Heat conduction problem help
 

There is one problem related to heat conduction. I was looking at a paper and it says this:

The 3D unsteady state conduction equation was solved for steel bath as well as refractory walls.
The tapping phenomenon was modelled with methodology mentioned below:
• 3D unsteady state conduction equation was solved for every one minute of tapping.
• The molten steel bath height was calculated after every minutes of tapping based on the ladle filling rate, and the level of molten steel was increased accordingly.
• The molten steel bath was homogenized after every minute with average bulk temperature of the molten steel in the ladle.

An analogy case will be:

The water filling in a bucket for some time and its height is changing. So, the bucket here is ladle and water is molten steel here.

Can any one suggest how to solve the problem using fluent and even please help on the modelling part of it.

There is one aproach with 2 phase problem solving but according to the researcher he has not used 2 phase problem. He has used simple conduction equation on single phase thing with change in height after every minute.