Abstract: In applications very often we meet heat transfer problems for bodies of complicate structure; particularly they can be represented as bodies consisting of finite number of tangentially connected canonical sub-domains. We propose to call such domains as regular non-canonical domains (or bodies). By canonical sub-domain we understand body of simple structure, e.g. rectangle, cylinder, ball. For canonical sub-domain with traditional type boundary conditions the Green function method (or variable separation method) can be applied in classical way, but it can’t be applied directly for the regular non-canonical domain. Typical example of regular non-canonical domain is system with extended surfaces in form of rectangular fin (L-shape domain).
The proposed modification of the Green function method for regular non-canonical domains is based on the idea: in each canonical sub-domain the junction conditions (e.g., conjugations conditions) on the common boundary with the alongside canonical sub-domain is replaced with certain classical boundary condition with unknown right hand side. Then the Green function method for each canonical sub-domain is applied in traditional form. The junction conditions finally allow expressing the exact solution of the original problem on the mentioned common boundary in the form of the system of 2nd kind Fredholm integral equations. For the regular non-canonical domain consisting of two canonical sub-domains the solution is reduced to one Fredholm integral equation. Simpler, but then approximate class of solutions for regular non-canonical domains can be obtained on the basis of original method of conservative averaging.
As main applications of both approaches we consider two important application areas: intensive steel quenching and heat transfer in systems with extended surfaces.

 

Brief Biography of the Speaker:
Professor Andris BUIKIS

- Professor, University of Latvia
Faculty of Physics and Mathematics, Department of Mathematics
- Head of Laboratory of Mathematical Technologies, Institute of Mathematics and Computer Science,
University of Latvia

Born: March 15, 1939, Valka, Latvia

Interests:

- Mathematical Modelling
- Mathematical Problems of Heat and Mass Transfer, Especially for Layered Media
- Analytical and Numerical Methods for Partial Differential Equations
- Innovative Energetic
- Philosophy of Science

Languages: German, English, Latvian, Russian

Education:

- University of Latvia (Faculty of Physics and Mathematics), 1963
- Dr.math. (Candidate of Science in former USSR), University of Latvia, 1970
- Dr.habil.math. (Doctor of Science in former USSR), University of Kasan, Russia, 1988
- Professor, University of Latvia, 1991

Experience:

- Junior Researcher, Senior Researcher, Computing Centre, University of Latvia, 1962 - 1972
- Assistant Professor and Head of Chair of Applied Mathematics, Faculty of Physics and Mathematics, University of Latvia, 1972 - 1976
- Assistant Professor and Head of Chair of Differential Equations and Numerical Methods, Faculty of Physics and Mathematics, University of Latvia, 1976 - 1984
- Senior Researcher, Faculty of Physics and Mathematics, University of Latvia, 1984 - 1986
- Assistant Professor, Chair of Differential Equations and Numerical Methods, Faculty of Physics and Mathematics, University of Latvia, 1986 - 1988
- Senior Researcher, Head of Laboratory of Mathematical Physics, Institute of Physics, Latvian Academy of Sciences, 1988 - 1991
- Director, Institute of Mathematics, Latvian Academy of Sciences and Latvian University, 1991 - 1996; 2003 - 2006
- Head of Laboratory of Mathematical Physics (1996 -2006 ) and Head of Scientific Council (1996 – 2003), Institute of Mathematics, Latvian Academy of Sciences and Latvian University
- Director, Science and Dialogue Centre of Latvia, 1993 -2007
- Head of Laboratory of Mathematical Technologies (2006-), Institute of Mathematics and Computer Science, University of Latvia