Latvian Maritime academy

Figure 1. Multi-zone air-conditioning systems [11]Mathematical ModelBasic expressions like humidity balance, energy balance and velocity balance equations are used forthe establishment of the mathematical model.Humidity balanceThe sum of humidity of entering air and water vapor given to the system is equal to the sum ofhumidity of exiting air and difference of humidity in the chamber. Mathematically speaking, equation ofhumidity is represented as follow [12]:dw1 (1)K1TWm K2fkTW Av( W 0,622)dt V R w W 0,378K , K , K (2)a k k1 2 30,622 P TkWk TkWkEnergy balanceIt is considered that difference between the energy input to the control volume and energy outputfrom the control volume represents energy gain or loss. The change of energy is defined as subtraction ofair enthalpy leaving the control volume and heat escapes from the control volume walls from the sum ofheat given by the heater to control volume, enthalpy of the air given to the control volume and watervapor enthalpy given for moisturizing. If the temperature is mathematically obtained from balance ofenergy, then we get the following expression [12]:15