Transient conjugated heat transfer in thick walled pipes for thermally developing laminar flow is investigated involving two-dimensional wall and axial fluid conduction. The problem is solved numerically by a finite-difference method for hydrodynamically developed flow in a two-regional pipe, initially isothermal in which the upstream region is insulated and the downstream region is subjected to a suddenly applied uniform heat flux. A parametric study is done to analyze the effects of four defining parameters namely, wall thickness ratio, wall-to-fluid thermal conductivity ratio, wall-to-fluid thermal diffusivity ratio and the Peclet number. The results are given by non-dimensional interfacial heat flux values, and it is observed that, heat transfer characteristics are strongly dependent on the parameter values. (C) 2010 Elsevier Ltd. All rights reserved.