The demand for increasingly small and lightweight products require micro-scale components made of materials which are durable and light. Polymers have therefore become a popular choice since they can be used to produce materials which meet industrial requirements. Many of these polymers are viscoelastic fluids. The reduction in the sizes of components make physical experimentation difficult and costly. Therefore computational tools are being sought to replace old methods of testing. This research has been concerned with the development of a finite volume algorithm for viscoelastic flow which can be readily applied to real world applications. A major part of the research involved the implementation of the Oldroyd-B constitutive equations and associated solution methods, in the 3-D multi-physics software environment PHYSICA+. This provides an unstructured finite volume solution technique for viscoelastic flow. This algorithm is validated using the 4:1 planar contraction and results are reported. The developed viscoelastic algorithm has also been coupled with two interface tracking techniques one of which includes surface tension effects. These techniques are the Scalar Equation Algorithm (SEA) and the Level Set Method (LSM). With both techniques the algorithms are able to take into account flow effects from both fluids (ie. air and polymer) in a two-fluid system. The LSM technique maintains a sharp interface overcoming the smearing of the interface which generally affects interface tracking techniques on Eulerian fixed grids, for example SEA, and enables the curvature of the interface to be calculated accurately to implement surface tension effects. This integrated viscoelastic flow solver and free surface algorithm is then illustrated by predicting two industrial flow processes as used in the electronic packaging industry.

Passive porous coatings have been proposed in literature as a means of delaying transition to turbulence in hypersonic boundary layers. The nonlinear stability of hypersonic viscous flow over a sharp slender cone with passive porous walls is investigated in this study. Hypersonic flows are unstable to viscous and inviscid disturbances, and following Mack (1984) these have been called the first and second Mack modes. A weakly nonlinear analysis of the instability of the flow to axisymmetric and non-axisymmetric viscous (first Mack mode) disturbances is performed here. The attached shock and effect of curvature are taken into account. Asymptotic methods are used at large Reynolds number and large Mach number to examine the viscous modes of instability, which may be described by a triple-deck structure. Various porous wall models have been incorporated into the stability analysis. The eigenrelations governing the linear stability of the problem are derived. Neutral and spatial instability results show the presence of multiple unstable modes and the destabilising effect of the porous wall models on them. The weakly nonlinear stability analysis carried out allows an equation for the amplitude of disturbances to be derived. The stabilising or destabilising effect of nonlinearity is found to depend on the cone radius. It is shown that porous walls significantly influences the effect of nonlinearity. They allow nonlinear effects to destabilise linearly unstable lower frequency modes and stabilise linearly unstable higher frequency modes.