# Homework Help: Heat transfer Question

1. Mar 20, 2008

### 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

Last edited: Mar 20, 2008
2. Mar 20, 2008

### 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.