What role does air play in the cooling tower? Why heat transfer in the cooling tower is ‘ Adiabatic’?

Role of Air in the cooling tower - Basics

The most important points to remember

[1] Air has practically very small energy compared to water. Air's energy is its sensible heat. Air has no stored energy except a tiny amount of water it carries for example at 50RH at ambient temp which is < 0.01%. That is air's latent heat to share in HX like CT. Air acts as a sink in CT where water dumps its energy while cooling.

[2] Energy transfer takes place always in the direction from high energy to low energy

[3] Except sensible heat transfer between air and water which maybe just a few degc, air does not contribute energy for water evaporation.

[4] Water at a high state of energy and air at a low state of energy can’t remain together. Both become unstable when in contact with each other. They share their energy to reach equilibrium to become stable.

[5] When water is sprayed in CT some molecules which have high kinetic energy escape from water to the surrounding air. Unsaturated air is unstable until it gets saturated. Air like a magnet pulls those water into its stomach. This process of molecular diffusion of water molecules in the air goes on until air has a capacity at a given temp to absorb water. This is the driving force for water evaporation in CT

[6] Since air pulls water vapor, water pushes water molecules to meet this requirement until the air reaches wet bulb temp by supplying energy from its internal energy and cools. The point at which air has saturated, Gibbs free energy change =0. Both water and air reach a state of equilibrium.

Why heat transfer in cooling tower is Adiabatic?

 Two modes of heat transfer are involved in cooling towers, [1] evaporation and [2] convection. The rate of heat transfer by both convection and evaporation increases with an increase in an air-to-water interfacial surface, relative velocity, contact time, and enthalpy difference. When water and air are in intimate contact in a properly designed mass transfer packed column it is like one energy donor and one acceptor of energy sitting next to each. Both become unstable and like to come to a stable state. Water loses energy and air gains energy in the form transfer of water molecules from one to another,. Water molecules act as carriers of heat which water loses and air gains. The speed of water molecules which carry the enthalpy by convection from water to air is more than sound. It is about 500 m/sec. [see the image] The process takes place instantaneously internally and therefore the process is called adiabatic, with no heat coming or going outside the cooling tower. dQ=0, dH=dU. Water loses its internal energy and cools. H is enthalpy and U is internal energy.

The high diffusion coefficient of water in air supports adiabatic heat transfer

This is supported by the fact that water has a very high diffusivity constant in the air at ambient temperature and pressure. Water’s diffusion coefficient comes in 3rd position after H2 and NH3. Diffusivity, mass diffusivity, or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species In this case it is the concentration gradient of H2O between water and air, The higher the diffusivity (of one substance with respect to another), the faster they diffuse into each other. Please see the table.

Thermodynamics

Let me put the subject in a completely different way. Essentially a CT is a heat rejection device. Water and unsaturated air come in contact at a certain designed flow rate and velocity in a packed column at atmospheric pr and temp, remain in contact in the packed column for a designed amount of time, water cools and the air gets saturated at the practically same temperature and they exit.

There is no denying that water evaporates in CT. Question: Why can’t air provide the energy? Answer: Air has no energy to provide water unless bonds between nitrogen atoms or oxygen atoms break in CT. Air has neither sensible heat nor latent heat. At the point where air enters CT, the dT between air and water is just a few degc. Question: Then what does air really have? Answer: a huge capacity to absorb water. Since air has a huge capacity to absorb water say at normal 50 RH and ambient temperature, water can evaporate and cool. Just to give an example, typical evaporation of water in CT is about 1.5% [L/G=1] from water to air, this is equivalent to 0.015x1000 = 15 Btu/lb heat rejection by water, that is 15 degF cooling of water

This summarizes the role of air in CT to contribute to cooling.

So how does water cool?

Let us look at thermodynamic. You are running a process at constant temp [air temp may change by 1-2 degc, let us ignore that] P and T both inside CT are constant. So V has to be constant, dV=0. Water is non-compressible and can't do any mechanical work. Let us look at air, since dV=0, work done by air =0, therefore, air does not need to borrow any energy from water or outside surrounding for work.

In this whole thermodynamic process, if you look at the equation, dH = dU + PdV, PdV=0, dH = dU. H is enthalpy, U is internal energy. Therefore cooling in CT takes place in the same proportion as its internal energy reduces. Nether there is any energy-in nor any energy-out from the CT. Such thermodynamics process is called the 'Adiabatic process'

Then how would you finally define a CT? Answer: water does heat transfer by evaporation by losing its mass to cool while air facilitates the cooling by enabling the mass transfer process to go forward by acting as a sink. Thus one complement the other.