Engineering Question
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1. Some of you might have seen Terminator 2, which features Arnold. Ultimately, he sacrifices himself by
drowning his body in a pool of molten steel kept at 1600°C. You want to apply your Heat Transfer
knowledge to understand what happens to Arnold in the pool. Assume that Arnold is made up of solid
stainless steel with a density of 7700 kg/m3, thermal conductivity of 30 W/m–K, and specific heat of 600
J/kg–K. Arnold is a big man with a protective robot skin area of 3 m2 and shaped as a rectangular brick of
a volume of 0.1 m3. The heat transfer coefficient between the molten steel and Arnold can be assumed as
50 W/m2–K, whereas his initial temperature can be assumed as 25°C. Is it appropriate to use the Lumped
Capacitance method, which involves ignoring the internal conduction resistance? Explain. Calculate the
time it takes for Arnold to reach the melting point of steel (1525°C).
2. A 5 cm diameter sapphire shaft is going through a manufacturing process in a furnace. The temperature
inside the furnace is at 1500 K and the gas provides a heat transfer coefficient to the rod of 30 W/m2K. The
initial temperature of the sapphire rod is 300 K. The thermophysical properties of sapphire are as follows:
ksapphire = 18.1 W/mK, cpsapphire = 1068 J/kg–K, ρsapphire = 3970 kg/m3.
a. Calculate the Biot number for this scenario
b. Find how long the shaft must remain in the furnace to achieve a centerline temperature of 800 K using
the lumped capacitance method.
c. Find how long the shaft must remain in the furnace to achieve a centerline temperature of 800 K without
assuming that the shaft behaves as a lumped capacitance.
3. Describe the following terms or concepts and discuss their significance.
a. Fourier Number
b. Biot Number
c. Lumped Capacitance Model
d. Thermal Diffusivity
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