Carbon at 1273 K is contained in a 7-cm-inner-diameter cylinder made of iron whose thickness is 1.2 mm. The concentration of carbon in the iron at the inner surface is 0.5 kg/m3 and the concentration of carbon in the iron at the outer surface is negligible. The diffusion coefficient of carbon through iron is 3 × 10?11 m2/s. The mass flow rate of carbon by diffusion through the cylinder shell per unit length of the cylinder is
(a) 2.8?×?10?9 kg/s
(b) 5.4?×?10?9 kg/s
(c) 8.8?×?10?9 kg/s
(d) 1.6?×?10?8 kg/s
(e) 5.2?×?10?8 kg/s
(a) 2.8?×?10?9 kg/s
T=1273 [K]
D_i=0.07 [m]
D_o=D_i+2*0.0012 [m]
rho_A_1=0.5 [kg/m^3]
rho_A_2=0 [kg/m^3]
D_AB=3.0E-11 [m^2/s] "Table 14-3b"
r_1=D_i/2
r_2=D_o/2
L=1 [m]
m_dot_diff=2*pi*L*D_AB*(rho_A_1-rho_A_2)/ln(r_2/r_1)
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