# Time to cool a cube

Hi, I'm trying to estimate the time to cool a liquid in a cube to a given
temperature. I've been looking around but I find a lot of large equations
which I'm not sure if they are the appropiate for the case. To refresh my
mind (it's some years since I studied this)I've downloaded
but I can't find anything.
With just a 2D estimation I've enough.
Maffer
The amount of heat that transfers is determined from the difference in temperature, the mass of liquid and the specific heat of the liquid. That's the easy part.
To determine the time required involves knowing about the heat transfer process (from the cube to the surroundings). What are the walls of the cube made of and how thick are they? How cold is the ambient and what is the initial fluid temperature? Is it cooling by natural convection in air, or is there also a conduction component? Etc., etc.
Don Kansas City
Need to know: Length of side of cube? Liquid type? cube full? air cooled / water cooled / free air? draft all sides? Blown draft? Start temperature? End temperature?
Regards
Brian W
It's a test cube for iron foundry. I'm not considering the effect of the filling, so I'm just considering the iron is at the pouring temperature minus some losses (1330ºC). So the walls are of sand (conductivity 0.75 W/mK), the liquid inside is melted iron (50 W/mK) and the h sand-iron 800 W/m2K. The sand and the ambient at (20ºC).
I want to see the effect of the sand wall thickness and what happens if I put a chill on one side (conductivity of chill 40 W/mK, h iron-chill 800 W/m2K) as well as the influence of the chill thickness.
If someone knows of a reference about this I will aprecciate it.
Thanks, Maffer
A good heat transfer textbook wouldn't hurt. It doesn't sound like too difficult a problem. You also will have to take into account the latent heat of solidification since the temperature will not change during crystallization of the iron, though heat is still transferring out of it.
Don Kansas City
I recall a related problem while working in the UK 50 years ago. My firm, which had a capable computation lab, was asked the question "how long will it take to thaw out a package of frozen fish?" - such pre-packaged foods were then coming on the market. I didn't know the computation results but someone suggested placing a few samples on a kitchen table and making some temperature measurements. The point here is that with quite a few variables in ambient conditions, a practical approach might be the best method for the molten iron problem Gord.
Looking at these problems you generally start out by finding the dimensionless Biot number Bi hL/k, which is a measure of the relative importance of internal conduction and external heat transfer - L is a characteristic dimension of the body. (Not sure how big your test sample is.) Anyway, how you proceed from here depends on Bi, but the interesting (and difficult cases) are when Bi is around unity (well between .05 and 20, which it looks like applies in your case).
It also looks like you are dealing with solidification here, so you get a moving boundary - in that case another dimensionless number, the Jakob number Ja = c(T_s-T_i)/h_fs, applies.
These sorts of problems are not really soluble using "cookbook" methods - you need to do a bit of analysis to understand the important parameters. A good reference for general heat transfer which does deals with these sorts of real world problems is Mills, Heat Transfer. Irwin. ISBN 0256-07642-1. He has a section on moving boundary problems - solidification and ablation.
Good luck...

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