# PCM wax freezing... outside solid, inside liquid

 P: 2 A colleague and I want to model how a slab of PCM (wax) solidifies as it cools off. What I have noticed in my experiments is that temperature sensors on the top and bottom of the slab say it should be solid, as they read well below the melting point. But when I peek at the sample, the center is still liquid. In order to get the full cooling effect of the PCM, it needs to be completely solid. How can we model the time for slabs of varying thickness to completely solidify? What we need is a starting point for this investigation. How can we get a first order approximation as simply as possible? Can we forget about the fact that the slab is part solid and part liquid, and just say that "heat in = heat out" and the solidification time is just the time to lose all the heat we stored in the slab? For example, one model we thought of: if we melt the slab using 10W and it takes 1 hr. to liquefy, then we remove the heat source, the slab will lose heat according to Newton's law, assuming ambient temperature is 20 degrees C. How many hours will it take to lose all of its stored heat. Assume the slab is 1 cm thick, 2 cm wide, 30 cm long. Assume the PCM is Rubitherm RT-28 (http://www.rubitherm.de/english/down...0RT28HC_EN.PDF).
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 Quote by CraigHyatt A colleague and I want to model how a slab of PCM (wax) solidifies as it cools off. What I have noticed in my experiments is that temperature sensors on the top and bottom of the slab say it should be solid, as they read well below the melting point. But when I peek at the sample, the center is still liquid. In order to get the full cooling effect of the PCM, it needs to be completely solid. How can we model the time for slabs of varying thickness to completely solidify? What we need is a starting point for this investigation. How can we get a first order approximation as simply as possible? Can we forget about the fact that the slab is part solid and part liquid, and just say that "heat in = heat out" and the solidification time is just the time to lose all the heat we stored in the slab? For example, one model we thought of: if we melt the slab using 10W and it takes 1 hr. to liquefy, then we remove the heat source, the slab will lose heat according to Newton's law, assuming ambient temperature is 20 degrees C. How many hours will it take to lose all of its stored heat. Assume the slab is 1 cm thick, 2 cm wide, 30 cm long. Assume the PCM is Rubitherm RT-28 (http://www.rubitherm.de/english/down...0RT28HC_EN.PDF).
This is a transient conductive heat transfer problem involving change of phase. It can definitely be modeled. The data you presented in your reference is adequate for solving for the temperature profile within the slab as a function of time. The answer will also depend on the nature of the boundary conditions on the surface. If it is sitting in air at 20C, that will give you slower heat transfer than if the surface is cooled in a different way.

The answer to this problem can be bounded by the solution obtained assuming the slab is infinitely wide in all lateral directions and 1 cm thick. This reduces the problem to 1 D .

You may be able to find a solution to the 1D problem in Conduction of Heat in Solids by Carslaw and Jaeger.

Chet
 P: 2 Thanks so much, Chet. In practice, the PCM will be in a container, but the container will always be cooled at roughly room temperature. We were thinking that assuming the surface is in contact with air would at least eliminate the container as a variable, plus make it simpler to confirm by experiment. We will investigate the effect of having the air boundary on the rate of cooling vs some solid material. Also thanks for confirming the 1D simplification. I wasn't sure about that. It is neat that we can get both a temperature profile as well as an upper bound for a given thickness. I will check the Carslaw and Jaeger reference. Thanks again, Craig.

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