Explanation Given: The length of the mussel layer is L m = 30 mm . The thickness of the skin layer is L s f = 3 mm . The heat loss rate from the body is q 1 = 142 W . The temperature of the infinity is T ∞ = 15 °C . The thermal conductivity of the mussel layer is k m = 0.5 W / m ⋅ K . The frequency is ω = 0.0005 s -1 . The density of body is ρ b = 1000 kg / m 3 . The specific heat of the body is c b = 3600 J / kg ⋅ K . The area of the body is A = 1.8 m 2 . The temperature of the arterial is T a = 37 °C . The core body temperature is T c = 37 °C . The comfortable body temperature of the body is T s = 33 °C . The convective heat transfer coefficient is h = 2 W / m 2 ⋅ K . The emissivity is ε = 0.95 . The Stefan Boltzmann constant is σ = 5.67 × 10 − 8 W / m 2 ⋅ K 4 . The surrounding temperature is T s u r r = 15 °C . Formula used: The expression for the heat loss rate from the skin surface to environment is given as, q = h A ( T s − T ∞ ) + ε σ A ( T s 4 − T s u r r 4 ) The expression for the temperature of the skin layer is given as, T i = T s − q L s f k s f A The expression for the parameter m is given as, m = ω ρ b c b k m The expression for the metabolism heat generation rate is given as, q ˙ m = ω ρ b c b [ q k m A m sin ( m L m ) + ( T i − T a ) cosh ( m L m ) + ( T c − T a ) cosh ( m L m ) + 1 ] Calculation: The heat loss rate from the skin surface to environment can be calculated as, q = h A ( T s − T ∞ ) + ε σ A ( T s 4 − T s u r r 4 ) q = { 2 W / m 2 ⋅ K × 1.8 m 2 [ 33 °C ( °C + 273 ) K − 15 °C ( °C + 273 ) K ] + 0.95 × 5.67 × 10 − 8 W / m 2 ⋅ K 4 × 1.8 m 2 [ { 33 °C ( °C + 273 ) K } 4 − { 15 °C ( °C + 273 ) K } 4 ] } q = 247

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Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine

Publisher: Wiley, John & Sons, Incorporated

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Chapter 3, Problem 3.166P

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Solution Summary: The author explains the metabolic heat generation rate, the thermal conductivity of the mussel layer, and the convective heat transfer coefficient.

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