The objective of this thesis is to develop and verify a non-linear transient finite element analysis capability for analyzing the thermal history of real welds. This has been achieved within a program called "IRONS".
After a concise review of the fundamental laws of heat transfer this report presents the theoretical formulation for a non-linear transient finite element analysis for heat flow using Galerkin's Weighted Residual Method. Non-linear temperature dependent material properties are accommodated using the method of successive approximations. Time integration is done with two point finite elements in the time domain.
A heat source model is developed with a Gaussian distribution of heat in space. This is the first model capable of analyzing strip electrode and electron beam welds. Previous models assumed circular or spherical symmetry. Equally important, the smoothness of heat distribution in this model significantly reduces the approximation error inherent in the finite element method.
Using this heat source model, the transient temperature distribution for a weld in a thick plate is obtained using IRONS finite element computer code developed at Carleton University. The temperature distribution is computed at a cross section perpendicular to the direction of the weld electrode movement. The results are compared to the experimental data for this weld as reported by Christensen et al  and Krutz et al . By assuming suitable values of thermal conductivity in the molten zone and the characteristic dimensions of heat flux distribution, excellent agreement between computed and measured temperatures is achieved at all times.
The method is extended to predict the temperature distribution, area of the fusion zone and heat affected zone, and the length of the molten pool trailing behind the moving electrode for submerged arc welding a thin plate.
A combined convection and radiation heat transfer coefficient is calculated using the data given by V.A.Vinokurov .
The source model permits a through thickness temperature variation which exists for some time after the initiation of welding. At a later time the problem effectively becomes one-dimensional, with heat flowing only in the direction perpendicular to the weld centre line.