During latent heat storage, the temperature of the material remains the same. So the question is what parameter changes during latent heat so that the energy stored inside the PCM material can be directly calculated as a function of X (just like we can calculate the energy in material as a function of temperature for sensible heat storage). I believe one of the parameters that changes are density. But what is the relation between the density of PCM material and energy content in it?? I am just stuck here.
Is there a way to determine the amount of heat sored in PCM material as a function of X (some simple equations) at any given time?
Also is the rate of energy stored constant during the phase changing process??
The enthalpy of fusion is the latent heat required to change a substance from solid to liquid. You can look up the latent heat of fusion for many substances. I think it would be fair to define the liquid fraction of your phase change material simply based on what percentage of the latent heat of fusion that you have added to your material. I assume that you are interested in solid to liquid phase change in the context of PCM materials. However for liquid to gas you want the latent heat of evaporation and in that case the dryness fraction may be useful. For example lines of constant dryness fraction are plotted in the liquid vapour dome on enthalpy - entropy diagrams for steam.
In a model, you can use temperature and melt fraction to get the total heat stored in a phase change material. The Temperature will give you the sensible heat storage via the specific heat, and the melt fraction will give you the latent heat storage via the material's latent heat of fusion. the sum of the two will give you total heat stored from an initial state.
Now you didn't specify but it sounds like you're looking for a measurable parameter for calculating heat storage in an experiment or a physical system? The same thing applies as above, but melt fraction isn't a simple measurable parameter. As you said, you'll need to infer it from something else that changes with melt fraction. Most materials do have a noticeable change in density between states (many PCM's see up to a 10% volume change on melting). If you have a very simple structure and a clearly visible material, you may be able to measure the current total PCM volume, then estimate what fraction must have melted to give you the measured change in volume. Note that this can quickly become impractical depending on your physical implementation and the fact that phase change is localized, with a moving phase front originating at the heat source, and volume expansion cannot be expected to occur uniformly or in a way that is simply measurable. Also, this assumes your working with a static solid-liquid phase change material. Something in a flow loop, like a pumped slurry, may have other options for getting local density of the fluid moving by.
Again, if you have a simple 1 or 2D structure with complete visibility and a single, easily located melt front, you could estimate melt fraction simply from the location or geometry of the phase front.
it is possible that other materials properties could be measured as well that would indicate melting (dielectric properties for non-conductors, electrical conductance for metallic PCMs, etc.) but again, these measurements would have to be well designed for your geometric situation.
The total heat stored in a phase change material depends on many factors; melting temperature, latent heat, temperature difference, and solidification point.
The dependency of heat stored with an X-value you asked depends on the step you are :
- If the step is below melting temperature, this is the quantity of sensible heat stored in the material; X is the temperature. Similarly, if you are above the melting point, the material is fully liquid and X is also temperature (with the addition of solid sensible heat and latent heat).
- If you are looking for an X-value during the melting process (at melting temperature), you can use the liquid fraction. The easiest way to have a good approximation could be visual observation with a camera. If it is not possible, you can try to measure the duration of melting (where the temperature is constant at the melting point). You would know the time needed for total melting and the quantity stored at any time. I did this for heat released vs. time for solidification of PCM in Article Experimental measurements of the residual solidification dur...
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