A methodology has been developed to study laminar flow and heat transfer behaviour in periodic non-straight passages with a heat transfer boundary condition of constant axial heat flux and constant peripheral temperature (HI). The technique uses Newton iteration to determine the wall temperature distribution required to satisfy the H1 boundary condition. The methodology is validated for hydrodynamically developed and thermally developing flow, as well as for hydrodynamically and thermally developed flow in straight ducts with various cross-sections. The methodology is extended to study fully developed flow in a periodic serpentine channel, consisting of a number of bends and straight sections, with a semi-circular cross-section. The results show the existence of a non-monotonic temperature distribution along the serpentine channels which exists because increased rates of heat transfer at bends lead to reductions in the local wall temperature in order to maintain a constant axial heat flux. Hot spots within the passage cross-section, typical of the H2 boundary condition, are removed in the HI case. (c) 2006 Elsevier Ltd. All rights reserved.