The transport phenomena underlying the extrusion of non-Newtonian fluids in single-screw extruders is investigated numerically and experimentally. 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 in 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 dawn-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 downstream conditions are not known. Two different numerical schemes used to simulate the fluid flow in a single-screw extruder for this circumstance, which often arises when dies with high flow resistance are used and which is termed as pressure back flow in the literature, have been discussed. One scheme is based on including the down-channel thermal diffusion, making the problem elliptic, and the other scheme uses a different coordinate system. Both formulations are found to yield results that are fairly close. Experiments were also carried out to measure the pressures at three different locations in a 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 nonisothermal, indicating the strong influence of thermal transport in this problem.