When viscous dissipation effects are important in duct flows the Brinkman number is widely used to quantify the relationship between the heat generated by dissipation and the heat exchanged at the wall. For Newtonian laminar fully developed pipe flow the use of the classical expression for this dimensionless group is appropriate, but under different conditions it can lead to misleading conclusions, such as when comparing flows through different cross-section ducts, flow regimes and mainly non-Newtonian flows. in this work a generalized Brinkman number is proposed, based on an energy balance for the power that allows proper quantification of viscous heating effects and reduces to the dissipated by friction, classical definition in laminar Newtonian pipe flow. The advantages of the new definition are shown and expressions are given for generalized Brinkman numbers in the most common cases. (C) 2008 Elsevier B.V. All rights reserved.