Evaporative cooling is a prime example of simultaneous heat and mass transfer. When air flows over a wet surface, heat is transferred to the liquid, evaporating it, while evaporated moisture diffuses back into the free air stream.

Energy Balance at the Interface

Under steady-state conditions, sensible heat flux from the hot air to the water film balances latent heat flux carried away by evaporation:

\[h (T_\infty - T_s) = h_m h_{fg} (C_{A,s} - C_{A,\infty})\]

Where \(h\) is the convective heat transfer coefficient, \(h_m\) is the mass transfer coefficient, and \(h_{fg}\) is the latent heat of vaporization.

The Lewis Relation

For air-water systems, the Lewis relation states:

\[\frac{h}{h_m C_p} \approx 1\]

This allows wet-bulb temperature meters to read humidity values directly using simple thermometer readings.

References

  • Treybal, R. E. (1980). Mass-Transfer Operations. McGraw-Hill.