The stability of boundary layers on curved heated plates

This paper is made available with the permission of the Australian Mathematical Society Inc. 21/11/08We consider the effect the competing mechanisms of buoyancy-driven acceleration (arising from heating a surface) and streamline curvature (due to curvature of a surface) have on the stability of boundary-layer flows. We confine our attention to vortex type instabilities (commonly referred to as Gortler vortices) which have been identified as one of the dominant mechanisms of instability in both centrifugally and buoyancy driven boundary layers. The particular model we consider consists of the boundary-layer flow over a heated (or cooled) curved rigid body. In the absence of buoyancy forcing the flow is centrifugally unstable to counter-rotating vortices aligned with the direction of the flow when the curvature is concave (in the fluid domain) and stable otherwise. Heating the rigid plate to a level sufficiently above the fluid's ambient (free-stream) temperature can also serve to render the flow unstable. We determine the level of heating required to render an otherwise centrifugally stable flow unstable and likewise, the level of body cooling that is required to render a centrifugally unstable flow stable.Jillian A. K. Stott and James P. Denie

Blowing-induced boundary-layer separation of shear-thinning fluids

PP Dabrowski & JP Denie

The effect of diffusive mass transfer on boundary-layer stability

IA Halatchev & JP Denie

The decay of the flow in the end region of a suddenly blocked pipe

We consider the decay to rest of initially laminar flow within the end region of a suddenly blocked pipe. Here the flow is dominated by two temporally developing boundary layers, one on the pipe wall and one located at the blockage. The evolution and interaction of these boundary layers contributes to the creation and annihilation of toroidal vortices in the end-region flow, the number and extent growing with increasing Reynolds numbers. For larger Reynolds numbers, these nonlinear vortices delay the decay process within the end region, decaying at a slower rate than flow far downstream of the blockage. Our numerical simulations for pre-blockage Reynolds numbers up to 3000 indicate that the flow in this end region is stable to axisymmetric disturbances.Nathaniel Jewell and James P. Denie

Weakly nonlinear wave motions in a thermally stratified boundary layer

James P. Denier and Eunice W. Mureith

An introduction to programming and numerical methods in MATLAB

MATLAB is a powerful programme, which naturally lends itself to the rapid implementation of most numerical algorithms. This text, which uses MATLAB, gives a detailed overview of structured programming and numerical methods for the undergraduate student. The book covers numerical methods for solving a wide range of problems, from integration to the numerical solution of differential equations or the stimulation of random processes. Examples of programmes that solve problems directly, as well as those that use MATLAB's high-level commands are given. Each chapter includes extensive examples and tasks, at varying levels of complexity. For practice, the early chapters include programmes that require debugging by the reader, while full solutions are given for all the tasks. The book also includes: a glossary of MATLAB commands appendices of mathematical techniques used in numerical methods. Designed as a text for a first course in programming and algorithm design, as well as in numerical methods courses, the book will be of benefit to a wide range of students from mathematics and engineering, to commerce.Simple calculations with MATLAB.- Writing scripts and functions.- Loops and conditional statements.- Root finding.- Interpolation and extrapolation.- Matrices.- Numerical integration.- Solving differential equations.- Simulations and random numbers.- Appendices.- A mathematical introduction to matrices.- Glossary of useful terms.- Solutions to tasks.463 page(s