The objective of this study is to explore a runaway mechanism for deflagration-to-detonation transition in narrow channels in the framework of a novel one-dimensional model. The proposed mechanism relies solely on the temperature sensitivity of the flame speed and the increase of flame surface in narrow channels. Results obtained from the numerical integration of the reactive Navier-Stokes equations for ideal gases with a single-step chemicalkinetics model are compared with the solution obtained when considering the flame as a discontinuity. The results show that the double feedback loop established by this model can cause a flame velocity runaway within a finite time. This finite-time singularity is likely to lead to the formation of the strong shock wave that triggers the onset of a detonation.