This is a collaborative research project from Manitoba Hydro. My involvement
in this project is recent and minimal to help find the compuatational
solution to the partial differential
equations that captures the physics of the ice melting problem.
Modeling aspect of the problem is carried out
by Prof. P.N. Shivakumar and his team at the Department of Mathematics.
A brief description of one of the collaboration is mentioned here.
The formation of ice on high voltage transmission lines (due
to freezing rain or other causes) and its disastrous consequences in loss
of property, loss of life and widespread inconvenience are well known. An
example of this catastrophe is the Ice Storm of Quebec and Ontario in January
problem also exists in a substantial way in many parts of North America
(example, in Louisiana). Although the present research is limited to
mathematical modeling and its practical application in mitigation of ice,
by the control of intensity of electricity in the transmission wires, the
work is itself a part of a very wide ranging topic which includes
mathematical modeling of ice formation, modeling instability of
transmission lines, use of chemicals to inhibit formation of ice, risk
analysis, CFD Solutions and robotic solutions for the extermination of ice. In this study,
the main objectives are
to develop mathematical models for the shape and
size of of the ice (provided by Hydro companies) taking into consideration
gravity, atmospheric conditions (wind, humidity, frost etc.)
process of melting ice from internal (current in the lines) sources
Development of software for Hydros and electrical utilities
The interface of
mathematical modeling and applying it in the field not only leads to
real world applications, but also involves developing newer directions
and applications of mathematical tools.
The main mathematical framework for
moving boundary problems is represented as Stephan's problem.
It is also proposed to develop a web page which will act as a
repository for worldwide information on the ice problem in general,
supplied by other organizations.
For a recent presentation on this activity click here
Graduate Research Assistant trained: Mr. Vishnu K. Narayanasami
*. P.N. Shivakumar, Ruppa K. Thulasiram, Shiu H. Lui, " Mathematical
Modeling of Ice on Transmission Lines",
Proceedings of the International Conference and Instructional Workshop on Industrial Mathematics
(ICIWIM02) December, 2002, Mumbai, India (to appear)