An approximate analytic solution of a particular boundary value problem

Abstract

This note is concerned with the three-dimensional quasi-steady-state heat conduction equation subject to certain boundary conditions in the whole x′y′-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.