AbstractThe conducto‐convective heat loss from a viscoelastic liquid, in the core of a double‐pipe heat exchanger arrangement, to a cooler Newtonian fluid flowing in the outer annulus is investigated with direct numerical simulations. A numerical algorithm based on the finite difference method is implemented in time and space with the Giesekus constitutive model for the viscoelastic liquids. The flow of both the annulus and core‐fluids is considered to be Poiseuille flow, driven by respective pressure gradients. In general, the results show that a viscoelastic core‐fluid leads to slightly lower (albeit comparable) attainable temperatures in the core‐fluid stream as compared with a corresponding Newtonian fluid. Copyright © 2008 John Wiley & Sons, Ltd.