In a manufacturing process, stainless steel cylinders(AISI

Chapter 5, Problem 5.147

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In a manufacturing process, stainless steel cylinders(AISI 304) initially at 600 K are quenched bysubmersion in an oil bath maintained at 300 Kwithh?500 W/m2?K. Each cylinder is of length2L?60 mm and diameter D?80 mm. Use theready-to-solvemodel in the Examplesmenu of FEHTto obtain the following solutions (a) Calculate the temperatures, T(r, x, t), after 3 min atthe cylinder center, T(0, 0, 3 min), at the center ofa circular face, T(0, L, 3 min), and the midheightof the side, T(ro, 0, 3 min).(b) Plot the temperature history at the center, T(0, 0, t),and at the midheight of the side, T(ro, 0, t), for0?t?10 min using the View/Temperatures vs.Timecommand. Comment on the gradients occur-ring at these locations and what effect they mighthave on phase transformations and thermal stresses.(c) Having solved the model for a total integrationtime of 10 min in part (b), now use the View/Tem-perature Contourscommand with the shaded bandoption for the isotherm contours. Select the FromStart to Stoptime option, and view the tempera-ture contours as the cylinder cools during thequench process. Describe the major features of thecooling process revealed by this display. Use otheroptions of this command to create a 10-isothermtemperature distribution for t?3 min.(d) For the location of part (a), calculate the tempera-tures after 3 min if the convection coefficient isdoubled (h?1000 W/m2?K). Also, for convec-tion coefficients of 500 and 1000 W/m2?K, deter-mine how long the cylinder needs to remain in theoil bath to achieve a safe-to-touchsurface temper-ature of 316 K. Tabulate and comment on theresults of parts (a) and (d).