# Thermal Evaluation of a Hybrid Dryer with Solar and Geothermal Energy for Agroindustry Application
## 1 Introduction
### Hybrid Dryer Sizing  
#### 1.1.1 Drying Chamber (Solar Energy as Main Source)  
Prior to the design of the experimental prototype, it is necessary to consider the following significant parameters that will influence the operation of the dryer to reach an acceptable efficiency of 40 to 50% of energy saving and obtain a uniformly dehydrated product [6; 7; 8]. * Product: thickness, drying temperature, wet weight, drying speed diagram, dry weight, thermal conductivity, dry-Bulb humidity, and drying time;
* Solar energy resources in the area;
* Dryer: dryer type, length, total area, construction material, material conductivity, wall thickness, heat transfer coefficient by convection, radiation, and conduction;
* Heat transfer mechanism: temperature, hot air humidity, speed, saturated air humidity, flow conditions (laminar or turbulent), latent vaporization heat, tray area, and conduction heat transfer coefficient in the trays;
* Variables associated with thermal operation: energy consumption, drying efficiency, and dryer efficiency;
* Handling and easy construction; and
* Cost of investment and operation. The design of the tray dryer will have a drying capacity of 7 kg. Metallic materials for the construction of the side walls and floor are intended, and the front wall and ceiling will be made of transparent polycarbonate plates (0.6 cm thickness of the plate). The transparent material will allow us to take advantage of the solar irradiation of the day, bringing heat to the system. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Drying Capacity (kg)**} & **Electricity** & **Electricity** & **Industrial LPG** \\  & **Consumption (kW)** & **Consumption (dollars)** & **Consumption (dollars)** \\ \hline
909–1363.6 & 437.5 & $50 & $150 \\
1363–1818 & 500 & $75 & $250 \\
1363.6–1818 & 640 & $190 & $500 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Estimate of electricity and industrial LPG consumption. To calculate the total energy needed to evaporate 45% of the product's water content, the methodology of the analysis of heat loss and gain in the chamber was used as well as the analysis of mass and heat transfer to the product [6; 7]. The total energy used, \(Q_{T}\) is determined by the summation of all losses and energy consumption in the form of heat needed by the chamber from its pre-heating, the evaporation of the product water, and loss of heat by the walls (structure) until the renewal of the air inside the drying chamber [8; 9]. \[Q_{T}=\sum Q_{1-6} \tag{1}\]  
Initial heating of the equipment \(Q_{1}\) (kcal)  
\[Q_{1}=\ V_{prod}\ d_{prod}\ X_{i}C_{p,\ prod}(T_{a,\ c}-T_{a}) \tag{2}\]  
where \(V_{prod}\) is the product volume; \(d_{prod}\) is the product density; \(T_{prod}\) is the product temperature; the material specific heat \(C_{p,prod}=0.265+0.001\)Tproduct (kcal/kg \({}^{\circ}\)C); \(X_{i}\) is the initial air humidity; \(T_{ac}\) is the heating temperature (\({}^{\circ}\)C); and \(T_{a}\) is the initial air temperature (\({}^{\circ}\)C). Heat required to raise the air temperature inside. \(Q_{2}\) (kcal)  
\[Q_{2}=\ V_{a,\ c}\ d_{a,\ c}\ C_{p,\ a,\ c}(T_{a,\ c}-T_{a}) \tag{3}\]  
where \(V_{a,c}\) is the camera volume (m\({}_{3}\)); \(d_{a,c}\) is the air density (kg/m\({}^{3}\)); and \(C_{p,\ a,c}\) is the specific heat of the air (kcal/kg C). Heat needed for water evaporation. \(Q_{3}\) (kcal) [10]. \[Q_{3}=\ V_{prod}.\ d_{prod}.(X_{i}-\ X_{f})\lambda_{w}+5\ (kcal/kg)*V_{prod}.\ d_{prod}. \tag{4}\]  
where \(V_{prod}\) is the product volume; \(d_{prod}\) is the product density; \(X_{i}\) is the initial air moisture content; \(X_{f}\) is the final air moisture content (kg water/kg dried air); and \(\lambda_{w}\) is the latent heat of evaporation (kcal/kg). Heat lost by structure \(Q_{4}\) (kcal)  
\[Q_{4}=\ U\ A(T_{a,\ c}-T_{a}) \tag{5}\]  
where \(U\) is the overall heat loss ratios determined by the convection coefficients \(hi\) and \(he\) (W/m\({}^{2}\) K); conduction \(k\) (W/m K) and radiation \(hr\) (W/m\({}^{2}\) K); \(U=1/(1/hi+e/k+1/(he+hr))\).