problem4-19

# problem4-19 - PROBLEM 4.19 KNOWN Relation between maximum...

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PROBLEM 4.19 KNOWN: Relation between maximum material temperature and its location, and scanning velocities. FIND: (a) Required laser power to achieve a desired operating temperature for given material, beam size and velocity, (b) Lag distance separating the center of the beam and the location of maximum temperature, (c) Plot of the required laser power for velocities in the range 0 U 2 m/s. SCHEMATIC: r b = 0.1 mm T max = 200°C = 2000 kg/m 3 c = 800 J/kg•K k = 27 W/m•K T 2 = 25°C U = 2 m/s ′′ q δ ρ α = 0.45 ASSUMPTIONS: (1) Steady-state conditions, (2) Constant properties, (3) Semi-infinite medium, (4) Negligible heat loss from the top surface. ANALYSIS: The thermal diffusivity of the materials is 3 - = k/ ρ c = 27 W/m K / (2000 kg/m 800 J/kg K) = 16.9 × 10 m /s α 6 2 (a) The Peclet number is -6 2 b Pe = Ur / 2 = 2 m/s × 0.0001 m / ( 2 × 16.9 × 10 m /s) = 8.38 α Since this value of the Peclet number is within the range of the correlation provided in the problem statement, the maximum temperature corresponding to a stationary beam delivering the same power would be 2 1,max,U=0 1,maxU 0 2 2 2 T = (1 + 0.301Pe - 0.0108Pe ) (T - T ) + T = (1 + 0.301 × 8.37 - 0.0108 × 8.37

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