  The paper presents an analytical theory quantitatively describing the
heterogeneous combustion of nonvolatile (metal) particles in the
diffusion-limited regime. It is assumed that the particle is suspended in an
unconfined, isobaric, quiescent gaseous mixture and the chemisorption of the
oxygen takes place evenly on the particle surface. The exact solution of the
particle burn time is derived from the conservation equations of the gas-phase
described in a spherical coordinate system with the utilization of constant
thermophysical properties, evaluated at a reference film layer. This solution
inherently takes the Stefan flow into account. The approximate expression of
the time-dependent particle temperature is solved from the conservation of the
particle enthalpy by neglecting the higher order terms in the Taylor expansion
of the product of the transient particle density and diameter squared. Coupling
the solutions for the burn time and time-dependent particle temperature
provides quantitative results when initial and boundary conditions are
specified. The theory is employed to predict the burn time and temperature of
micro-sized iron particles, which are then compared with measurements, as the
first validation case. The theoretical burn time agrees with the experiments
almost perfectly at both low and high oxygen levels. The calculated particle
temperature matches the measurements fairly well at relatively low oxygen mole
fractions, whereas the theory overpredict the particle peak temperature due to
the neglect of evaporation and the possible transition of the combustion
regime.
