The human body must maintain its core temperature inside a

Chapter 11, Problem 11.55

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The human body must maintain its core temperature inside a rather narrow range around 37C. Metabolic processes (notably, muscular exertion) convert chemical energy into internal energy deep in the interior. From the interior, energy must ow out to the skin or lungs, to be lost by heat to the environment. During moderate exercise, an 80-kg man can metabolize food energy at the rate of 300 kcal/h, do 60 kcal/h of mechanical work, and put out the remaining 240 kcal/h of energy by heat. Most of the energy is carried from the interior of the body out to the skin by forced convection (as a plumber would say): Blood is warmed in the interior and then cooled at the skin, which is a few degrees cooler than the body core. Without blood ow, living tissue is a good thermal insulator, with a thermal conductivity about 0.210 W/mC. Show that blood ow is essential to keeping the body cool by calculating the rate of energy conduction, in kcal/h, through the tissue layer under the skin. Assume that its area is 1.40 m2, its thickness is 2.50 cm, and it is maintained at 37.0C on one side and at 34.0C on the other side.