Owing to the exponential dependence of the rate constant for most chemical reactions on temperature, heat transfer through the wall of a tubular chemical reactor is usually necessary to control the rate of reaction. Energetic reactions have been known for some time to affect the Nusselt number critically but prior results are fragmentary. New, coherent and essentially exact numerical results are presented for uniform heating in fully developed laminar and turbulent flow. These results reveal chaotic variations as well as unbounded and negative values. This behavior is explained on both mathematical and physical grounds. (c) 2007 Published by Elsevier Ltd.