Question 10.3: Determine the frequency range for through heating aluminum b......
Determine the frequency range for through heating aluminum bar 0.02 m diameter to 500°C. The average resistivity of aluminum is 5.83 × 10^{-8} ohm.m. What will be the frequency range if the bar diameter is 0.01 and 0.1 m?
According to Equation (10.7) the frequency range will be
3 \times 10^6 \frac{\rho_w}{\mu_\gamma D_w{ }^2}<f_c<6 \times 10^6 \frac{\rho_w}{\mu_\gamma D_w{ }^2} (10.7)
For aluminum \mu_\gamma = 1.0
\begin{aligned}\frac{3 \times 10^6 \times 5.83 \times 10^{-8}}{0.02^2} & <f_c<\frac{6 \times 10^6 \times 5.83 \times 10^{-8}}{0.02^2} \\400 & <f_c<800\end{aligned}Hence, the frequency should be in the range of 400–800 Hz.
Repeating the same calculations for d = 0.01 and 0.10 m diameters
for 0.01 m diameter 1700<f_c<3400 \simeq 2 \ \mathrm{kHz}
for 0.10 m diameter 17<f_c<34 \simeq 50 \ \mathrm{~Hz}
Note: The recommended frequencies are much more (~450 kHz) than the above calculated values. Perhaps this is because the concept does not involve the power required to get the temperature in desired time. The maximum frequencies should be multiplied by a factor 3–5.