Exact series solutions for the computation of temperature in parallel plate channels and circular passages are well known. The inclusion of the contribution of axial conduction leads to a set of modified Graetz type problems for these fluid passages. The emphasis of this paper is the study of the asymptotic variations of wall heat flux values adjacent to the thermal entrance location for parallel plate ducts. The acquired results show interesting variations for different values of the Peclet number near the thermal entrance location. This study reports the unique variations of the wall heat flux Values near the location where the wall temperature changes as the Peclet number changes. (c) 2008 Elsevier Ltd. All rights reserved.