In this thesis, we investigate flow past an array of micro-electro-mechanical-type (MEMS-type) heating elements placed on a flat surface, where MEMS devices have hump-shaped surfaces, using the triple deck theory. In this work we start by investigating the problem with a single heating element. MEMS devices can be used to control the fluid dynamics over the surface. Hence, we present a review of the boundary layer and the triple deck theories, followed by a literature review of the problem of flow past an array of MEMS devices. Next, we formulate our problem with the aid of the method of matched expansions for supersonic and subsonic flows. Thirdly, we solve analytically the linear version of the problem for supersonic flows. Thereafter, the non-linear problem is solved numerically where a detailed description of a hybrid method to solve the formulated non-linear problem for supersonic flow is exhibited. Fourthly, for subsonic flows we continue investigating flow past a heating element placed on a flat surface. Linear analysis of this problem is conducted. A novel numerical method to solve the non-linear problem for subsonic flows is described. The results are then discussed. In a similar context, we formulate a problem which can be considered as an the extension of previous subsonic flow problem to the three dimensional case. Analytical results are obtained using the Fourier transform where the linear approximation of the problem is considered and numerical results are then obtained using the Fast Fourier Transform. Finally, we consider a case of transonic flow past a heating element placed on a flat surface, where MEMS device has a hump-shaped surface. This transonic flow problem is non-linear in the upper deck and the lower deck equations where they should be solved simultaneously. Hence, a numerical method is required where we will use a finite difference method in stream-wise direction and Chebyshev collocation method in the wall normal direction. The results are then analysed. In conclusion, the use of localised heating elements in boundary layers for flow types considered in the thesis can contribute to the possibility of favourably controlling the fluid flow perturbations.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:727868 |
| Date | January 2016 |
| Creators | Aljohani, Abdulrahman |
| Contributors | Gajjar, Jitesh |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/applications-of-triple-deck-theory-to-study-the-flow-over-localised-heating-elements-in-boundary-layers(a3174ce1-f4db-47d8-b0a7-a712461a8211).html |
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