A Galerkin-type finite-element approach was used to study the effect of two-dimensional wall conduction on laminar convective heat transfer inside pipe flows. This conjugate heat transfer problem was studied for cases in which the external surface of the pipe is subjected to constant wall heat flux and constant wall temperature conditions. The wall conduction effects were found to be more significant for low Peclet number flows than their high Peclet number counterparts. The extent of preheating extends as far as 22 radii and 7 radii for constant wall heat flux and constant wall temperature conditions, respectively. © 1988 Taylor 8 Francis Group, LLC.