The flow of a polymer and the associated heat transfer in a fully intermeshing, co-rotating twin screw extruder are investigated numerically. The control volume technique is used for numerical modeling and simulation, considering both Newtonian and non-Newtonian fluids. The velocity distributions in the screw channel are compared with experimental results and good agreement is obtained. Owing to limitations arising from the physical aspects of the problem, the numerical results show that not all operating conditions are feasible. A feasible domain, in terms of screw speed and mass flow rate, in which the extruder operation is satisfactory, is obtained for pure starch. To improve the applicable range of this model, an axial formulation is adopted for the translation region that characterizes the domain away from the intermeshing zone of the extruder. This model yields results consistent with the earlier down-channel model while the feasibility region is extended towards lower mass flow rates. For the upper limit, a physical restriction arises in terms of the maximum flow rate for a pressure rise in the extruder. Thus, the model can be used for simulating a wide range of operating conditions while retaining the appropriate physical behavior of the process.