For the prediction of chemical reactions in a premixed medium, the dissipation time scale of the concentration fluctuations and of the turbulent kinetic energy are crucial quantities. Nevertheless, in classical turbulent combustion models where these scales are taken into account, proportionality between these quantities is very often assumed, even when experimental studies show the ratio of the two scales is not constant and varies for different flows. Another means of calculating the dissipation time scale of a scalar (concentration, temperature) is to use a transport equation for the dissipation rate of the fluctuations of this scalar epsilon(gamma). In this study, the validity of the transport equation for unsteady turbulent flows with chemical reactions is considered. Moreover, an analysis of this equation based on ''order of magnitude'' arguments is also presented and demonstrates the predominance of the stretching and dissipation terms. Closure assumptions are proposed in the case of very fast chemical reactions introducing a laminar flame function. In the case of very high turbulent Reynolds number and very fast chemical reactions, the model leads to a new formulation of the well known Eddy Break-Up model, in which the rate u'/U(L) occurs, which represents the interaction between laminar flamelet and turbulence. Moreover, epsilon(gamma) can be connected to the flame surface per unit volume SIGMA and our study leads to a transport equation for SIGMA which is close to that of Marble and Broadwell in their ''coherent flame'' model. The equation for epsilon(gamma) is applied to the initial development and free propagation of a premixed spherical flame ignited at a point in a homogeneous turbulent medium. Information concerning the dissipation time scale of the concentration fluctuations through the flame front is also given. The model reproduces the experimental growth of flame kernel found by Abdel-Gayed et al. Further work is in progress with this model concerning more detailed studies of a propagating turbulent flame, in order to obtain a better assessment and improvements.