International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 8, Pages 513-520
An approximate analytic solution of a particular boundary value problem
School of Optics, Center for Research and Education in Optics and Lasers (CREOL), Mechanical, Materials and Aerospace Engineering Department, University of Central Florida, Orlando 32816, FL, USA
Received 8 January 2001
Copyright © 2001 Ugur Tanriver and Aravinda Kar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This note is concerned with the three-dimensional quasi-steady-state
heat conduction equation subject to certain boundary conditions in the whole -plane and finite in -direction. This type of boundary value problem arises in laser welding
process. The solution to this problem can be represented by an
integral using Fourier analysis. This integral is approximated to
obtain a simple analytic expression for the temperature distribution.