A mathematical model for microbial growth is presented which combines a Michaelis-Menten kinetics for oxygen and a substrate inhibition kinetics of the Haldane-type of phenol. It is applied to flow calorimetric experiments of the growth of Pseudomonas putida on phenol and other aromatic compounds. The model describes features of the growth well and makes unexpected predictions which have been experimentally verified and compared with as yet unexplained observations from the literature. Possible applications to batch and flow calorimetric investigations of microbial growth are discussed with respect to the critical evaluation of the chosen instrumental set-up.