Explanation Given: The length of the mussel layer is L m = 30 mm . The length of the skin fat layer is L s f = 3 mm . The temperature of the inner surface of the skin layer is T i 1 = 34.8 °C . The heat loss rate from the body is q 1 = 142 W . The thermal conductivity of the mussel layer is k m = 0.5 W / m ⋅ K . The thermal conductivity of the skin fat layer is k s f = 0.3 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 temperature of the skin layer is T s = 34 °C . The rate of energy generation per unit area of the mussel surface is q ˙ m = 5600 W / m 3 . The latent heat of vaporization is h f g = 2421 × 10 3 J / kg . The density of the mass is ρ = 994 kg / m 3 . Formula used: The expression for the temperature of the skin layer is given as, T s = T i 1 − q 1 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 temperature difference is given as, θ c = − q ˙ m ω ρ b c b The expression for the temperature of the inner surface of the skin layer is given as, T i = T s sinh ( m L m ) + k m m L s f k s f [ θ c + ( T a + q ˙ m ω ρ b c b ) cosh ( m L m ) ] sinh ( m L m ) + k m m L s f k s f cosh ( m L m ) The expression for the heat transfer from the skin surface is given as, q 2 = k s f A ( T i − T s ) L s f The expression for the heat removed from the skin by perspiration is given as, q ′ = q 2 − q 1 The expression for the mass flow rate of perspiration is given as, m ′ p e r = q ′ h f g The expression for the volume rate of perspiration is given as, V ˙ = m ′ p e r ρ Calculation: The temperature of the skin layer can be calculated as, T s = T i 1 − q 1 L s f k s f A T s = 34.8 °C − 142 W × 3 mm ( 1 m 1000 mm ) 0.3 W / m ⋅ K × 1.8 m 2 T s = 34 °C The parameter m can be calculated as, m = ω ρ b c b k m m = 0.0005 s -1 × 1000 kg / m 3 × 3600 J / kg ⋅ K 0.5 W / m ⋅ K m = 60 m -1 The temperature difference can be calculated as, θ c = − q ˙ m ω ρ b c b θ c = − 5600 W / m 3 0.0005 s -1 × 1000 kg / m 3 × 3600 J / kg ⋅ K θ c = − 3

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ISBN: 9780470501962

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 3.165P

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The perspiration rate to maintain same skin temperature.

Solution Summary: The author explains the perspiration rate to maintain the same skin temperature. The thermal conductivity of the mussel layer is k_m=0.5W.

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