significantly enhance the favourable wall shear reduction properties as compared to the thermally heated flat plate elements. In addition by changing the extent of the heated region relative to the extent of the hump, smoother wall shear profiles can be obtained in contrast to the flat plate elements.…”

Tollmien–Schlichting wave cancellation via localised heating elements in boundary layers

“…The ideas suggested by Lipatov (2006) have been applied to a variety of other situations involving predominantly steady localised heating including subsonic and supersonic flows, see Koroteev & Lipatov (2009, 2012, 2013). In a series of recent papers, Aljohani & Gajjar (2017 a , b , 2018) have investigated steady boundary layer flow with localised heating but over hump-shaped elements to understand how localised heating can affect a separated flow. Both two-dimensional as well as three-dimensional hump-shaped elements were studied for an oncoming subsonic or transonic flow.…”