Propagation and extinction of gaseous premixed flames seeded with inert particles were analytically and numerically investigated for the one-dimensional, planar H_2/O_2/N_2 and CH_4/air flames, with particular interest on the joint effects of gas-particle heat conduction, gas―particle radiation heat loss, and gas―particle velocity lag. Analytical expressions were derived for the non-adiabatic particle-laden flame speed and the state of extinction allowing for the first two effects. These results reduce to the classical theories for the non-adiabatic particle-free flame and the adiabatic particle-laden flame in the limits of vanishing particle concentration and vanishing radiative heat loss, respectively. It is shown that small particles behave like a diluent gas and induce a flammability limit based on the particle concentration. For moderate particle size, there are multiple flame regimes and extinction points due to the combined effects of the gas―particle conduction heat transfer and radiative heat loss. For large particle size, the fast flame extinction limit is extended, while the slow flame regime is narrowed. Numerical calculations allowing for all effects show that the particle velocity lag greatly affects the flame speed and the state of extinction. Comparison of the numerical and analytical results with the literature experimental data shows good agreement for small particle size. It is emphasized that the existence of multiple solutions is an intrinsic feature of particle-laden flames.
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