Transient conjugated heat transfer for laminar flow in the thermal entrance region of pipes is investigated by considering two dimensional wall and axial fluid conduction. The problem is handled for an initially isothermal, infinitely long, thick-walled and two-regional pipe for which the upstream region is insulated and solved numerically by a finite difference method for hydrodynamically developed flow with a step change in the ambient fluid temperature in the heated downstream region. A parametric study is done to analyse the effects of five defining parameters namely, wall thickness ratio, wall-to-fluid conductivity ratio, wall-to-fluid thermal diffusivity ratio, the Peclet number and the Biot number. © 2003 Published by Elsevier Science Ltd.