GATE 2026 PI – Question 53
In laser machining, $t_m=\frac\pi\alpha\left[\frac{(\theta_m-\theta_0)k}{2H}\right]^2$, with diffusivity α, melting temperature θ_m, conductivity k and absorbed heat flux H. A uniform 1 kW beam of diameter 0.1 mm machines tungsten carbide from θ₀ = 32°C, with 10% absorption. Given θ_m = 3400°C, k = 2.15 W/(cm·°C), α = 0.79 cm²/s and π = 3.14, find t_m (µs, one decimal).
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Correct answer: 31 to 33
Explanation
Absorbed power is 100 W. Diameter is 0.01 cm, so beam area is $3.14(0.01)^2/4=7.85\times10^{-5}$ cm² and $H=100/A\approx1.27389\times10^6$ W/cm². Substitution gives $t_m=(3.14/0.79)[3368(2.15)/(2H)]^2=3.21072\times10^{-5}$ s = **32.1 µs**.