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

This paper discusses the formalization of the energy variation rate of a small particle encountered in the modeling of an unsteady-state soot particle temperature and diameter during laser-induced incandescence. A derivation of the particle energy equation is presented based on the first law of thermodynamics applied to an open system. Problems associated with an incorrect particle internal energy variation rate used in the literature are discussed. Numerical calculations are presented to demonstrate the effects of several incorrect particle internal energy variation rates on the calculated particle temperature and diameter.