Table 1.

Detailed form of the $\varphi$, ${\Gamma }_{\varphi }$, $S_{\varphi }$, and $S_{p\varphi }$ in Equation (1).

Equation type	$\varphi$	${\Gamma }_{\varphi }$	$S_{\varphi }$	$S_{p\varphi }$
Mass conservation equation	1	0	0	$\frac{\Delta m_d}{m_{d,0}}{\dot{m}}_{d,0}$
Momentum conservation equation in the x direction	$u$	$\mu$	$-\frac{\partial p}{\partial x}$	$\sum \left[\frac{3\mu C_D\mathrm{Re}}{4{\rho }_d{d}^2}\left(u_d-u\right)\right]{\dot{m}}_d\Delta t$
Momentum conservation equation in the y direction	$v$	$\mu$	$-\frac{\partial p}{\partial x}-\rho g$	$\sum \left[\frac{3\mu C_D\mathrm{Re}}{4{\rho }_d{d}^2}\left(v_d-v\right)\right]{\dot{m}}_d\Delta t$
Momentum conservation equation in the z direction	$w$	$\mu$	$-\frac{\partial p}{\partial z}$	$\sum \left[\frac{3\mu C_D\mathrm{Re}}{4{\rho }_d{d}^2}\left(v_d-v\right)\right]{\dot{m}}_d\Delta t$
Energy conservation equation	$T$	$\frac{\lambda }{c_p}$	0	$\frac{\overline{m_d}}{m_{d,0}}{c}_{p,d}\Delta T_p$