In the present work, authors have performed a finite element modelling and simulation of the solvent based extrusion 3D printing process. The present work can be considered as a pioneering work as there is no available literature on the modelling aspects of the solvent based extrusion 3D printing process. Two physics interfaces of a commercially available multiphysics modelling tool, such as computational fluid dynamics, and heat transfer along with a mathematical approach such as the Arbitrary Lagrangian-Eulerian method were integrated to simulate the aforementioned 3D printing process. The physical model consisted of a homogenous solution of polycaprolactone polymer and a volatile solvent namely methylene chloride. A two dimensional axisymmetric model was formulated to simulate the flow behaviour and evaporation behaviour of the polymer solution from the nozzle inlet to the platform on which the solution gets deposited. The velocity and temperature field of the polymer solution during the printing of one layer is analyzed. Furthermore, the evaporation mechanism followed by evaporative cooling of the deposited layer is also illustrated. It was observed that the flow velocity obtained was 16 mm/s at the nozzle exit for a feed rate of 40 mm/min at the nozzle inlet. The evaporative cooling of the Methylene chloride solvent resulted in the reduction in temperature with an evaporation rate of 1.74 g/m3s.