The optimal variation of wall thickness to minimize the pipe wall axial conduction for a conjugate heat transfer problem is considered. The variable pipe wall outer radius corresponding to the optimal wall thickness is determined via variational calculus. Using the optimal outer radius for an existing solution procedure of the conjugate heat transfer problem, a noticeable increment in heat gain of the flowing fluid yielded by the raising wall temperature is observed. The effect of the optimal and linear variations together with the constant outer radius of the pipe on heat transfer characteristics is comparatively presented. It was found that the axial conduction is minimized when the wall thickness decreases in the optimal manner in the flow direction. The magnitude of the minimization of wall axial conduction and resulting enhancement in heat transfer to flowing fluid can be controlled by the proper prescription the wall to fluid thermal conductivity ratio and the Bi number. (C) 2002 Elsevier Science Ltd.