  A theoretical analysis is developed to investigate the effects of gas
expansion due to heat release on unsteady diffusion flames evolving in a pipe
flow in which the mixing of reactants is controlled by Taylor's dispersion
processes thereby extending a previously developed theory based on the
thermo-diffusive model. It is first shown that at times larger than radial
diffusion times, the pressure gradient induced by the gas expansion is, in the
first approximation, small in comparison with the prevailing pressure gradient
driving the flow, indicating that corrections to the background velocity
profile are small. The corrections to the velocity components along with the
leading-order mixing variables such as the concentrations, temperature and
density are solved for a Burke-Schumann flame. Due to the dependence of the
effective Taylor diffusion coefficients on the gas density, quantitative and
sometimes qualitative departures in predictions from the thermo-diffusive model
are observed.
