Overview
please remember to write out what is known about the problem, what you are trying to find, a schematic of
the situation that you are trying to analyze, and any assumptions you made 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