We analyze the phenomenon of steady heat transfer enhancement due to chaotic particle paths in steady, laminar flow through a tube. The performances of two different coils, one with regular mixing and the other with chaotic mixing, are numerically analyzed and compared. For the latter case, axially periodic boundary conditions over a unit cell are used: Velocity vectors and temperature fields are computed. Poincare maps of fluid particles being repeatedly mapped from inlet to outlet of this cell are presented as function of system geometry. Point and periodic attractors with chaotic windows are found. Lyapunov exponents are used to establish the presence of chaotic mixing. Flow fields and isotherms are examined to reveal the mechanisms of enhanced heat and momentum transfer through modification of the wall and internal boundary layers. Spatially varying local and constant bulk Nusselt numbers and bulk friction factors are determined for a range of governing parameters.