Hydrodynamically developed, thermally developing, steady, laminar conjugate heat transfer of a liquid flow in the entrance region of a microtube is studied numerically. The finite volume method is used. The effects of the thermal conductivity ratio, the diameter ratio, the channel length and the viscous dissipation on the Nusselt number as well as on the temperature and the interface heat flux distribution are examined in detail. In the entrance region, large reductions are observed in the Nusselt number with increasing k(s)/k(f) and d(o)/d(i). This is considered to be due to the axial conduction, which also extends to the exit region. The results also show that the Nusselt number decreases with increasing viscous dissipation for fixed values of k(s)/k(f) and d(o)/d(i). (C) 2012 Elsevier Ltd. All rights reserved.