Calculating Heat Transfer Time for Steel Immersed in Zinc Bath

[loopster]

If I had a piece of steel 0.25" thick 1 meter wide and 1 meter long and it was at 100 deg C and it was immersed in a bath of zinc at 460 deg C how long would it take to heat the piece of steel to 460 deg C?


Would this be down the lines of Fourier's Law of conduction?


q= 42*1*(460-100)/0.0635?

FYI... I am a process engineer at a steel company and my son directed me to this sight for help

 

[Mapes]

Hi loopster, welcome to PF. A simple way to estimate the heating time is

$$t\approx\frac{L^2}{D}$$

where $L$ is the characteristic length and $D$ is the thermal diffusivity. I'd take half the thickness, 1/8", as the characteristic length because the zinc bath is on both sides. It looks like the thermal diffusivity of steel is about 10^-5 m²/s = 0.0155 in²/s. This predicts the heating time to be about a second. Is this helpful?

Incropera & DeWitt's Fundamentals of Heat and Mass Transfer is a great reference if you have to solve a lot of these types of problems.