A steel cube [p = 7800 kg/m, Cp 0.5 kJ/kg-°C, and k 50 W/m-°C] is uniformly heated to Ti = 800°C. It is to be hardened by suddenly dropping it

into an oil bath at T» = 40°C.The heat transfer coefficient between the oil and the cube is 700 W/m2.°C. Determine the temperature at the points P and Q (as shown in the figure below) 2 minutes after the start of cooling. (а)Is the lumped system analysis applicable for this problem? Why? (b)Determine the temperature Tp and To by use of the Heisler Charts. (c)Determine the temperature Tp and To by use of the finite difference method. (d)If the lumped system analysis were used in this problem, what would the error be in the temperature prediction? (e)What will the steady-state temperature be?

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