Problems for Graduate Student Workshop
The problems which will be considered for the Graduate Student Workshop (Saturday 26 January 2008) are listed.
- Temperature variations in a parked car
On a hot summer day the temperature levels within a car parked in the sun can be as much as 20oC above that outside the car. Pets and children left in such a parked car suffer heat stress and in fact a number of deaths are reported each year in Australia and South Africa as a result of owners or parents leaving a pet or child in a parking lot while shopping.
Our aim is to develop a theoretical model for predicting the temperature development in a parked car given readily available meteorological and car variables. In this context we would like to assess the effect of meteorological variables (solar radiation, outside air temperature,? as a function of time) on cabin temperatures. Also the car orientation and colour, and other car features may significantly effect the temperature development. The model should be fitted to experimental data collected in March 2005 on a parked car in Perth, Western Australia. This data will be presented at the Workshop.
For a simple model for determining the solar azimuthal angle and solar elevation as a function of time see (in the Appendix) J.E. Marsden and A. Tromba, 2003 ?Vector Calculus?.
Wikipedia also has useful solar geometry and radiation information. -
Model of an active vehicle suspension system
We develop a model of an active vehicle suspension system via an optimal control problem. The problem is modelled by a system of differential equations. We investigate how the active suspension could be improved by the use of a non-linear feedback control with non-quadratic cost function. -
Undersea oil detection
Electromagnetic waves generated by a coil trailing behind a boat can be used to detect the presence of oil bearing rock under the ocean. An analogous and mathematically similar problem is the thermal detection problem. Here the aim is to determine the presence, location and thickness of a thin layer of material with different conductivity from that of the surroundings using an oscillatory heat source on the surface.