# How to Calculate Evaporation Rate and Surface Temperature of a Cylinder in Different Conditions

## a) What is the evaporation rate of water per unit length of the cylinder (kg/sm)?

To calculate the evaporation rate of water per unit length of the cylinder, we need to consider the heat and mass transfer occurring at the surface of the cylinder. Given the relative humidity of air (RH) = 20%, temperature of air (T∞) = 35°C, velocity of air (V) = 15 m/s, and diameter of the cylinder (D) = 20 mm, how can we determine the evaporation rate per unit length?

## b) After all the water is evaporated, what will be the temperature of the surface?

After a long period of operation where all the water is evaporated from the coating on the cylinder and its surface is dry, how can we estimate the temperature of the surface considering the same free stream conditions and heater power from part (a)?

## Answer:

Given the conditions provided for the cylinder and the air flowing over it, we can calculate the evaporation rate of water per unit length and the resulting surface temperature after all the water is evaporated.

In order to determine the evaporation rate of water per unit length of the cylinder, we need to apply principles of heat and mass transfer. By considering the relative humidity of the air, temperature of the air, velocity of the air, and diameter of the cylinder, we can utilize equations for convective heat transfer coefficients, Nusselt number, and mass transfer to calculate the evaporation rate.

Once all the water has evaporated from the coating on the cylinder, the surface temperature will approach the adiabatic wall temperature. This temperature can be estimated using the Blasius formula for turbulent boundary layers, taking into account the air temperature and velocity. Understanding these calculations allows us to predict the surface temperature after the water has completely evaporated.

Through these calculations and considerations, we can gain valuable insights into the evaporation process and resulting surface temperature of the cylinder under different conditions. By applying fundamental principles of thermodynamics and fluid mechanics, we can explore the dynamic behavior of the system and make informed predictions about its behavior.