A Walk in the Sun. Consider a poor lost soul walking at 5 km/h on a hot day in the desert wearing only a bathing suit. This person's skin temperature tends to rise due to four mechanisms: Challenge Problems 609 (i) energy is generated by metabolic reactions in the body at a rate of 280 W, and almost all of this energy is converted to heat that flows to the skin; (ii) heat is delivered to the skin by convection from the outside air at a rate equal to k'Askin (Tair - Tskin), where k'is 54 J/h. Co m2 the exposed skin area Askin is 1.5 m2, the air temperature Tair is 47°C, and the skin temperature Tskin is 36°C; (iii) the skin absorbs radiant energy from the sun at a rate of 1400 W/m2 ; (iv) the skin absorbs radiant energy from the environment, which has temperature 47°C.
(a) Calculate the net rate (in Watts) at which the person's skin is heated by all four of these mechanisms. Assume that the emissivity of the skin is e = 1 and that the skin temperature is initially 36°C. Which mechanism is the most important?
(b) At what rate (in µ/h) must perspiration evaporate? From this person's skin to maintain a constant skin temperature (The heat of vaporization of water at 36°C is 2.42 X 106 J/kg.)
(c) Suppose instead the person is protected by light-colored clo1hlug (e = 0) so that the exposed skin area is only 0.45 m2 • what rate of perspiration is required now? Discuss the usefulness of the traditional clotting worn by desert peoples.