26 November 2009
Modelling phase change in the presence of a flowing thin liquid film There are numerous physical phenomena that involve a melting solid surrounded by a thin layer of liquid, or alternatively a solid forming from a thin liquid layer. This talk will involve two such problems, namely contact melting and the Leidenfrost phenomenon. Contact melting occurs, for example, when a solid is placed on a surface that is maintained at a temperature above the solid melting temperature. Consequently the solid melts, while the melt layer is squeezed out from under the solid due to its weight. This process has applications in metallurgy, geology and nuclear technology, and also describes a piece of ice melting on a table. Leidenfrost is similar, but involves a liquid droplet evaporating after being placed on a hot substrate. This has applications in cooling systems and combustion of fuel or a drop of water on a hot frying pan. The talk will begin with a brief introduction into one-dimensional Stefan problems before moving on to the problem of melting coupled to flow. Mathematical models will be developed, analysed and compared with experimental results. Along the way the Heat Balance Integral Method (HBIM) will be introduced. This is a well-known method primarily used by engineers to approximate the solution of thermal problems. However, it has not proved so popular with mathematicians, due to the arbitrary choice of approximating function and a lack of accuracy. The method will be demonstrated on a simple example, then it will be shown how it may be modified to significantly improve the accuracy. In fact, in the large Stefan number limit the modified method can be shown to be more accurate than the asymptotic solution to second order.
- Differential Equations and Applications Seminar