In welding and wire-arc additive manufacturing (WAAM), a moving arc is the heat source that enables the deposition of metals, and the resulting properties of the final product. because the arc involves temperatures of the order of 20 000 K, and gas velocities of the order of 300 m/s, there are only few experiments and few models available to determine optimal, or at least acceptable, parameters for the operation such as current, voltage, arc length. The lack of engineering guidance results in costly and time-consuming trial and error, which also involve wasteful use of energy and scrap parts. In this work, a numerical model of the gas-tungsten arc welding (GTAW) arc was created and validated against experiments. The model considers the arc interactions between a non-consumable electrode and the weld pool, and accounts for multiple coupled heat transfer mechanisms: Joule heating, conduction, advection, radiation, and Thomson effect. The conditions considered cover the vast majority of GTAW welding operations. The results are generalized in the form of engineering expressions suitable to be embedded in metamodels, in which the heat source is just a part. Applications include penetration and width of welds and deposition rate in external-wire WAAM.