Heat and Mass Transfer in Cooling Towers

The water side heat and mass-transfer
Define Lewis number :
Le hc hD c pa
By substitution Lewis number in above equation
Combining above equation with earlier equations, given below
Effect of Temperature Ratio on Tower Performance
Effect of Temperature Ratio on Tower Performance
Performance Vs Water Outlet Temperature
Effect of Temperature Ratio on Tower Size
The cooling tower effectiveness e is defined as the ratio of actual
energy to the maximum possible energy transfer.
•General correlations for heat and mass transfer of cooling towers in terms of physical characteristics do not exist. •It is usually necessary to correlate the tower performance data for specific tower designs. •Mass transfer data are typically correlated in the form
• tw,i= 35.0°C, • tw,o=30.0°C, • hi = 76.6 kJ/kg, and • mw /ma˙=1.00.
Selection of Process Parameters
Selection of Flow Velocities and Reynolds Numbers
• Then in the second step enthalpy of inlet air is increased by
a small amount (h+Dh).
• The resulting incremental change in water temperature is
calБайду номын сангаасulated by the equation:
• The heat and mass transfer coefficients hc, hc,w, and hD, required for calculating Le and NTU can be determined experimentally.
• Experimental values of the above coefficients, as functions of Reynolds number and packing parameters.
• On the other hand, in a typical rating problem the exit cooled water temperature is obtained given volume of the tower or NTU, water inlet temperature, inlet air dry-bulb temperature, inlet air wet bulb temperature and the mass flow rates of water and air.
The solution is iterative with respect to the air humidity ratio and temperatures (W, t, and tw)
Water operating line on enthalpy-temperature diagram
Complete Descriptions of Air-water System : The Complete System of Equations
Dtw
m a m wcw
Dh Wh f ,w
• Next, the state of saturated air in equilibrium with water temperature is calculated at this increased water temperature. •The procedure is repeated until we get the water temperature equal to the water inlet temperature.
Variation of Maximum Mass flow Ratio
Heat and Mass Transfer in Cooling Towers
P M V Subbarao Professor
Mechanical Engineering Department I I T Delhi
Loss Vs Cooling of Water….
The air side Mass transfer of water-vapor
where c and n are empirical constants specific to a particular tower design.
Multiplying both sides of the above equation by m w m a and considering the definition for NTU
The rate of change of enthalpy w.r.t. change in humidity.
The Driving Force for Heat and Mass Transfer
Using the approximation of constant cpa ,the driving force
This equation describes the condition line on the psychometric chart for the changes in state for moist air passing through the tower.
The Condition Line
• For given water temperatures (tw,i , tw,o),Lewis number (Le), inlet condition of air and mass flow rates, following equations are solved numerically for exit conditions of both the air and water stream.
Experimental and calculated values of cooling tower parameters
Design/Rating of Cooling Towers
• A classical problem of designing a cooling tower is to calculate the required tower volume or NTU, given the type of packing, the wet bulb temperature of the entering air, water inlet temperature, water outlet temperature and mass-flow rates of water and air.
The Tower Volume
• If the value of (hDAV) is known, the required tower volume may be obtained by using
•The integral in the above equation is solved numerically. •The number of transfer units of the tower are calculated by
• The designer of cooling towers should determine experimentally, the above coefficients based on the given packing geometry.
Case Study : Design Problem
Solution Method
• Initially inlet condition of air and the condition of saturated air in equilibrium with leaving water temperature are known.
• The quantity dh/dW is calculated.