Question

On a windy day, we can define the wind-chill temperature T_wc as the air temperature that would give the same rate of heat loss if experienced on a calm day. Consider a day when the air temperature is 2°C and the wind speed is 12 m/s, giving a convective heat transfer coefficient of 45 W/m²⋅K (compared with 10 W/m²⋅K on a calm day). Assume a person has a 3 mm layer of skin (k = 0.37 W/m⋅K), a body surface area of 1.9 m²,clothing equivalent to 25 mm-thick cotton (k=0.06 W/m⋅K), and a body temperature of 37°C below the skin. Thermal radiation can be neglected.

a)Draw a thermal resistance network that represents the total heat transfer between the body’s internal temperature and the surroundings. Compute all thermal resistances (per unit area) for both the calm and windy days.You may ignore thermal radiation.

b)Compute the wind-chill temperature.

c)Compute the difference between the person’s internal temperature and skin surface temperature on the windy day.

d)Suppose a flask of coffee, initially at 37°C, is insulated with the same total thermal resistance as the person’s skin and clothing. Will the coffee freeze? Why or why not? (Assume the freezing point is the same as water, 0°C.)

Answer 1

Draw a thermal resistance network. k,A h A k A Calculate the total thermal resistance per unit area for windy days 0.003 0.025 1 0.37 0.06 45 0.446997 K/W/m1 0.447 K/W/m Calculate the total thermal resistance per unit area for calm days 0.003 0.025 1 0.37 0.06 10 0.524775 K/W/m2 0.525 K/W/m^

Compute the wind chill temperature. Heat loss during windy days -Heat loss during calm days 37-T 37-2 0.447 0.525 37-2 (0.447) 0.525) T. 375 -7°C Calculate skin surface temperature on the windy day

37-7 T-T 0.447 1 37-7 T-7 0.447 45 37-7 0.447x 45 - 8.4914 °C 8.49 °OC Calculate the difference between the person's intermal temperature and skin surface temperature on the windy day 37-8.49 - 28.51°C Calculate the total heat loss from body during windy days 37-7 0.447 -67-114 w/m 2 Calculate the amount of heat required to freeze the coffee

T-T R, 37-2 0.447 7830 W/m Since, required amount of heat is greater than the heat loss from the body. Therefore, the coffee will NOT freeze.