Rarefaction Effects in Small Particle Combustion

The unsteady-state energy conservation equation for a small spherical particle in LII modeling

“…The particle internal energy expression used by Hiers [20,21], (10), is consistent with this definition of specific heat, whether LIU et al The unsteady-state energy conservation equation for a small spherical particle in LII modeling 117 the specific heat c p is temperature dependent or not. However, the definition of specific heat, (11), is not recovered in the expression of K&H (u = c p T ) unless a temperature independent c p is assumed.…”

“…where u is the specific (per unit mass) particle internal energy, T ref and u ref are respectively the reference temperature and the specific particle internal energy at the reference temperature, which were set to 0 J and 0Krespectively in [20,21]. Equation (10) reduces to the expression used by K&H, (9), only under the assumption that the particle specific heat c p is temperature independent.…”

“…The effect of using these different expressions for the particle internal energy variation rate on the calculated particle temperature and diameter is shown later. It suffices to mention here that neither the expression of K&H, (6), nor that of Hiers [20,21], (12), for the particle internal energy variation rate is correct.…”

“…The specific heat c p is in general a function of T and is linked to the particle internal energy U,for example in a study of nano-sized soot particle combustion, Hiers [20,21], as…”

“…However, the definition of specific heat, (11), is not recovered in the expression of K&H (u = c p T ) unless a temperature independent c p is assumed. By allowing both the particle temperature and its mass (or diameter) to vary with time, Hiers [20,21] derives the particle energy conservation equation using the following expansion…”