# Hot Air and Microwave Combined Drying of Potato Monitored by Infrared Thermography
## 3 Results
However, at the end of drying, the surface temperature decreases when the product already has low moisture. Figure 3: Emissivity in the HAD treatment with regard to (**a**) moisture on a dry basis and (**b**) IR energy emitted by the sample. In order to understand the phenomena that occur at the sample/air interface, it is necessary to calculate the thermal energy consumed on the potato surface. The convective heat that the surface receives is used to evaporate the water that has reached the sample surface and to heat this interface. Therefore, the thermal energy expended in evaporation (\(Q^{V}\)) is estimated as (see Equation (1)):  
\[Q^{v}=\frac{\Delta M_{w}\cdot\Delta G^{v}}{S\cdot\Delta t} \tag{1}\]  
where \(\Delta M_{w}\) is the water loss (g) in \(\Delta t\) time (s), \(\Delta G^{v}\) is the latent heat of water (J/g) and \(S\) is the sample surface (m\({}^{2}\)). The thermal energy consumed by surface heating (\(Q^{U}\)) will depend on the increase in surface temperature, the heat flowing to the inside of the sample by conduction (\(q^{cl}\)), the specific heat of the sample and the sample mass. The relation between the thermal energy consumed in the interface and the heat flowing to the inside of the sample by conduction can be expressed as follows (see Equation (2)):  
\[Q^{U}-q^{cl}=\frac{\Delta T\cdot M\cdot C_{P}}{S\cdot\Delta t} \tag{2}\]  
where \(\Delta T\) is the surface temperature variation in \(\Delta t\) time, \(M\) is the mass of the sample (g) and \(C_{P}\) is the specific heat of the potato, estimated with the water and starch mass fraction (kJ/kgK). If this calculation is carried out, the thermal energy relation oscillates between 3% and 0.1% of the heat consumed by evaporating water, making it practically negligible. On the other hand, the heat that reaches the surface can be estimated by the following equation:  
\[q^{cv}=h\cdot S\cdot(T^{e}-T^{s}) \tag{3}\]  
Figure 4: Evolution of surface temperature in the HAD treatment (\(\blacksquare\)), HAD + 4 W/g treatment (A) and HAD + 6 W/g treatment (\(\ast\)). where \(q^{cp}\) is the heat by the convective mechanism (W), \(h\) is the individual coefficient of heat convection (W/m\({}^{2}\)K), \(T^{c}\) is the external or air-drying temperature (\({}^{\circ}\)C) and \(T^{S}\) is the surface or interface temperature (\({}^{\circ}\)C). In the case of the HAD treatment, the energy consumption in the interface is equal to the heat received by convection; therefore, it is possible to calculate the individual coefficient of heat convection using the following equation:  
\[h=\frac{Q^{p}+Q^{U}-q^{cd}}{S\cdot(T^{c}-T^{s})} \tag{4}\]  
where \(T^{c}\) is the air-drying temperature (\({}^{\circ}\)C), \(T^{S}\) is the surface temperature (\({}^{\circ}\)C), \(Q^{U}-q^{cd}\) is estimated using Equation (2) and \(Q^{V}\) is estimated using Equation (1). Figure 5 shows the individual coefficient of heat convection estimated by Equation (4) for the HAD treatment. In Figure 5a, it is possible to observe how h increases exponentially when the interface reaches the air-drying temperature. The same occurs in Figure 5b, where the h evolution increases with the treatment time, and the external resistance of heat transmission can be neglected after approximately 230 min. The individual coefficient of heat convection will depend on the turbulence and the interface temperature; thus, it is possible to apply the relation between h and the surface temperature to obtain the h evolution in HAD-MW combined treatments. Furthermore, h can be defined by the relation between the thermal conductivity of air and the boundary layer depth. The air thermal conductivity can be estimated with the water mass fraction in air, calculated with the thermodynamic properties of air [11]. Thus, the boundary layer depth can be estimated as follows:  
\[\delta^{BL}=\frac{k_{air}}{h}=\frac{k_{dry\ air}\cdot(1-x_{v})+k_{w}\cdot x_{v} }{h} \tag{5}\]  
Figure 6a shows the variation of water and dry air thermal conductivity with the temperature needed in Equation (5).