Nanjing Univ, Dept Astron, Nanjing 210093, Peoples R China
; Chinese Acad Sci, Inst High Energy Phys, LCRHEA, Beijing 100039, Peoples R China
In previous works, a generic dynamical model has been suggested by Huang. et al., which is shown to be correct for both adiabatic and radiative blast-waves, in both ultra-relativistic and non-relativistic phases. In deriving their equations, Huang et al. have assumed that the radiative efficiency of the fireball is constant. They then applied their model directly to realistic cases where the radiative efficiency evolves with time. In this paper, we abandon the above assumption and re-derive a more accurate dynamical equation for gamma-ray burst remnants. Numerical results show that the model presented by Huang et al. is accurate enough in general cases.