Abstract: An axisymmetrical model based on the magnectohydrodynamics (MHD) is established to study the effect of external longitudinal magnetic field (LMF) on heat transfer and fluid flow characteristics of welding arc. The profiles of temperature and voltage drop, distributions of arc pressure and current density, etc., are simulated by utilizing the fluid dynamic theory coupled with Maxwell equations. The quantitative analysis and comparison of anodic heat fluxes in the cases of LMF strength of 0 T and 0.06 T applied are also obtained. The results show that the applied LMF could drive particles to rotate so as to expand the arc, a negative pressure area appears at the center and induces an anti-gravity flow through the arc core, concentrating the anodic energy to the cathode. Meanwhile, the arc rotating at high speed could increase the convection heat loss, and reduce the thermal efficiency. When the magnetic induction strength is 0.06 T, the distribution of current density, anodic heat flux and arc pressure shift from the arc center to periphery and shows a bimodal pattern.