A very long steel tape with rectangular cross section (h = 15 mm, b = 50 mm) and thermal diffusivity a = 3.8 · 10 −6 m 2 /s is pulled through an oil bath of length L = 4.0 m. The oil bath is at the...

A very long steel tape with rectangular cross section (h = 15 mm, b = 50 mm) and thermal diffusivity a = 3.8 · 10⁻⁶
m²/s is pulled through an oil bath of length L = 4.0 m. The oil bath is at the constant temperature ϑ_F
= 50 ◦C; the steel tape has a temperature of ϑ₀
= 375 ◦C as it enters the oil bath. The heat transfer coefficient between the steel tape and the oil is so large that the surface of the steel tape assumes the temperature ϑ_F. With what speed w does the steel tape have to pulled through the oil for it to leave the oil bath with a temperature at its central axis of ϑ_k
= 65 ◦C? The axial heat conduction may be neglected.