Sample Exam 2 - law(i Write down the expression for the...

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EMA 3010 TIME 50 MINUTES; MAE B 211 12.50 - 1.40 am. March 4, 09 CLOSED BOOK; ANSWER ALL QUESTIONS; FORMULAS AND CONSTANTS ARE GIVEN BELOW; YOU ARE ALLOWED TO BRI NG A CALCULATOR Diffusion Coefficient D = D o exp (-Q/RT) ; Concentration versus time = (C-Co)/(Cs-Co) = 1 – erf (x/2(Dt) 0.5 ) Erf(0) = 0.; erf(0.5) = 0.5; erf(1.0) = 0.84; erf(2.0)= 0.9953 Hooke’s Law σ = E ε Critical resolved Shear stress = σ cos θ cos λ Angle between planes Cos θ = (h 1 h 2 + k 1 k 2 + l 1 l 2 )/[(h 1 2 + k 1 2 + l 1 2 ) ( h 2 2 + k 2 2 + l 2 2 )] 1/2 Fracture toughness = Y σ ( π a) 0.5 Assume Y = 1.0 1: The surface of iron is being carburized by heating treating one surface iron in a furnace in an atmosphere of carbon monoxide. The carbon monoxide decomposes into carbon at the iron surface and diffuses into the solid. The diffusion profile of carbon inside iron is given, by the expression 10 20 (1-erf ( x/2) atoms/cm 3 , where x is the distance in microns from the surface. This concentration profile is the solution to the Ficks’ second
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Unformatted text preview: law. (i) Write down the expression for the Ficks’s second Law for one dimensional diffusion [ 5 pts] (ii) What are the boundary conditions for which expression for the concentration profile of carbon in iron are valid. [ 7 pts] (iii) What is the ratio of concentration of carbon at a distance 10 micron from the surface compared to the surface concentration. [ 7 pts] (iv) What is the carbon flux at the surface. [ 5 pts] (v) Carbon diffuses by a interstitial mechanism in iron. How will the diffusion coefficient change if the mechanism changes to vacancy mechanism. Explain two reasons for your answer. [ 5 pts] (vi) Calculate the distance from the surface, when the concentration of of carbon is half of its maximum value. { 12 pts} (vii)What is the diffusion coefficient of carbon in iron if the diffusion time is 10 minutes. [Bonus 15 points]...
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Sample Exam 2 - law(i Write down the expression for the...

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