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The present paper investigates the laminar forced convection heat transfer for a generalized Casson fluid flow through a horizontal circular pipe and between two parallel plates maintained at a uniform wall temperature. This study focuses on the effect of yield stress and flow index as well as Peclet number on thermal transport characteristics for both the entrance and the fully developed regions. Because of the viscous character of this kind of fluids, viscous dissipation is taken into account. The regularized Papanastasiou model is considered to avoid the discontinuous-viscosity behavior of the fluid. The governing equations are discretized by means of the finite volume method using the power law scheme. The numerical simulations are conducted using a source code based on the FORTRAN language. The results show that the increase in the Peclet number leads to the increase in the heat transfer rate at the inlet. Furthermore, the Nusselt number decreases when the flow index increases and increases downstream when the Casson number increases. Heat transfer is also significantly improved when viscous dissipation is taken into account. A correlation is proposed at the end of the study; it gives the asymptotic Nusselt number over a wide range of the Casson number (0 B Ca B 20), when viscous dissipation is neglected and taken into account. The comparison between both geometrical configurations shows that, from a thermal point of view, it is more interesting to use parallel plates than a pipe. Keywords Generalized Casson fluid Á Viscous dissipation Á Yield stress Á Uniform wall temperature Á Finite volume method Á Nusselt number List of symbols a, b, c Constants of Eq. (12) Br Brinkman number, = l p U e 2 /k(T e -T w ) CaCasson number, ¼ s 0 D h l p U e C p Specific heat at constant pressure (J kg -1 K -1