Mathematical
models require a deep understanding of the physics and the ability to implement
the underlying equations. Mosts tasks
are solved using spreadsheets, an engineering (Newton’s method) equation solver, or a programming
language (Fortran, Pascal, Delphi, Visual Basic). Many models are spreadsheet-based so that they are portable and
accessible for the client to run if they choose.

INDEX

Wastewater treatment device hydraulics

Kinematic model of steering shaft.

Transient temperature field in a pipeline wall exposed to the sun

For associated simulation and experimental work
see “wastewater treatment” under Fluid Mechanics. A combination of numerical modeling (CFD), mathematical modeling
and experimental work was valuable to this project.

This model was created to predict the velocity
ratio through a multiple-jointed shaft with generalised geometry. It applies matrix methods to spatial
transforms as used in robotics. Used in
the automotive industry. Such
prediction can be done today with advanced commercial CAD packages, but this
special spreadsheet tool is still more convenient in many cases.

This model, for an American client, was used to
predict the performance of a domestic hot water system using a venturi-driven
hot water circulation concept.

This is a simple example of a mechanism (Watt’s linkage) solved using a Newton’s method equation solver.

This is an example of a finite element model coded in Delphi™, used to predict the wall temperature in pipelines given latitude, pipe direction etc.