The Evaporative Head-Cloth Ceiling: A Humidity Bound on the Cooling a Wetted Head and Neck Wrap Can Deliver

Wetting a cloth and wrapping it around the head and neck is one of the most widely used heat remedies in the world, and one of the least quantified. This paper derives a bound on what such a cloth can deliver. Evaporation from a fully wetted wrap of 0.08 m² is modelled with a mass-transfer coefficient obtained from the heat–mass transfer analogy, with the cloth surface held at the wet-bulb temperature. Cooling is called useful only if the gross evaporative power reaches 15 W, about the resting heat production of the head itself. At 35 °C in a light walking breeze of 1.0 m/s, the cloth delivers 17.6 W at 10% relative humidity and 14.49 W at 30%, so the humidity ceiling for useful cooling is 27% relative humidity: above 27% the remedy no longer meets the useful threshold at that temperature and airflow. In still air (0.2–0.5 m/s) the cloth never reaches 15 W at 30 °C or 35 °C at any humidity. A stronger breeze of 2.0 m/s raises the ceiling to 47% relative humidity at 35 °C and to 54% at 40 °C. Where the cloth is useful it is cheap in water: 21.5 ml per hour at 35 °C and 30% relative humidity, and a 250 ml wetting lasts about 698 minutes of evaporation at that rate. A plain hat of equal stated cost, by contrast, saves a humidity-independent 9.8 W of solar load; the cloth's gross power falls below the hat's saving above 52% relative humidity at 35 °C and 1.0 m/s. The plain statement of the result is that the wet cloth is a dry-air remedy: in humid heat, or in still air, it stops working as a cooling device, however wet it is kept, and shade is worth more.