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Heat Chap14-042

# Heat Chap14-042 - Chapter 14 Mass Transfer Steady Mass...

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Chapter 14 Mass Transfer Steady Mass Diffusion Through a Wall 14-42C The relations for steady one-dimensional heat conduction and mass diffusion through a plane wall are expressed as follows: Heat conduction : Q k A T T L cond = - - 1 2 Mass diffusion : m D A w w L D A L diff,A,wall AB A,1 A,2 AB A,1 A,2 = - = - ρ where A is the normal area and L is the thickness of the wall, and the other variables correspond to each other as follows: rate of heat conduction Q cond ←→ m diff,A,wall rate of mass diffusion thermal conductivity k ←→ D AB mass diffusivity temperature T ←→ A density of A 14-43C ( a ) T, ( b ) F, ( c ) T, ( d ) F 14-44C During one-dimensional mass diffusion of species A through a plane wall of thickness L, the concentration profile of species A in the wall will be a straight line when (1) steady operating conditions are established, (2) the concentrations of the species A at both sides are maintained constant, and (3) the diffusion coefficient is constant. 14-45C During one-dimensional mass diffusion of species A through a plane wall, the species A content of the wall will remain constant during steady mass diffusion, but will change during transient mass diffusion. 14-19

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Chapter 14 Mass Transfer 14-46 Pressurized helium gas is stored in a spherical container. The diffusion rate of helium through the container is to be determined. Assumptions 1 Mass diffusion is steady and one-dimensional since the helium concentration in the tank and thus at the inner surface of the container is practically constant, and the helium concentration in the atmosphere and thus at the outer surface is practically zero. Also, there is symmetry about the center of the container. 2 There are no chemical reactions in the pyrex shell that results in the generation or depletion of helium. Properties The binary diffusion coefficient of helium in the pyrex at the specified temperature is 4.5 × 10 -15 m 2 /s (Table 14-3b). The molar mass of helium is M = 4 kg/kmol (Table A-1). Analysis We can consider the total molar concentration to be constant ( C = C A + C B 2245 C B = constant), and the container to be a stationary medium since there is no diffusion of pyrex molecules ( N B = 0 ) and the concentration of the helium in the container is extremely low ( C A << 1). Then the molar flow rate of helium through the shell by diffusion can readily be determined from Eq. 14-28 to be ( . )( . . N r r D C C r r diff AB A,1 A,2 2 3 m m)(4.5 10 m / s) (0.00073 0) kmol / m 1.50 1.45 kmol / s = - - = × - - = × - - 4 4 145 150 180 10 1 2 2 1 15 15 π The mass flow rate is determined by multiplying the molar flow rate by the molar mass of helium, ( m MN diff diff kg / kmol)(1.80 kmol / s) = = × = × - - 4 10 15 7.2 10 kg / s 15 Therefore, helium will leak out of the container through the shell by diffusion at a rate of 7.2 × 10 -15 kg/s or 0.00023 g/year.
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Heat Chap14-042 - Chapter 14 Mass Transfer Steady Mass...

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