Wet bulb temperature is the temperature at which the rate of heat transfer from the gas is equal to the vapor of the liquid. This is done at equilibrium state. This concept is seen when a stream of gas (not saturated) is passed over a liquid surface, the temperature of the gas is increased while the temperature of the liquid is decreased. The wet bulb temperature is achieved at a steady state and at adiabatic state; condition in a continuous passage of gas. At wet bulb temperature, the rate of heat transfer from gas to liquid is represented as:
Where Q is the heat flow in the system
h is the coefficient of heat transfer
θ is the temperature of the gas
θw is the temperature of water
A is the area for heat transfer
If the contact area between the gas and liquid is small; gas flow-rate is high, the humidity and temperature of the gas stream is unchanged. It should be noted that the evaporation of liquid into the gas is diffusion process. At the interface; the diffusion is caused by concentration difference (Cv-Cg).Where Cv and Cg is the concentration of vapor and the content surface. Therefore evaporation rate is given as:
Also, at wet bulb temperature, the rate of heat transfer can be equated to produce of rate of rate of vaporization and sum of the latent at the temperature of the gas. Therefore, introducing this concept together with the partial pressure operating in the system; in relation to humidity, we have
Where λ is latent heat of vaporization of the liquid, h and hD are film dependent. For a water air system, h/hDρA is approximately equal to one.
ADIABATIC SATURATION TEMPERATURE
When a curve of humidity is plotted against temperature for gases, adiabatic cooling is obtained.
Adiabatic saturation temperature results when a continuous passage of gas in the system leads to a gradual decrease in heat relative to the heat of the evaporated liquid. The system must be insulated. At saturation, S= h/hDρA which for most water-vapor system equals 0.047 and humidity is low.
Coulson and Richardson’s chemical engineering. Sixth edition (volume 1) by pergamon press (1999). ISBN 0750644443