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The effects of flame stretch and thermal/molecular diffusion on the flame acceleration in channels are quantified by means of the analytical and computational endeavours. The internal transport flame properties are accounted in the theory by means of the Markstein number, Mk. Being a positive or negative function of the thermal-chemical combustion parameters, such as the thermal expansion ratio and the Lewis and Zeldovich numbers, the Markstein number either moderates or promotes the flame acceleration. While Mk may provide a substantial impact on the flame acceleration rate in narrow channels, this effects diminishes with the increase of the channel width. The analysis is accompanied by extensive computational simulations of the Navier-Stokes combustion equations, which clarify the impact of the Lewis number on the flame acceleration. It is obtained that, for Le below a certain critical value, at the initial stage of flame acceleration, a globally-convex flame front is splits into two or more "fingers", accompanied by a drastic increase in the flame surface area and associated enhancement of the flame acceleration. Overall, the thermal-diffusive effects substantially facilitate the flame acceleration scenario, thereby advancing a potential deflagration-to-detonation transition.