Second Generation Weld Heat Source Models
Second Generation weld heat source models replace the point, line and plane models that mathematically are delta functions, with distribution functions. The first of these was a distributed flux model by Pavelic  and by Rykalin , see Chapter II. This distributed flux model was particularly effective for low power density welds in which the weld pool does not have a nail head or other form of deep penetration. However it could not model deep penetration welds such as electron beam, laser or plasma welds and most high power arc welds such as those with a nail head cross-section. Goldak et al  proposed a distributed power density model that could model deep penetration welds with somewhat more complex weld pool shapes. The last of these Second Generation models is the prescribed temperature model proposed by Goldak et al [2 and 14], see sections 3-3-2-2-2 and 3-4. It could easily model weld pool shapes of arbitrary complexity. Later we will see that if the only equation to be solved is the heat equation, then the only functions that could be distributed in a weld heat source model are the power density, a prescribed flux and a prescribed temperature. Of course one might choose various distribution functions and one could pulse or weave the heat source. However, there can be no other classes of functions for Second Generation weld heat source models because we define them to be based solely on the heat equation.
Second Generation weld heat sources immediately remove most of the limitations of the First Generation models. They can model domains of complex geometry. Nonlinearities such as temperature dependent thermal conductivity, specific heat, radiation and convection boundary conditions, latent heats of phase transformation and microstructure evolution are easily included or coupled. These models can have but need not have a weld pool. If the region being modeled is defined to be just outside the weld pool, then any temperature distribution in the region that would be occupied by the real weld pool is fictitious. Even if these models include the weld pool, the temperature distribution in the weld pool and the shape of the weld pool are often crude approximations of reality. Since these models have no velocity distribution in the weld pool, this contributes an additional error in any computed temperature field computed in the weld pool by these models. Thus these models ignore most of the physics of the weld pool. Nevertheless, the weld pool shape and position data can be realistic, because these models can compute accurate temperature distributions outside of the weld pool.