CRITICAL TIMES OF HEAT AND MASS TRANSPORT THROUGH MULTIPLE LAYERS

Abstract

Heat and mass transport through multiple layers has applications to a wide range of areas, including industrial, geological, and medical problems. An important aspect of multilayer transport is the phenomenon of ‘critical time’, which is a measure of how long the diffusive process takes. For example, how long until the coldest point of a steel coil reaches the annealing temperature during heating? The goals of this thesis are to: 1. explore the effect of layered structures on the critical time, thus demonstrating the limitations of the traditional averaging method for multilayer diffusion. 2. find simple approximate expressions of critical time that accurately reflect the multilayer behaviour, for both diffusion and reaction diffusion processes. 3. conduct a thorough comparison of prominent definitions currently in the literature, in particular finding when they are equivalent. 4. determine an averaging method which simplifies the multilayer reaction diffusion model to an analogous single layer system. In this thesis, an exact solution for multilayer diffusion is used to demonstrate the limitations of traditional averaging methods, which are only accurate for a large number of layers or in the steady state. The averaging method does not capture the asymmetric behaviour of the multilayer system. The exact solution is used to find elegant approximations for seven definitions of critical time, which accurately capture the multilayer behaviour. Each critical time definition is appropriate for different physical applications, with the most important difference being whether the definition is spatially dependent or independent. A thorough comparison between the critical time definitions is conducted.