Problem 5: (30 points) In metallurgy, the cooling rates and thermal history of a metal alloy can dramatically affect the properties of the finished product. Consider a continuously processed square bar of nickel alloy (very long) that is 15cm on each side, and has a heat capacity =460 J/kgC, density of 8170kg/m3, and a thermal conductivity of 10W/mC. The surrounding air has a temperature of 25C and a convection coefficient of 200W/m2C a) How long will it take for the center of the bar to cool to 75C if it had a continuous initial temperature of 425C ? (15 points) b) How much heat lost per unit length would have occurred at this time? (15 points)