Conjugate heat transfer by forced convection through an externally heated pipe has many important engineering applications. In the present work, the radial and axial heat conductions and thermal stresses in a pipe with uniform or non-uniform wall heat flux of fully developed laminar forced convective conjugate heat transfer have been considered for analysis. The analysis is based on the two-dimensional steady-state heat conduction equation and laminar boundary layer equation for the flowing fluid by using a finite difference scheme. Water has been used as a fluid. Numerical calculations have been performed by using the FLUENT 4.5 and HEATING7 computer codes. The temperature and stress ratio distributions inside the pipe wall, heated from the outer surface by applying uniform and non-uniform heat fluxes, have been presented for two different mean flow velocities. The temperature distributions of the flowing fluid inside the pipe have also been presented for all investigated cases. (C) 2003 Elsevier Ltd. All rights reserved.