Calculate Heat Transfer from Metal Ladle 1

[unbound]

Hello Guys

1. I need to calculate the surface temperature of a metal ladle.
2. Also to determine the temperature the ladle stand is subjected to, when it is 400mm away from the surface of the ladle. The ladle stands are concrete.

Info I have:
Ladle diameter = 4m
Ladle height = 4.52m
Ladle surface area = 56.25mm
Distance to ladle stand = 0.4m
Metal temp = 1500 deg C
Ambient temp = 30 deg C
Ladle internal refractory thickness = 0.279m
Refractory conductivity = say 2.6W/mK
Steel Ladle metal thickness = 0.032m

I would be grateful if somebody could advise the formulas and constants.

Thanks and regards
Jeff

 

[vc66]

Student posting isn't allowed.

V

 

[unbound]

Thank you vc66 for your reply, but I am not a student. I am in my mid 40's and working in the steelmaking industry. This is an actual problem on site.

Regards
Jeff

 

[corus]

In general the refaactory lining has a relatively low thermal inertia and slow to heat up. Shell temperatures for ladles are thus dependent on the time spent during the process, ie. after pre-heating, and time empty and full etc. For a worst case though, you could assume it was at steady state when full.

The problem is generally non-linear though, as refractory and shell conductivities vary with temperature. On top of that the outer shell bounday condition is heat loss via natural convection and radiation to the ambient. It's more complicated if you're looking at the underside of the ladle, where you'd really need to use a 2D axisymmetric analysis of the ladle taking into account the thicker base lining (plus different materials) and the stiffening ring around the vertical wall. You'd have to use finite elements for that. For the vertical wall you could simplify the problem by assuming 1D heat flow and simplify the outer non-linear boundary condition to forced convection with a constant heat transfer coefficient for the effects of natural convection and radiation. I'll get an appropriate figure tomorrow.

corus

 

[corus]

Heat Transfer Coefficient is about 20 W/m C, and so your shell temperature works out at 495 C on the outside, 501 C on the inner face. These temperatures are way too high, and you should have temperatures less than 350 C to satisfy design codes.

You can check the figures by calculating the flux k.(T1-T2)/x across each material of thickness x. The values should be roughly the same.



corus

 

[unbound]

Thank you for your in-depth reply. I am positive that the ladle will comply with the maximum 350C allowed so I will check the refractory. Although, I cannot get the formula to give a sensible answer. Could I ask you to be more explicit?

Then I hope to use the same formula to determine the temperature at the ladle stand.

Thanks again.

 

[corus]

The outer temperature is given by :

To = (1500+30.h.R)/(1+h.R) where R is the sum of the resistances xi/ki and h is the heat transfer coefficient.

The value of h I quoted earlier might be a little low. If you try a value of 30 W/m^2K (for a surface temperature of 400C) then your shell temperature comes down to 377 C for steady state conditions.

I'm not sure how you use this formula for the ladle stand as the problem then is radiation and not conduction.

corus