A three-dimensional numerical model has been developed to investigate the fluid flow and heat transfer behaviors in multilayer deposition of plasma arc welding (PAW) based wire and arc additive manufacture (WAAM). The volume of fluid (VOF) and porosity enthalpy methods are employed to track the molten pool free surface and solidification front, respectively. A modified double ellipsoidal heat source model is utilized to ensure constant arc heat input in calculation in the case that molten pool surface dynamically changes. Transient simulations were conducted for the 1st, 2nd and 21st layer depositions. The shape and size of deposited bead and weld pool were predicted and compared with experimental results. The results show that for each layer of deposition the Marangoni force plays the most important role in affecting fluid flow, conduction is the dominant method of heat dissipation compared to convection and radiation to the air. As the layer number increases, the length and width of molten pool and the width of deposited bead increase, whilst the layer height decreases. However these dimensions remain constant when the deposited part is sufficiently high. In high layer deposition, where side support is absent, the depth of the molten pool at the rear part is almost flat in the Y direction. The profile of the deposited bead is mainly determined by static pressure caused by gravity and surface tension pressure, therefore the bead profile is nearly circular. The simulated profiles and size dimensions of deposited bead and molten pool were validated with experimental weld appearance, cross-sectional images and process camera images. The simulated results are in good agreement with experimental results. (C) 2018 Elsevier Ltd. All rights reserved.