A thick plate of pure iron at 1000C is subjected to

Chapter 14, Problem 14.44

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A thick plate of pure iron at 1000C is subjected to acarburization process in which the surface of the plateis suddenly exposed to a gas that induces a carbonconcentration CC,sat one surface. The average diffu-sion coefficient for carbon and iron at this temperatureis . Use the correspondencebetween heat and mass transfer variables in address-ing the following questions.(a) Consider the heat transfer analog to the carburiza-tion problem. Sketch the mass and heat transfersystems. Show and explain the correspondence between variables. Provide the analytical solu-tions to the heat and mass transfer problems.(b) Determine the carbon concentration ratio, CC(x, t)/CC,s, at a depth of 1 mm after 1 h of car-burization.(c) From the analogy, show that the time dependenceof the mass flux of carbon into the plate may beexpressed as . Also, obtainan expression for the mass of carbon per unit areaentering the iron plate over the time period t.