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...

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 ϑF = 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 ϑF. 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 ϑk = 65 ◦C? The axial heat conduction may be neglected.