Heat and mass transfer properties of counter flow wet cooling tower are obtained through the balance of mass and energy equations. The assumptions made for deriving the governing equations are listed below [14, 15]:

• Heat and mass transfer take place only normal to the flow direction.

• Heat transfer to the environment through the walls are negligible.

• Heat transfer from cooling-tower fan is negligible.

• Specific heats of water and dry air are constant.

• Heat and mass transfer coefficients are constant throughout the tower.

• Water lost by drift is negligible.

• Water temperature is uniform at each section of the tower.

• Cross-sectional area of tower is constant

Mathematical equations

Consider a counter-current cooling

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For the given values; water temperatures at the inlet and outlet , water to air mass flow rate, wet and dry inlet air temperatures , the cross-section area of the cooling tower , and the cooling tower characteristic , the governing equations for air and water outlet temperatures must be solved numerically. Calculations start from the bottom of the tower and by doing the same procedure at each section continues toward the end of the tower. Variations in air enthalpy, , and the absolute humidity ratio, , can be obtained using equations (4-5). Therefore, can be calculated from eq (6).

The relation for water mass flow rate, which decreases continuously from the top to the bottom of tower due to evaporation, can be written

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Since is unknown at the bottom of the tower (at H=0), an initial guess for at the bottom of the tower is used. An iterative procedure is performed until the difference between the calculated value and the value obtained by experiments for inlet water flow rate is within the defined tolerance. The solution procedure is shown in fig 5. Figure 5- flowchart of the solution procedure

Exergy calculations

Specific exergy in cooling tower process, like other psychrometric processes, comprises two parts of chemical exergy and thermo-mechanical exergy: (8)

Specific thermo-mechanical exergy is expressed as: (9) where are enthalpy and entropy in defined temperature, respectively, and are enthalpy, entropy, and temperature at the dead-state condition.

For an ideal gas and constant specific heat, the relation may be written as[5]: (10)

Specific exergy for a mass transfer process is expressed as [17]: (11)

In which are mole fraction, and the chemical potential in restricted dead state and environmental conditions, respectively.

Therefore, combining equations (9) and (11), the specific exergy is: