  The role of viscous stress in heating of the fuel mixture in
deflagration-to-detonation transition in tubes is studied both analytically and
numerically. The analytical theory is developed in the limit of low Mach
number; it determines temperature distribution ahead of an accelerating flame
with maximum achieved at the walls. The heating effects of viscous stress and
the compression wave become comparable at sufficiently high values of the Mach
number. In the case of relatively large Mach number, viscous heating is
investigated by direct numerical simulations. The simulations were performed on
the basis of compressible Navier-Stokes gas-dynamic equations taking into
account chemical kinetics. In agreement with the theory, viscous stress makes
heating and explosion of the fuel mixture preferential at the walls. The
explosion develops in an essentially multi-dimensional way, with fast
spontaneous reaction spreading along the walls and pushing inclined shocks.
Eventually, the combination of explosive reaction and shocks evolves into
detonation.
