Several projects are available related to the mathematical theory of flame propagation, a fascinating multi-disciplinary area of applied mathematics involving ordinary and partial differential equations; combustion basics will be introduced to candidate. The approach will typically adopt a combination of analytical techniques (asymptotic methods) and/or numerical techniques (solution of ODEs or PDEs). The multi-disciplinary experience in combustion involved will be useful for tackling research problems in other fields of application, and will constitute a valuable asset for jobs in industry (such as the automobile or the aeronautics industry). Depending on the preference of the candidate, each of the projects can be tailored in its scope and the methodology of study.
Suggested sample projects:
- Ignition in a flow field (such as a Poiseuille flow) and in mixing-layers. The main aim is to determine the critical energy of the initial hot kernel (or spark) to ignite a flowing reactive mixture.
- Propagating Flames and their Stability: This involves the investigation of the various instabilities of flames using analytical and/or numerical approaches. The flames will be modelled as travelling wave solutions to reaction-diffusion-convection equations, which may, or may not, include full coupling with the hydrodynamics (the Navier-Stokes equation).
- Flame initiation and propagation in spatially non-uniform mixtures: This is a problem of considerable interest in combustion, whenever the reactants are spatially separated. The approach will be based on asymptotic and/or numerical methods. The Combustion basics needed for the projects will be provided and explained to the candidate.