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Exchanges of energy and mass across interfaces or boundaries are crucial phenomena that have to be investigated intensively and extensively in order to control/optimise product formation in industry. Many heat and mass transfer phenomena have already been examined analytically and numerically. These phenomena are certainly one of the most joyful objectives for research and the related partial differential equations are most likable in many ways. Many mathematical solutions have been published. When these phenomena are coupled with chemical reactions, on the other hand, the degree of difficulty in gaining an analytical solution increases dramatically. In fact, even in some cases where analytical solutions have been obtained, they are expressed in very complicated formulas that do not allow us to see the physics or chemistry involved in a straightforward manner.
Over the last half of a century, we have seen a rapid expansion of computing power, coupled with mankind\222s other talents, which have brought super effective numerical solutions to solve seemingly the most complex engineering problems, heat and mass transfer problems included. The solution methods seem to be so robust that some excellent commercial software for computation and graphing such as Comsol, Fluent and CFX and so on, have become available.
Despite the advances in the numerical simulations in terms of complexity and comprehensiveness, there is a room for simple solutions to the complex problems where the simplifications are based on the good understanding of the physical-chemical process. In particular, the application of the `characteristic transport length (CTL)' to simplify the related partial differential equations to be linearized one has been explored in study. This approach (and its simple solution formats) can help illustrate the insights of the complex transfer processes (with or without reactions) more explicitly. The solutions in their expressions can be used as a guide for practical applications. Where possible, previous laboratory results have been employed to validate the model solutions. Three problems in industry have been investigated: (i) material segregation in a three-component system (oil, sugar and protein) in spray drying of a solution or (ii) a suspension droplet (a dairy milk droplet system), material segregation in a two-component system (protein-sugar) and (iii) a problem or relationship in exothermic property measurement (self-ignition). (ii) and (i) are related but the work was firstly carried out for (i) where the oil phase has much larger particle size than the other two components. After the application of the continuum theory being successful against the laboratory results, it was decided to work on a `similar' and `simpler' system (ii). It turned out to be a real +challenge as it was realised that continuum model alone would not work. A +molecular interpretation through a geometrical approach has been devised which +has been seen to be successful. Finally, during the course of this thesis, a +different problem, self-ignition, was tackled using the same methodology of the +characteristic transport length. A useful and explicit relationship between the +crossing-point-temperature (access) and the exothermic reactivity has been +obtained. The experiences gained in this work may well be extended to other +systems of practical interests in chemical and food industry.