Explanation Given: The temperature of air is T ∞ = 40 ° C . The temperature of garment is T s = 25 ° C . The characteristic length garment in the vertical direction is L c = 1 m . Formula used: The mean temperature is given as, T f = T s + T ∞ 2 The Schmidt number is given as, S c = v D AB Here, D A B is the binary diffusion coefficient, v is the viscosity. The invoking heat mass analogy is given as, S h L ¯ = 0.59 ( G r L S c ) 1 4 The mass transfer coefficient is given as, h ¯ m = D A B L S h ¯ L The density of mixture in the quiescent fluid is given as, ρ ∞ = P B , ∞ R B T ∞ Here, P B , ∞ is the pressure of dry still air, The pressure of air at the surface is given as, P B , s = P B , ∞ − P A , s Here, ρ A , ∞ is the density of water vapor at the surface. The density of air at the surface is given as, ρ B , s = P B , s R B T s The density of mixture at the surface is given as, ρ s = ρ A , s + ρ B , s Here, ρ A , s is the density of water vapor at the surface, ρ B , s is the density of dry air The mean boundary layer density is given as, ρ = ρ s + ρ ∞ 2 The Grashof number is given as, G r L = g ( ρ ∞ − ρ s ) L 3 ρ v 2 The drying rate is given as m ˙ A = h m ¯ × L ( ρ A , s − ρ A , ∞ ) Calculation: Refer table A.6 “Thermophysical properties of liquid metals” Water vapor at T s = 298 K , obtain value for P A , s = 0.0317 bar ρ A , s = 0.02660 kg / m 3 The mean temperature can be calculated as, T f = T s + T ∞ 2 = 298 K + 313 K 2 = 305 K Refer table A.4 “Thermophysical properties of gases at atmospheric pressure” At p = 1 atm , T f = 305 K obtain values for, v = 16.39 × 10 − 6 m 2 / s Refer table A.8 “Binary diffusion coefficients at one atmosphere” water vapor at At p = 1 atm , T f = 305 K obtain values for D A B = 0.27 × 10 − 4 m 2 / s The Schmidt number can be calculated as, S c = v D AB = 16.39 × 10 − 6 m 2 / s 2.70 × 10 − 5 m 2 / s = 0.607 The density of mixture in the quiescent fluid can be calculated as, ρ ∞ = P B , ∞ R B T ∞ = 1

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ISBN: 9780470501979

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

Publisher: Wiley, John & Sons, Incorporated

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Chapter 9, Problem 9.117P

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The drying rate per unit width of the garment.

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Chapter 9, Problem 9.116P

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Chapter 9 Solutions

Fundamentals of Heat and Mass Transfer

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