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Case Study 1

# Case Study 1 - vaporization temperature energy is absorbed...

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Case Study: Laser Drilling Source: Andrews and McLone, Mathematical Modeling , Butterworths, Boston, 1976. Fulford and Broadbridge, Industrial Mathematics , Cambridge Univ. Pr., 2002. There is considerable interest in industry in the use of high power lasers and electron beams for both cutting and welding of sheet metal. The essential idea is to focus a large amount of energy onto a small area of surface of the metal. This intense heating causes vaporization of the metal, forming a hole. The energy from the laser is absorbed by the sheet metal surface, the temperature of the metal rises, and heat is conducted through the metal. The temperature can not rise indefinitely. At a certain temperature, the
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Unformatted text preview: vaporization temperature, energy is absorbed by the metal as it changes from solid to vapor. There are a number of mathematical questions associated with this problem. The one we address is to determine how rapidly the hole is formed for a given value of the power per unit area of irradiating beam. This is a heat conduction problem with a phase change (solid to gas), and a moving boundary. There are several calculations to be done. One involves calculating the time for the boundary x = 0 to heat to the vaporization temperature. Another calculation justifies that it is reasonable to neglect heat flow in the x and y directions....
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