Heat transfer in gas-stirred vessels

[Koarle]

Hello,

I am working in the domain of pyrometallurgy and wanted to get someones opinion on the following problem.

I am modeling a zinc fuming process for the reduction and evaporation of zinc from a molten slag bath at 1350 °C. In this slag bath, hot blast air and CH4 are injected at the bottom of the furnace (diameter of the furnace = 3 meter, heigth = 5 meter). The injection of hot blast air and CH4 in the bath causes reduction reactions mainly of ZnO_slag to Zn(g). This injection of blast air a is very turbulent process and causes substantial mixing and splashing of the slag bath. An schematic representation of the furnace can be found in Figure 1 on the following link:

http://www.mtm.kuleuven.be/Research/THERMO/hightemp/vessel.html

The particular problem for me is that the sidewalls of this furnace are not protected by refractory, but are water-cooled. Important is to estimate the heat transfer coefficient from the bath to the vertical sidewalls. My question is if there exist any correlations to estimate the heat transfer coefficient of the bath to the vertical sidewalls, preferrably as a function of Re, Pr, and the macroscopic process variables (bath height, bath diameter, rate of blast air injection etc.)

I have looked everywhere to find appropriate correlations for this, but I couldn't find anything useful. (e.g. there are many papers on the heat transfer from the bubbles to the bath, or on the hydrodynamic aspects of this kind of flow, but so far nothing on heat transfer from the bath to the vertical sidewalls.) The closest literature I found was on steel making ladles, however this is not very applicble to my problem since I work with a liquid slag bath instead of a liquid steel bath.

Is there anybody who has experience in this area or who may be able to me an indication how to tackle this problem please?

Thanks in advance!

Karel

 

[johnp]

Karel, When in doubt go back to basics.

1 - The heat transfer of air to liquid can be estimated using normal mass heat balance.

2 - The heat loss at the surface needs a bit more study. Perhaps the bubble papers can give you a lead. However it is limited by the contents in the heated volume. What doesn't escape out of the bath must go up into the vapour volume.

3 - You then have a heat loss interface between your hot liquid, though the slab, into the water bath. The heat transfer properties of water, including boundary layer insulating effects, are well documented.

4 - The U-factor, or insulating properties of slab need to be identified. This can be done in a laboratory if you can't find previously tested, published data.

5 - That leaves the estimation of the boundary layer insulation hot liquid to slag. If you don't need to be very accurate then you can take a reasonable guess of the U-factor of the boundary layer. At the temperature differential you are looking at this will be a small component. If you need more accuracy you will have to pay a laboratory to measure it for you.

That covers the heat loss in the wetted surface. Now apply the same reasoning in the vapour zone. Here the boundary layer between vapour to slag is likely to be more significant, but still not too tragic at the temperature differentials involved.