The thermal analysis computes an FEM approximate solution to the transient 3D energy equation (3-2), see chapter III, using tf-node bricks with backward Euler time integration. It is solved on the current deformed geometry for each time step. Temperature dependent thermal conductivity and specific enthalpy, including the effect of latent heats of phase transformations were used,[l 1].
The heating affect of the arc is described by a Dirichlet boundary condition on nodes in the weld pool. The weld pool size, shape and position (as a function of time) are taken as data determined from experiment for each weld pass. The temperature in a weld pool is assumed to vary parabolically from the melting point at the boundary of the weld pool to a maximum temperature of the melting point plus 400 °K at the weld pool centroid. Temperatures in the weld pool liquid/solid boundary were prescribed to 1526 °С (2780 °F, 1800 °AT).The maximum temperature in the weld pool was prescribed to 1927 °С (3500 °F, 2200°K). The size and shape of the weld pool was estimated from macrographs contained in .
External boundaries of the structure which are assumed to be in still air, have a convection boundary condition with ambient temperature of 300 °K and convection coefficient of 10 W/m2 °K. The pipe is filled with water and tilted slightly to avoid trapped air under the weld. On the internal surface of the water-filled pipe a coefficient in the range 500 to 5000 W/m2 °K and ambient temperature of 27 °С (80 °F, 300 °K) was applied. For each weld for a fixed weld pool length, the thermal flux from the weld pool was computed for this range of convection coefficients on the internal pipe surface.
Assuming a weld efficiency factor of 0.65, the computed net heat input from the arc was compared to the total heat input for the weld estimated from data taken from . The convection coefficient that provided best agreement between weld nugget geometry and heat input data taken from  was 1500 W/m2 °K. Convections coefficients in the range 1000 to 2000 W/m2 °K did not substantially change the results.