Determine the depth of penetration for 0.4% carbon steel heated from 30–900°C at 1000 Hz. The resistivity and permeability at various temperatures is given below.

Question

Accepted Answer

[latex]\delta=5030 \sqrt{\frac{ ho}{\mu_\gamma f}} \ \mathrm{~cm} \ For \ 30°C \ f = 1000 \ Hz, \ ho = 16 imes 10^{-6} \ ohm.cm, \ \mu_\gamma = 40[/latex]

Substituting

[latex]\begin{aligned}\delta_{30} & =5030 \sqrt{\frac{16 imes 10^{-6}}{40 imes 10^3}} \& =0.101 \ \mathrm{~cm}\end{aligned}[/latex]

Similarly

[latex]\begin{aligned}& \delta_{200}=0.135\ \mathrm{~cm} \& \delta_{400}=0.174 \ \mathrm{~cm} \& \delta_{600}=0.219 \ \mathrm{~cm} \& \delta_{760}=1.62 \ \mathrm{~cm} \& \delta_{900}=1.70 \ \mathrm{~cm}\end{aligned}[/latex]

Temperature °C	Resistivity $\rho \times 10^{-6}$ ohm.cm	Permeability $\mu \gamma$
30	16	40
200	29.6	36
400	49.3	30
600	76.6	15
760	104.2	1
900	114.6	1

Question 10.1: Determine the depth of penetration for 0.4% carbon steel hea......

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