On Diffusion and hydrodynamic problems with moving boundaries

The present work deals with mathematical models of continuum of known shape or interphase boundary position, referred to as free or moving boundary problems. The term moving is related to time-dependent problems, while free relates to time-independent ones. Both free and moving boundary problems have a wide range of engineering applications.The present work consists of two parts. The first part deals with movingboundary diffusion problems, and applications to Stefan problems are taken as examples. Some of the most popular analytical and approximate methods are studied in detail due to their importance in the present work; this study is followed by the development of a new semi-analytical method to solve one- dimensional two-phase problems, in which the moving boundary equation is derived in terms of the boundary condition at x = 0, and the properties of the medium.Phase-change problems are also solved numerically ’using the boundary ele-ment method which is a popular numerical method based on integral equations.New iteration schemes are developed to solve one-dimensional phase-changeproblems, with one or two phases.The second part of the present work deals with free boundary problems, andcavitation phenomena are taken as example of study. Due to the complex anal-ysis and approximations made to the mathematical model, very few analyticalsolutions are available.The boundary element method is applied to solve the cavitation problem,using a new iteration scheme developed to cover all possible geometries of theobstacle. The new iteration scheme is applied to a wide range of differentexamples, and the results show a very good agreement with available analyticaland numerical solutions.