## 2 Materials and Methods
### Computational Modeling  
The mesh quality is very important to get accurate data and computational convergence. Thus, due to the geometric complexity of the scale model of CBP barn, it was opted to utilize the ANSYS ICEM CFD(r) software for construction of a tetrahedral computational mesh, which allows for obtaining results with fewer errors [22]. Several meshes with different levels of refinement were evaluated to adopt one that provides a balance between computational time and accuracy.  
Airflow rates are associated with turbulent flows and combined with heat transfer rates, generating a complex system of coupled equations difficult to resolve. Therefore, the CFD technique was utilized to solve the average Navier-Stokes and energy equations, determining velocity, temperature and pressure by the finite volume technique. The general model for non-isothermal fluid flow is described by equation of mass, continuity, energy and species transport, simplified as follows [23].  
\[\frac{\partial\rho}{\partial t}+\
abla\cdot(\rho U)=0 \tag{2}\]  
\[\frac{\partial(\rho U)}{\partial t}+\
abla\cdot(\rho UU)=\
abla p+\left[\mu_{ \tau}(\
abla U+\
abla U^{T})\right] \tag{3}\]  
Figure 5: Diagram of modeled and simulated scale model of compost bedded pack (CBP) barn.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Location** & **Boundary Condition** & **Value** \\ \hline \multirow{3}{*}{1} & \multirow{3}{*}{Inlet} & Average air speed & 0.1 m s\({}^{-1}\) \\  & & Air temperature & 22.0 \({}^{\circ}\)C \\  & Outlet & Atmospheric pressure & 101.325 kPa \\  & Floor & Temperature of surface compost & 30.0 \({}^{\circ}\)C \\ \hline \multirow{3}{*}{2} & \multirow{3}{*}{Inlet} & Average air speed & 1.0 m s\({}^{-1}\) \\  & & Air temperature & 22.0 \({}^{\circ}\)C \\ \cline{1-1}  & Outlet & Atmospheric pressure & 101.325 kPa \\ \cline{1-1}  & Floor & Temperature of surface compost & 30.0 \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table}
Table 3: Boundary conditions utilized in the computational fluid dynamics (CFD) model.  
\[\frac{\partial\big{(}\mathrm{C_{P}T}\big{)}}{\partial t}+\
abla\big{(}-kVT+\rho C_{ \mathrm{p}}TU\big{)}=0 \tag{4}\]  
\[\frac{\partial\mathrm{C_{A}}}{\partial t}+\mathrm{U\cdot}\
abla\mathrm{C_{A}}= \
abla\mathrm{\cdot}(DVC_{A}) \tag{5}\]  
where, \(\rho\) is the specific mass (kg m\({}^{-3}\)); t is the time (\(s\)); U is the velocity field; p is the pressure (N m\({}^{-2}\)); \(\mu_{\tau}\) is the dynamic viscosity of the fluid (kg m\({}^{-1}\) s\({}^{-1}\)); T is the temperature (K); C\({}_{\mathrm{p}}\) is the specific heat (W kg\({}^{-1}\) K\({}^{-1}\)); k is the thermal conductivity (W m\({}^{-1}\) K\({}^{-1}\)); C\({}_{A}\) is the concentration of specie A (g m\({}^{-3}\)) and D is he diffusion coefficient (m\({}^{2}\) s\({}^{-1}\)).  
The Reynolds tensor was modeled using standard \(k-\varepsilon\) model, which evaluates turbulent viscosity (\(\mu_{\tau}\)) from the ratio between turbulent kinetic energy (\(k\)) and dissipation of the turbulent kinetic energy (\(\varepsilon\)). The ANSYS CFX(r) software was used to simulate the propose model. It belongs to the Federal University of Vicosa (Vicosa, Minas Gerais, Brazil). The following considerations were assumed: (a) steady state, (b) incompressible flow, (c) turbulent flow and (d) residue level of \(10^{-4}\) was adopted as a convergence criterion.