problem4-18 - PROBLEM 4.18 KNOWN: Power, size and shape of...

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PROBLEM 4.18 KNOWN: Power, size and shape of laser beam. Material properties. FIND: Maximum surface temperature for a Gaussian beam, maximum temperature for a flat beam, and average temperature for a flat beam. SCHEMATIC: P = 1W r b = 0.1 mm r b Flat Gaussian T max T max T 2 = 25°C k = 27 W/m•K α= 0.45 ′′ q ′′ q ASSUMPTIONS: (1) Steady-state conditions, (2) Constant properties, (3) Semi-infinite medium, (4) Negligible heat loss from the top surface. ANALYSIS: The shape factor is defined in Eq. 4.20 and is q = Sk Δ T 1-2 (1) From the problem statement and Section 4.3, the shape factors for the three cases are: Beam Shape Shape Factor T 1,avg or T 1,max Gaussian Flat Flat b 2r π b r π 2 b 3r / 8 π T 1,max T 1,max T 1,avg For the Gaussian beam, -3 -6 1 S = 2 π × 0.1 × 10 m = 354 × 10 m For the flat beam (max. temperature), -3 -6 2 S = × 0.1 × 10 m = 314 × 10 m π
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This note was uploaded on 12/07/2010 for the course MAE Heat Trans taught by Professor Lee,j.s. during the Spring '10 term at Seoul National.

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