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The ultimate goal of this project is to describe the heat transfer mechanism during welding processes in a new and comprehensive way via analytical modelling. The employed methodology which includes dominant balance, self-consistency, modelling and simulation of process operations, asymptotic analysis, and dimensional analysis is inexpensive, reliable and directly-used in industrial application. It is based on formulas representing the most important welding parameters. Important metallurgical outputs like maximum temperature and the cooling rate, which is essential in determining the strength and toughness of the weld can be optimized with the obtained predictive equations with high accuracy.

The foundation of the analytical modelling is the Gaussian distributed heat source model, which synthesizes typical welding processes such as laser cladding and laser heat treatment into heat transfer dominated problem under a moving heat source of Gaussian distributed power intensity. Ease-of-use formulae for peak temperature, which helps determine whether substrate would melt and appropriate heat input, and maximum isotherm width, which means bead width in welding processes have been obtained with maximum relative errors below 0.19% and 3.72% respectively. Those formulae are simple enough to be calculated by anyone with basic math skills with a handheld calculator in a few minutes and the error generated from the obtained formulae approaches the limit of the ability to measure parameters in most heat treatment processes.