Spec01: Maths for Energy (2018-2019)

Dr Vassilios Dallas
Course Term: 
Course Overview: 

Mathematics for Energy will examine four major energy topics: oil extraction, boiler dynamics, photovoltaic devices and energy storage. For each topic, we will discuss the high level issues and then focus on specific problems where the use of mathematics provides useful insight. Examples will include water intrusion in porous media, multiphase flow, and solar cell device behaviour. Mathematical techniques that will be employed include: WKB, homogenisation, and singular perturbations.

Course Synopsis: 

Oil: General framework and issues of energy production and use; Porous media flow homogenisation; Seismic and WKB methods; Hele-Shaw oil intrusions problems Buckley-Leverett

Multiple-phase problems: boiler dynamics; boiling flow in a pipe; Rayleigh-Benard convection; enthalpy methods; homogenisation techniques

Solar: Operation and efficiency of solar cells; Inorganic solar cells including PN diodes

Reading List: 

D. Mackay, Sustainable energy – without the hot air, (download from http://www.withouthotair.com/)

A. Fowler, Mathematical Geoscience, Springer, 2011

C. E. Brennen, Fundamentals of Multiphase Flow, CUP, 2005