Consider the conditions of Example 3.12 for an air environment, except now the air and surroundings temperatures are both 15°C. Humans respond to cold by shivering, which increases the metabolic heat generation rate. What would the metabolic heat generation rate (per unit volume) have to be to maintain a comfortable skin temperature of 33°C under these conditions?
The temperature at the inner surface of the skin/fat layer was given as 35°C. In reality, this temperature depends on the existing heat transfer conditions, including phenomena occurring farther inside the body. Consider a region of muscle with a skin/fat layer over it. At a depth of Lm = 30 mm into the muscle, the temperature can be assumed to be at the core body temperature of Tc = 37°C. The muscle thermal conductivity is km = 0.5 W/m∙ K. The metabolic heat generation rate within the muscle is m = 700 W/m3. The perfusion rate is ω = 0.0005 s-1; the blood density and specific heat are b = 1000 kg/m3 and cb = 3600 J/kg ∙ K, respectively, and the arterial blood temperature Ta is the same as the core body temperature. The thickness, emissivity, and thermal conductivity of the skin/fat layer are as given in; perfusion and metabolic heat generation within this layer can be neglected. We wish to predict the heat loss rate from the body and the temperature at the inner surface of the skin/fat layer for air and water environments.
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