A numerical study of the propagation of regular detonation waves is conducted in the context of narrow channels undergoing strong wall confinement. To deal with shock waves, chemical reactions, heat and viscous stresses, a high-order Navier-Stokes solver based on Weighted Essentially Non-Oscillatory (WENO) scheme, coupled with the Strang splitting method, is used in the framework of multi-species reacting mixtures. Results show that the wall dissipative effects decrease the speed of the detonation wave compared to the Chapman-Jouguet (CJ) detonation velocity. In addition, the multidimensional results reveal that the development of the thermo-diffusive boundary layers behind the leading shock wave induces an expansion flow, which then determines the contour of the sonic envelope. From the Master Equation and the generalized CJ condition, which are derived and compared to the results of the current simulations, the main energy withdrawals are found to be related to the streamline divergence as well as to the growth of the boundary layer. Moreover, a fraction of the released energy is trapped in the vicinity of the wall and does not contribute to drive the shock front. The influence of the channel height is also investigated. It was found that the transverse instabilities are damped when the channel is scaled down, which results in an increase of the dissipative effects. Finally, the validity of the Fay model is discussed with regard to the channel height and the curvature of the detonation front.