heat transfert through a cast iron ladle.

[bilou]

hi all ,

I have a big problem, my boss ask me to make an optimisation of the thermal dissipation of our cast iron ladle .
Actually we make them with a conical casing , insulated by a thermic resistant concrete.
I think by experience , that it will be exist a relation between the outlet surface ( cast iron/air) which is a convective dissipation and the lateral surface ( cast iron /concrete) which is a radiative dissipation and the external temperature of the casing ( human dangerous potentiel accident).
In function of the conical form ( mass of cast iron liquid, diameters and height) I must calculate the thickness of insulated media to reach the lowerest temperature of the skin of casing !!!!

If you have ever worked on this problem, or if you can help me , I will be very grateful.

If you know somes books or software who discuss about this problem ( high temperature, liquid metal comportment ...)

thanks very much

 

[chicopee]

since you know the temperature of the medium(liquid metal in laddle you can approximate conduction heat transfer thru refractory and cast iron ladle keeping surface temp. of ladle still unknown; then you can claculate heat transfer of combined convection and radiation from ladle surface area to ambient air. You can then combined the heat transfer equations above into one equation for a heat transfer between two temp. being that of liquid metal and ambient air.
A conical shape may not approximate a perfect flat surface nor a perfect sphere however I believe that if you treated the ladle as a inclined flat surface and then as a sphere, the two answers will probably represent the limits of the true answer.

From the above procedure, the inside wall temp. for conduction heat transfer would be that of the liquid metal. For convective heat transfer coefficient in still air, you are looking at a range of 1 to 5 btu/hr-sq ft-F. For emissivity of ladle I would look at about .5 to .9. For conductivity of refractory and cast iron ladle, check any book on heat transfer.

 

[ko99]

Bilou, perhaps I misunderstood the description but I picture the ladle as giant coffee cup, insulated but uncovered.

If so, the heat dissipation will be dominated by the hot liquid-to-ambient air thermal path (ie, almost all the heat will escape out the top). A rough estimate is fairly easy if you know the exposed surface area of the liquid and the temperatures of the liquid and air.

Convection loss = heat transfer coeff x area x delta T
Radiation loss = C x emissivity x area x (T1^4 - T2^4)
C=Stefan-Boltzmann constant

You could use the same formulas to estimate heat loss from the insulated surface-to-ambient air using temp and area of the cone surface instead of the liquid surface. There are ways to get more accurate but I'm not sure you need to.

All of this assumes that whatever is holding the ladle is well insulated. If not, perhaps you can provide a more detailed description.

Kevin O'Connor

http://www.ECooling.biz

 

[poetix99]

ko99, I think that this was more a human safety issue w.r.t. the sides of the ladle, rather than h.t. from the top of the ladle...

bilou,
The surface temperature will continually (but diminishingly) decrease as one adds thickness to the insulation. You should decide what surface temperature is acceptable, and then work from that.

As a related aside, there is a "critical thickness" of insulation, often defined for cylinders (as for piping) where the total amount of heat transfer is maximized - this being related to the rate of increase of surface area vs. the rate of decrease of h.t. per unit of surface area.

 

[corus]

Normally finite element methods are used to predict the temperature distribution of ladles assuming that the ladle is axisymmetric and can be modelled as a 2D object in the R-Z plane. The inside of the lining is assumed to be at the hot metal temperature, about 1500C. Due to the expansion of the lining on to the ldalde wall you can assume perfect conductivity through the lining and outer shell where on the outer surface natural convection and radiation is assumed to an ambient 20C. Take emmissivity to be about 0.9. For the underside of the ladle look at McAdam's for heat transfer from the underside of a flat plate. Similarly for the top of the ladle.
If you don't have finite element methods then consider a slice of the ladle away from the top and bottom of the ladle (where 2D effects occur) and assume one dimensional axi-symmetric heat flow. If the ladle has a large radius then you can use normal slab (XY) geometry. The inner and outer boundary conditions are stated above though you might want to approximate convection and radiation by a heat transfer coeffecient of about 10 W/M^2 C to 20 C

 

[corus]

My mistake, the overall heat transfer coefficient from a vertical surface which has a temperature of about 300C is 30 W/m^2 C, and not 10 as I said before. the ambient temperature is taken to be 20C in most countries.