Compare the rate of heat loss from a human body with the typical energy intake from consumption of food (4.325 MJ/day). Model the body as a vertical cylinder 30 cm in diameter and 1.8-m-high in still air. Assume the skin temperature is 2°C below normal body temperature. Neglect radiation, transpiration cooling (sweating), and the effects of clothing.

Question

GIVEN

• Human body idealized as a vertical cylinder in still air

• Diameter (D) = 30 cm = 0.3 m

• Height (L) = 1.8 m

• Skin temperature (Ts) = 2°C below normal body temperature (37°C) = 35°C FIND

• Heat loss (q) and compare to consumption of food 4.325 MJ/day

ASSUMPTIONS

• Steady state

• Radiation, transpiration cooling, and clothing effects are negligible

• Ambient air temperature (T?) = 20°C

• Heat loss from the top of the cylinder is small compared to that from the sides

SKETCH



PROPERTIES AND CONSTANTS

for dry air at the mean temperature of 27.5°C

Thermal expansion coefficient (?) = 0.00333 1/°C

Thermal conductivity (k) = 0.0257 W/(m K)

Kinematic viscosity (?) = 16.4 × 10–6 m2/s

Prandtl number (Pr) = 0.71

Answer 1

The Grashof number based on the height is



Therefore, the flow is turbulent.

For turbulent boundary layer, the average heat transfer coefficient is given by



The rate of convective heat loss from the sides of the cylinder is



COMMENTS

The heat loss calculated for the idealized human is about 46% greater than the average food

consumption. This point out the importance of clothing.