# Heat exchange in a thermal storage based on phase change materials

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• DianeLR
In summary, a thermal battery based on phase change materials (PCM) is being modeled using a plate heat exchanger immersed in a PCM bath. The temperature at each moment and from everywhere in the battery is being determined, with the assumptions of natural convection being neglected, no supercooling or superheating, an incompressible and Newtonian heat transfer fluid, and neglecting kinetic and potential energy variations. The PCM parts are being modeled in 2D while the heat transfer fluids are modeled in 1D. There is a question about the correctness of certain equations, particularly Eqn. 10, which is related to the enthalpy behavior of solid and liquid phases at different temperatures. There is also a concern about a potential
DianeLR
Hello,

I want to model a thermal battery based on phase change materials (PCM). It is a plate heat exchanger immersed in a PCM bath. The diagram is given in the attached file.
I want to determine the temperature at each moment and from everywhere in the battery. The hypotheses are the following:

- Natural convection neglected (pure conduction),
- No supercooling or superheating,
- incompressible and Newtonian heat transfer fluid,
- Kinetic and potential energy variations are neglected,
- Homogeneous, isotropic and pure body PCM,
- Isothermal phase change,
- Density variation of PCM during the change of state neglected,
- Thermophysical properties independent of temperature (and different for liquid and solid phases).

These assumptions allowed me to obtain the equations visible in the attached file. The MCP parts are modeled in 2D (in x and y) while the heat transfer fluids in 1D (in y).
Do the equations seem correct to you?

#### Attachments

• PCM_storage_eqs_V2.png
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I kind of see what you are solving here, but part of it confuses me.

The are two regions of PCM, 1 and 2. Region 1 is next to the hot side of the heat exchanger and 2 is next to the cold side. Both regions can have solid (at temperatures below the melting point), liquid at temperatures above the melting point, or a combination of solid and liquid (liquid fraction f) at the melting point. Correct so far?

I have a problem with Eqn. 10. The enthalpy per unit mass behavior should be as follows:

##h=c_s(T-T_{M})## for ##T<T_M##

##h=Lf## for ##T=T_M##

##h=L+c_l(T-T_M)## for ##T>T_M##

Are you assuming that solid and liquid can exist together at temperatures other than the melting point?

In Eqns. 3 and 4, the final terms on the RHS (axial conduction terms) are negligible except for liquid metals.

It's correct what you said.
For the enthalpie, I used that equation to determine the equation inside the PCM (see picture)

And thanks for the equations (3) and (4). It will be easier to solve with one less term

#### Attachments

• Annotation 2023-02-06 092121.png
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I think I am making a mistake with equation (4). The hot heat transfer fluid is against the flow of the cold. Shouldn't there be a minus sign before $$m c_p$$ (on the left of the equality)?

DianeLR said:
For the enthalpie, I used that equation to determine the equation inside the PCM (see picture)
It doesn't look the same as what I gave. It might be easier to integrate 9 and 10 in terms of enthalpy than in terms of temperature.
DianeLR said:
I think I am making a mistake with equation (4). The hot heat transfer fluid is against the flow of the cold. Shouldn't there be a minus sign before $$m c_p$$ (on the left of the equality)?
Yes

Thank you for your response. I will check for the integration in terms of enthalpy.

## What are phase change materials (PCMs) used in thermal storage?

Phase change materials (PCMs) are substances that absorb and release thermal energy during the process of melting and freezing. When a PCM melts, it absorbs a large amount of heat from its surroundings (latent heat) without a significant rise in temperature. Conversely, when it solidifies, it releases the stored heat. These materials are used in thermal storage systems to regulate temperature and store energy efficiently.

## How does heat exchange occur in a PCM-based thermal storage system?

In a PCM-based thermal storage system, heat exchange occurs primarily through the phase transition of the material. When the surrounding temperature rises above the melting point of the PCM, it absorbs heat and changes from solid to liquid, storing energy in the process. When the temperature drops below the melting point, the PCM releases the stored heat as it solidifies, thus providing thermal energy to the surroundings.

## What are the advantages of using PCMs for thermal storage?

PCMs offer several advantages for thermal storage, including high energy storage density, the ability to maintain a nearly constant temperature during phase change, and the potential for long-term energy storage. They can help improve energy efficiency, reduce peak energy demand, and provide a stable temperature environment for various applications such as building temperature regulation, solar energy storage, and electronic cooling.

## What are the common types of PCMs used in thermal storage systems?

Common types of PCMs used in thermal storage systems include organic PCMs (such as paraffin waxes and fatty acids), inorganic PCMs (such as salt hydrates and metallics), and eutectic mixtures (combinations of different substances that melt and solidify at a single temperature). Each type has its own set of properties, such as melting point, latent heat capacity, and thermal conductivity, making them suitable for different applications.

## What are the challenges associated with using PCMs in thermal storage systems?

Challenges associated with using PCMs in thermal storage systems include the need for proper encapsulation to prevent leakage, potential degradation over multiple thermal cycles, limited thermal conductivity which can affect heat transfer rates, and the cost of materials. Additionally, selecting the appropriate PCM for a specific application requires careful consideration of the material's thermal properties and compatibility with the system's operating conditions.

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