SolutionsHW3

SolutionsHW3 - HW #3 Problem 5.7 a. To Find: The distance...

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Unformatted text preview: HW #3 Problem 5.7 a. To Find: The distance from the high-pressure side at which the concentration of nitrogen in steel equals 2.0 kg/m 3 under conditions of steady-state diffusion. b. Given: D = 6 10-11 m 2 /s at 1200 o C J = 1.2 10-7 kg/m 2-s Concentration of nitrogen at high-pressure 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) One-dimensional 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 co-ordinate of the high-pressure side be x A = 0. Let the x co-ordinate where concentration of nitrogen is C B be x B . Then, the distance from the high-pressure side at which the concentration of nitrogen in steel equals 2.0 kg/m 3 under conditions of steady-state diffusion = x B-x 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 10-3 m = 1 mm Hence, distance from high-pressure side = x B - x A = x B - 0 = x B equals 1 10-3 m = 1 mm Problem 5.8 a. To Find: The diffusion co-efficient of C in Fe at 725 o C b. Given: xB xA = 1 mm J = 1.4 10-8 kg/m 2-s 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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SolutionsHW3 - HW #3 Problem 5.7 a. To Find: The distance...

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