Analytical model for the temperature field around a nonuniform three-dimensional moving heat source: friction stir welding modelling

A transient semi-analytical solution is devised to find the temperature distribution around a nonuniform three-dimensional heat source in a finite rectangular plate with cooling surfaces and nonhomogenous boundary conditions. This solution can serve as a viable tool to find the temperature field and consequently provides useful insights into material modelling and response in a variety of industrial applications, including friction welding processes. As a numerical example, the established solution is applied to the friction stir welding as a solid-state welding method. The comparison between the obtained analytical results and the results found through FEM and experiment showed that the analytically obtained results and the numerical and experimental data are in good agreement.