Two-dimensional heat transfer problem using the boundary integral equation

✍ Scribed by Young W. Chun

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 340 KB
• Volume: 329
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(92)90008-5

✦ Synopsis

Mathematical properties of the variational solution and solution of the boundary integral equation of a two-dimensional heat transfer problem are studied. It is first reviewed that a boundary integral expression is valid for the classical solution, and then it is shown that a unique solution of the boundary integral equation is identical to the vuriational solution in Sobolev space H'(Q) even when the classical solution does not exist. To represent the boundary integral equation ,for the two-dimensional problem, Green's ,formula in Sobolev space is utilized on the solution domain excluding a circle with a small radius p centered at the singular point. By letting p tend to zero it is shown that for the heat transfer problem, a boundary integral expression is valid for the variational solution. From this fact, one can obtain a numerical approximation of the variational solution by the boundary element method even when the classical solution does not exist.