A numerical study is carried out on the conjugate thermal transport and solidification in polymer melts flowing through channels. A continuum model with the enthalpy formulation is used for a laminar, two-dimensional, axisymmetric, incompressible, and steady flow. The influences of axial diffusion, viscous dissipation, and temperature-dependent viscosity are Included. A fully elliptic, control volume, finite difference method is employed to solve the governing equations. Numerical results are analyzed by examining the effects of outer wall temperature, Blot number, and mass flow rate. Isotherms and other results are also presented.