# Relationship Between Surface and Core Temperature of Steel

1. Oct 1, 2012

### DrewGerhan

Hey guys,
First off, I apologize if this is in the wrong section. I am currently an intern taking 6 months off from my senior year pursuing a mechanical engineering degree. Having not taken a heat transfer class yet, I am stumped as to how to go about tackling my latest project.

Basically what I need to figure out is how to relate the surface temperature of a piece of stock (1045 steel) that is found using either an IR or contact thermometer to the internal, core, temperature of that same piece. The goal of the project is to be able to take the temperature of the outside of the part, look at a chart and find out the internal temperature and whether or not the part is done cooling.

The biggest piece in question is around 20" diameter and varies down to 8" diameter and will have been in a furnace set at 2300*F with enough time to soak.

Not asking for anyone to do this for me, just help me get started in the right direction.

Drew

2. Oct 1, 2012

### Astronuc

Staff Emeritus
One would have to know the original temperature, the size of the heat, density and heat capacity, and some idea of the heat transfer in air, or the thermal conductivity. One solves a time dependent heat conduction equation and may assume that the rate of heat transfer at the surface is more or less constant, and relate that to the thermal gradient.

3. Oct 2, 2012

### DrewGerhan

Astronuc, I think I have gotten to that point. I have attached my work up to this point in the pdf. If my calculations are correct, the core of a 20" diameter piece would be around 1200F after 13 hours if it started at a uniform 2300F.

The original temperature of the part would either be 2300F or 1550F after it comes out of the forging furnace or normalizing furnace respectively. We assume they are uniform temperature as they have have been allowed to soak for 1 hr/in of diameter. I found density to be ρ=7870kg/m3, heat capacity to be 486 J/kg-C and thermal conductivity to be 51.9 W/m-C.

How does the thermal gradient come into play?

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4. Oct 5, 2012

### ChaseRLewis73

I didn't check your exact numbers but BiFo equation is how you should calculate the time.

He mentioned the thermal gradient because you asked how to determine it as a function of surface temperature. However, that is a complicated mess as the dT/dr is a function of time also. Doing it by time is how most in industry do it because it takes so long because of the high heat capacity of the objects they use (as you calculated 13 + hours to cool).

5. Oct 11, 2012

### DrewGerhan

Well we've decided to take another approach to this project. My task now is to drill to holes into a scrap piece of stock to put thermocouples in and directly measure the temperature to get a cooling curve.

My question now is, how do I account for thermal expansion when I drill these holes? Obviously the bar its self will grow in volume when it is heated and therefore the hole diameters will shrink. I'v attached a picture in pdf format to try to show how I plan on setting this up. The stock in this case will be roughly 10" diameter 1045 steel.

#### Attached Files:

• ###### Crankshaft Temperature Measuring Setup.pdf
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6. Oct 15, 2012

### DrewGerhan

Anyone able to shed some light on this for me?

7. Oct 16, 2012

### brightonk

Hey I am also an intern and taking time out of uni so i may not be the most reliable person. But from some work I have done on thermal expansion - your holes will not shrink, they will also increase. So basiclally if you had a steel bar with an extruded hole in the centre, your OD and ID both increase. Think of the thermal expansion as a scale up.