We present the mathematical equations that govern heat transfer in a polymer melt flowing in a circular tube with constant ambient temperature, taking into account the viscous dissipation effects. This leads to a nonlinear parabolic partial differential equation. It is shown that the exact solution of a linearized version of the governing equation can be presented in terms of the Whittaker function. A finite difference scheme is used to produce an approximate solution of the linearized problem. This numerical solution is shown to be a good approximation to the exact solution found in terms of the Whittaker function. The finite difference scheme is then modified to approximate the nonlinear parabolic partial differential equation and is compared with the results found using the finite element method. (c) 2006 Wiley Periodicals, Inc.