Explanation Given: The length of tray 1, tray 2, tray 3 is 0.5 m, 1 m, 1 .5 m respectively. The relative humidity is 40 % . Concept used: Properties of air from Table A-4: The kinematic viscosity is 15.89 × 10 − 6 m 2 / s . Properties of air-water vapor from Table A-8: The mass diffusivity is 0.26 × 10 − 4 m 2 / s . Properties of saturated-water vapor from Table A-6: The saturated density is 0.0256 kg / m 3 . The latent heat of vaporization is 2438 kJ / kg . Write the expression for Reynolds number. Re = u L ν ....... (1) Here, L is length; Re is Reynolds number, ν is kinematic viscosity and u is the velocity of the fluid. Write the expression for Schmidt number. S c = ν D A B ....... (2) Here, Sc is Schmidt number, ν is kinematic viscosity and D A B is mass diffusivity of fluid. Write the expression for convective mass transfer rate for tray 1. h m , l = 0.664 Re 1 2 S c 1 3 ( D A B ) x 1 ....... (3) Here, h m , l convective mass transfer. Write the expression for the rate of heat transfer in tray 1. q t r a y 1 = h m , l x 1 ( ρ A , s a t ) ( 1 − ϕ ∞ ) h f g ....... (4) Here, ρ A , s a t is density, q t r a y 1 heat transfer in tray 1, h f g is the latent heat of vaporization and ϕ is relative humidity. Write the expression for convective mass transfer rate tray 2 h m , 0 − 2 = ( 0.037 Re x 4 5 − 871 ) S c 1 3 ( D A B ) x 2 ....... (5) Here, h m , 0 − 2 convective mass transfer. Write the expression for the rate of heat transfer in tray 2. q t r a y 2 = ( x 2 h m , 0 − 2 − x 1 h m , 0 − 1 ) ( ρ A , s a t ) ( 1 − ϕ ∞ ) h f g ....... (6) Here, ρ A , s a t is density, q t r a y 2 heat transfer in tray 2, h f g is the latent heat of vaporization and ϕ is relative humidity. Write the expression for convective mass transfer rate tray 3. h m , l = ( 0.0296 Re x 4 5 ) S c 1 3 ( D A B ) x 3 ....... (7) Here, h m , l convective mass transfer. Write the expression for the rate of heat transfer in tray 3. q t r a y 2 = ( x 2 + x 3 2 ) ( x 3 h m − x 2 h m ) ( ρ A , s a t ) ( 1 − ϕ ∞ ) h f g ....... (8) Here, ρ A , s a t is density, x 2 is the distance of tray 2, x 3 is the distance of tray 3, q t r a y 3 heat transfer in tray 3, h f g is the latent heat of vaporization and ϕ is relative humidity. Calculation: Substitute 0.5 m for L, 15.89 × 10 − 6 m 2 / s for ν and 12 m / s for u in equation (1) Re = ( 12 ) ( 0.5 ) 15.89 × 10 − 6 = 3.77 × 10 5 Substitute 15.89 × 10 − 6 m 2 / s for ν and 0.26 × 10 − 4 m 2 / s for D A B in equation (2) S c = 15.89 × 10 − 6 0.26 × 10 − 4 = 0.611 Substitute 3.77 × 10 5 for Re, 0.26 × 10 − 4 m 2 / s for D A B , 0.5 m for x 1 and 0.611 for Sc in equation (3). h m , l = ( 0.26 × 10 − 4 0.5 ) ( 0.664 ) ( 3.77 × 10 5 ) 1 2 ( 0.611 ) 1 3 = 1.8 × 10 − 2 m / s Substitute 1.8 × 10 − 2 m / s for h m , l , 0.5 m for x 1 , 0

7th Edition

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 7, Problem 7.125P

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The rate of energy supplied to the each of the three trays to maintain the water at 300 K .

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Chapter 7, Problem 7.124P

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Fundamentals of Heat and Mass Transfer

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The rate of energy supplied to the each of the three trays to maintain the water at 300 K .

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