This monograph deals with the structure, generation and stability of flames from a mathematical point of view. It uses a specific mathematical approach to provide a unified theoretical description of fundamental flame phenomena. Its importance stems from the fact that it provides the first clear evidence that combustion can be legitimately treated as a mathematical science as well as an empirical one. The book will be of interest to researchers in combustion, fluid mechanics and applied mathematics, as well as to graduate students taking advanced courses in these areas.
The general analysis developed in Parts 1 and 2 of three-dimensional duct flows subject to a strong transverse magnetic field is used to examine the flow in diverging ducts of rectangular cross-section, the walls of which are electrically non-conducting. A dramatically different flow is found in this case from that studied in Part 2, where the side walls parallel to the magnetic field were highly conducting. Now it is found that the core velocity normalized with respect to the mean velocity is of O(M−½) while the velocity in the side-wall boundary layers is of O(M½), so that these boundary layers carry most of the flow. The problem of entry is solved by analysing the change from fully developed Hartmann flow in a rectangular duct to the flow in the diverging duct. It is found that the disturbance in the upstream duct decays exponentially. The analysis of the side-wall boundary layers is more difficult than that in Part 1 on account of the different boundary conditions and requires the solution of two coupled integro-differential equations. Numerical solutions are obtained for a duct whose width increases linearly in the flow direction.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.