Boundary conditions constitute one of the key factors influencing combustion in chambers with large aspect ratios such as narrow channels or pipes. Specifically, the flame shape and propagation velocity are impacted by wall friction and wall heat transfer. Both factors continuously influence the shape of the flame front, thereby resulting in its larger surface area as compared to a planar flame front. Such a corrugated flame consumes more fuel per unit time and thereby propagates faster than the planar flame at the same thermal-chemical conditions. Consequently, a flame accelerates due to the boundary conditions. In the recent years, there have been many studies scrutinizing the role of boundary conditions in flame acceleration scenario by means of analytical formulations, numerical studies or experimental measurements. However, the majority of these works was limited to equidiffusive flames, where the thermal-to-mass diffusivity ratio (the Lewis number; Le) is unity. In this respect, the present work removes this limitation by analyzing non-equidiffusive (Le < 1 or Le > 1) flames propagating in pipes of various widths. Specifically, a parametric study has been conducted by means of simulations of the basic hydrodynamic and combustion equations. In this particular study, two-dimensional channels with smooth walls and different thermal conditions such as isothermal and adiabatic walls, have been employed for various Lewis numbers in the range 0.2 ≤ Le ≤ 2.0, and for various Reynolds number associated with the flame propagation in the range 5 ≤ Re ≤ 30. As a result, a strong coupling between the wall conditions and the variations of the Lewis and Reynolds numbers is demonstrated. Specifically, it is observed that the increase in the Lewis number results in moderation of flame tip acceleration. It is also found that there is a change in the burning rate and surface area of the flame front at the lower Lewis numbers, where flames appear unstable against the diffusional-thermal flame instability. Moreover, a substantial difference between the cases of isothermal and adiabatic wall conditions is demonstrated.