This paper considers the steady state conduction of heat from a wall to a fluid moving at a uniform velocity. The wall is heated by a step change in temperature. Although this appears to be a classical heat conduction problem, its application to various convective heat transfer problems is new. The mathematical procedure leads to the computation of the temperature field and the heat transfer coefficient. In the presence of a step change in the wall temperature, it is shown that the Stanton number is a function of the Peclet number alone. The acquired analytical results show that, near the thermal entrance location, heat conduction dominates and the local heat flux becomes independent of velocity. This phenomenon applies to classical convection problems in various-shaped ducts. (c) 2008 Elsevier Ltd. All rights reserved.