The transport phenomena in the extrusion of non-Newtonian fluids is investigated. The viscosity of the investigated fluids is a strong function of the temperature and, for the non-Newtonian case, of the shear rate. Therefore, the governing equations of motion are coupled to the energy equation through the viscosity. The velocity in the down channel direction of the screw extruder is a result of both shear and pressure driven transport. The pressure acts in a direction opposite to that of the drag flow, and comparatively high pressures arise at the die by typical extruders. When a narrow die is used in the screw extruder, the pressure gradient in the down channel direction becomes so large that the down channel velocity near the screw root becomes negative in terms of the coordinate system fixed to the screw. The conventional marching schemes fail to simulate the fluid flow when the down channel velocity becomes negative, since the information down stream is not known. A numerical scheme to simulate the fluid flow in a single screw extruder, for this circumstance which often arises at low flow rates and high screw speeds and which is termed as pressure back flow in the literature has been discussed. Experiments were carried out to measure the pressures at three different locations of the single screw extruder. The computed results were found to be in good agreement with the experimental results. The pressures at the die obtained numerically by treating the flow as isothermal are found to be lower than those obtained when the flow is treated as non-isothermal, indicating the strong influence of thermal transport in this problem.