## 3 Model Development  
The cooling system, whose geometry is given in Figure 1, consists of two parts. The first of these is the pre- and post-cooled desiccant wheel part and the second is the room which is the cooled environment. For this reason, it is necessary to obtain both heat transfer (for temperature change) and mass transfer (for relative humidity change) models for both sections. Since the main purpose is to test the temperature and relative humidity control performance of the control strategy developed in the study, simple heat and mass transfer equations were used during the modeling, and a black box system modeling that produced the correct output for the given inputs was made. According to the results of the experimental study by [PERSON] et al. [18], temperature and relative variation models were obtained for both the room and the cooler in these models. In the model created for the temperature change of the atmospheric air taken into the cooler at the cooler outlet, firstly, a relation was established between the temperature of the air taken in the cooler and the speed of the fan. While extracting this relation, it is assumed that the initial temperature of the air taken into the cooler is equal to the atmospheric temperature. \[V_{fan}K_{conv}=T_{f}=T_{atm} \tag{1}\]  
where \(V_{fan}\), \(K_{conv}\), \(T_{f}\) and \(T_{atm}\) denote the speed of the fans, the coefficient, which is used for conversion from rpm to temperature, the temperature of the intake air, and the temperature of the atmospheric air, respectively. After that, this temperature is used to calculate heat  
Figure 1: A scheme of the proposed independent controlled pre-cooled desiccant cooling system. gained in the cooler due to this hotter intake air from the atmosphere. The gained heat is shown as:  
\[\frac{T_{f}}{R_{cooler}}=\frac{\partial Q_{f}}{\partial t} \tag{2}\]  
where \(R_{cooler}\) denotes the thermal resistance of the cooler. Then, the variation of the temperature in the cooler is determined as:  
\[\frac{\partial T_{cooler}}{\partial t}=\left(\frac{\partial Q_{f}}{\partial t }+\frac{\partial Q_{dist,c}}{\partial t}\right)\frac{1}{M_{air}c} \tag{3}\]  
where \(T_{cooler}\), \(Q_{f}\), \(Q_{dist,c}\), \(M_{air}\) and \(c\) represent the temperature of the air at the outlet of the cooler, the gained heat due to intake of atmospheric air, heat gained due to disturbing effects in the cooler such as convection and conduction from the cooler and other unknowns, the mass of air inside of the cooler and the heat capacity of the air, respectively. Finally, the relation between the fan speed and temperature variation of the air due to the cooling process is obtained. Thus, the temperature change process, which will be used in the control strategy for adjusting the cooling performance of the cooler by adjusting the fan speeds, is obtained. The fan in the room operates at the same speed as the other fans in order to ensure successful air circulation. For this reason, heat transfer takes place between the air at the temperature \(T_{cooler}\) at the cooler outlet fed to the room and the existing air in the room. This heat transfer continues until an equilibrium is established in the room. In addition, there are disruptive effects in the room that try to disrupt this balance. Heat gain from windows, doors and roofs, and heat gains from people and machines in the environment constitute these disruptive effects. While the cooling air supplied to the room tries to cool the room, the room air is forced to warm up due to these disruptive effects. This significantly affects the comfort of the room. With the effect of the cooler air at the cooler outlet fed to the room, the heat loss in the room air is compensated by Equation (4):  
\[\frac{T_{room}-\frac{T_{cooler}+T_{room}}{2}}{R_{room}}=\frac{\partial Q_{ cooler}}{\partial t} \tag{4}\]  
where \(T_{room}\), \(R_{room}\) and \(Q_{cooler}\) denote the temperature of the room air, the equivalent thermal resistance of the room, and heat losses, respectively.