Display omitted •Developed free surface based model for laser spot welding.•Interface evolution dynamics is considered.•In-depth comparison with the conventional flat surface based model.•Significant difference in temperature, phase interface, thermal cycle and flow field.•Local solidification conditions in the melt pool are quantified and compared.•Indicative as-solidified weld grain structure estimated based on GR and G/R. In this article, a free surface based thermo-fluidic model for conduction mode laser spot welding has been developed. This approach is different from the conventional numerical modelling of conduction mode laser spot welding which assumes flat top surface. The development of metal-gas interface in this model is captured by integrating a free surface capturing scheme with the thermo-fluidic model. The free surface is tracked by using Volume of Fluid (VOF) method. This numerical model solves mass, momentum and energy conservation equations coupled with phase change (melting and solidification) and VOF. The present model accounts for the interfacial forces, such as surface tension and Marangoni force responsible for curvilinear evolution of the interface. This additional physics of interfacial forces is completely ignored in the conventional flat surface based models. The results from the free surface model is validated with the experimental results reported in literature. For evaluation purpose the predictions made by free surface model are compared in detail with those from the conventional flat surface model. The evolution of melt pool characteristic, temperature distribution, phase boundary, velocity field and thermal cycle are compared for both models. Also, the local solidification condition as well as non-dimensional thermo-fluidic parameters are described and compared. The free surface model showed larger melt pool dimensions, higher peak temperature and velocity, along with delay of overall solidification in the computational domain. The calculated local solidification conditions in the melt pool are used to estimate the indicative as-solidified weld grain structure based on GR and G/R values.