# Kinetic Models of Wood Biomass Drying in Hot Airflow Systems
## 4 Theoretical Predictive Research
For these calculations, they used mostly experimentally collected thermophysical data, the rest being obtained by literature review. The results obtained with their model were compared with those obtained by [PERSON]'s model (1966) [71] and those obtained experimentally. The model was based on:  
\[h_{m}=\frac{D_{w}\cdot Sh}{D_{h}}\]  
where \(h_{m}\) is the mass transfer coefficient (water), \(D_{w}\) is the water diffusion coefficient caused by the moisture gradient, \(Sh\) is the Sherwood number [31; 32; 33; 34; 72], and \(D_{h}\) is the hydraulic diameter (consecutive distance between two rows of samples). When comparing results between the model proposed by [73] and that of [PERSON], it was found that, although both models showed the same evolution in the moisture content of the sample throughout the drying process, the differences in the evolution of temperature were wide. It should be noted that the proposed model did not take into account factors such as the hygroscopic and non-hygroscopic domains of the adult species [71]. This model is still used in recent studies of drying but needs to improve due to significant deviations [12]. Some authors have introduced a new factor to their research on the drying process, namely the porosity of the material. Thus, [PERSON] et al. (2009) [74] investigated the impact of pore size distribution on heat and moisture transfer in porous materials during drying. For this purpose, they used both theoretical and experimental approaches and estimated moisture transfer coefficients from them. Thus, the diffusivity of water (\(D_{W}\)) was estimated as:  
\[D_{w}=\frac{\sigma_{w}}{\eta_{W}}Kx^{3}=(1.604T-394.3)Kx^{3}\]where \(\sigma_{w}\) is the surface tension of water, \(\eta_{w}\) is the viscosity of water, and \(K\) is the transfer constant of water. Both \(\sigma_{w}\) and \(\eta_{w}\) depend on the temperature, while \(K\) depends on the pore structure. \(T\) is the temperature of the material. [PERSON] et al. (2009) [PERSON] et al. (2009) analysed the trend that when the sum of convection and radiation heat at the surface of the material is greater than the conduction into the mass, evaporation of moisture at the surface of the material begins and the surface temperature increases. In the first period, the following equations are fulfilled. First, the heat used in the evaporation of water at the surface is equal to the heat received by convection plus the heat received by radiation minus the heat transferred to the interior of the part by conduction. \[\dot{m}_{w}\cdot\dot{A}_{w}=q_{conv}+q_{rad}-k\,\frac{dT}{dr}\bigg{]}_{r=R}\]  
Only when the core temperature reaches the surface temperature does the evaporation rate \(\dot{m}_{w}\) become constant. On the other hand, the flux of water in the interior of the mass and the evaporated water at the surface is equivalent:  
\[\dot{m}_{wi}=\dot{m}_{w}\]  
\[\dot{m}_{air}\cdot[(Cp_{air}\cdot T+\omega\cdot(\lambda+Cp_{steam}\cdot T))-( Cp_{air}\cdot T_{1}+\omega_{air1}\cdot(\lambda+Cp_{steam}\cdot T_{1}))]=K\cdot A \cdot h_{w}\cdot(x-x_{e})+h\cdot A\cdot(T-T_{b})\]0  
In the second stage, if there is no local moisture present at the surface (moisture content below critical), the internal water flux \(\dot{m}_{wi}\) cannot become equal to \(\dot{m}_{w}\), and the evaporation plane \(\delta\) moves inwards into the material. The value of \(\dot{m}_{w}\) decreases because the thermal resistance in the dry region of the material increases, starting the period of decreasing drying rate. At this stage, the heat received by convection and radiation from the surface is equal to the heat dissipated by conduction into the mass. The plane of desiccation recedes inwards away from the surface. In this plane, a part of the heat received by conduction from the surface is transferred to the evaporating water, and another part is also transferred inwards by conduction.