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Unformatted text preview: HW #3 Problem 5.7 a. To Find: The distance from the highpressure side at which the concentration of nitrogen in steel equals 2.0 kg/m 3 under conditions of steadystate diffusion. b. Given: D = 6 × 1011 m 2 /s at 1200 o C J = 1.2 × 107 kg/m 2s Concentration of nitrogen at highpressure side, C A = 4 kg/m3. Concentration of nitrogen within the surface (at the location in question), C B = 2 kg/m3 c. Assumptions: (i) Linear concentration profile, i.e., steady state diffusion condition. (ii) Onedimensional diffusion, i.e. diffusion occurs only along the axis parallel to the thickness of the plate. (iii) ‘Steel’ is a generic term. The diffusivity of nitrogen in steel may vary from grade to grade, depending on the concentrations of alloying elements. It is assumed that the diffusivity values mentioned correspond to the particular steel considered in the question. d. Solution: (It would be great but not necessary to have a figure here, illustrating the given situation.) Let the axis parallel to the thickness of the plate be x axis. Let the x coordinate of the highpressure side be x A = 0. Let the x coordinate where concentration of nitrogen is C B be x B . Then, the distance from the highpressure side at which the concentration of nitrogen in steel equals 2.0 kg/m 3 under conditions of steadystate diffusion = x Bx A . From equation 5.3: B A B A x x C C D J = − − − = A B A B x x C C D J or − − − b − = J C C D x x B A A B b × − × = − s m kg m kg m kg x / 10 2 . 1 / 2 / 4 /s m 10 6 2 7 3 3 2 11 B ) ( b B x = 1 × 103 m = 1 mm Hence, distance from highpressure side = x B  x A = x B  0 = x B equals 1 × 103 m = 1 mm Problem 5.8 a. To Find: The diffusion coefficient of C in Fe at 725 o C b. Given: xB – xA = 1 mm J = 1.4 × 108 kg/m 2s Concentration of C at x = x A , C A = 0.012 wt% Concentration of C at x = x B , C B =0.0075 wt%. c. Assumptions: (i) Linear concentration profile, i.e., steady state diffusion condition....
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This note was uploaded on 02/14/2012 for the course MSE 2090 taught by Professor Leoindzhiglei during the Fall '10 term at UVA.
 Fall '10
 leoindzhiglei

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