Equations
$m_{i} c_{p, i} \frac{d T_{i}}{d t} = \sum_{j} Q_{i, j} + Q_{f, i}$	(8)
$\frac{\partial (ε ρ_{f})}{\partial t} + \nabla \cdot (ε ρ_{f} u_{f}) = 0$	(9)
$\frac{\partial}{\partial t} (ρ_{f} ε c_{f} T_{f}) + \nabla \cdot (ρ_{f} ε u_{f} c_{f} T_{f}) = - \nabla \cdot [- c_{f} \frac{μ_{f}}{σ_{T}} \nabla T_{f}] + \sum_{i = 1}^{n} Q_{f, I}$	(10)
$Q_{f, i} = h_{c o n v} A_{i} (T_{f} - T_{i})$ heat transfer coefficient $h_{c o n v} = N u_{i} λ_{f} / d_{p}$ .	(11)
$Q_{i, j} = h_{i, j} (T_{j} - T_{i})$	(12)
$h_{i, j} = 2 λ_{p} {[\frac{3 f_{n} r^{}}{4 E^{}}]}^{1 / 3}$	(13)
$\begin{matrix} f_{d r a g, i} = v_{i} β (u_{f} - u_{s}) / (1 - ε) \\ ε = 1 - \frac{\sum_{i = 1}^{n} V_{i}}{Δ V} \end{matrix}$	(14)
$β = {\begin{array}{l} 150 \frac{{(1 - ε)}^{2}}{ε^{2} d_{p, i}^{2}} + \frac{1.75 (1 - ε) ρ_{f}}{ε d_{p, i}} \| u_{f} - u_{s} \| \\ \frac{3}{4} C_{D r a g} \frac{(1 - ε) ρ_{f}}{d_{p, i}} \| u_{f} - u_{s} \| ε^{- 2.65} \end{array}$	(15)
$\begin{matrix} R e_{i} < 2 \times 10^{4} ε = 0.26 - 1 \\ N u_{t u r b} = [0.037 {(R e_{i} / ε)}^{0.8} P r] / [1 + 2.443 {(R e_{i} / ε)}^{- 0.1} (P r^{2 / 3} - 1)] \end{matrix}$	(16)