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

Ugur Tanriver and Aravinda Kar

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 xy-plane and finite in z-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.