Table 3.

Governing equations of discrete phase.

Mass equation	$\frac{d{m}_p}{dt}=-\dot{m}$
Momentum equation	$m_{\mathrm{p}}\frac{d{u}_{\mathrm{p}}}{dt}=-f_{\mathrm{D}}$
	$-f_{\mathrm{D}}=\frac{1}{8}\mathrm{\pi }{d}_{\mathrm{p}}^2\rho C_{\mathrm{D}}|U-U_{\mathrm{P}}|\left(U-U_{\mathrm{P}}\right)$
Energy equation	$m_{\mathrm{p}}{C}_{\mathrm{p}}\frac{d{T}_{\mathrm{p}}}{dt}=h_{\mathrm{i},conv}{A}_{\mathrm{p}}\left(T_{\mathrm{g}}-T_{\mathrm{p}}\right)+\sum \frac{d{m}_{\mathrm{p}}}{dt}{H}_{\text{reac}}+A_{\mathrm{p}}{\epsilon }_{\mathrm{p}}{\sigma }_{\mathrm{B}}\left(T_{\text{rad}}^4-T_{\mathrm{p}}^4\right)$