For calculating the exergy stored in the PCM, the choice of temperature TTT in the exergy equation is crucial. The exergy stored can generally be expressed as:

Exstored=∫T0T(1−T0T)dQEx_{stored} = \int_{T_0}^{T} \left( 1 - \frac{T_0}{T} \right) dQExstored​=∫T0​T​(1−TT0​​)dQ

where:

• T0T_0T0​ is the ambient (reference) temperature,
• TTT is the PCM temperature,
• dQdQdQ is the infinitesimal heat added to the PCM.

A common approach is to use the mass-averaged temperature of the PCM, given by:

Tavg=∫VρcpTdV∫VρcpdVT_{avg} = \frac{\int_V \rho c_p T dV}{\int_V \rho c_p dV}Tavg​=∫V​ρcp​dV∫V​ρcp​TdV​

where cpc_pcp​ is the specific heat, ρ\rhoρ is the density, and VVV is the PCM volume.

However, since the PCM undergoes phase change, an alternative approach is to consider the exergy change separately for the sensible and latent heat components:

Exstored=∫T0Tsolidus(1−T0T)ρcpdT+λ(1−T0Tmelt)+∫TliquidusT(1−T0T)ρcpdTEx_{stored} = \int_{T_0}^{T_{solidus}} \left( 1 - \frac{T_0}{T} \right) \rho c_p dT + \lambda \left( 1 - \frac{T_0}{T_{melt}} \right) + \int_{T_{liquidus}}^{T} \left( 1 - \frac{T_0}{T} \right) \rho c_p dTExstored​=∫T0​Tsolidus​​(1−TT0​​)ρcp​dT+λ(1−Tmelt​T0​​)+∫Tliquidus​T​(1−TT0​​)ρcp​dT

where:

• TsolidusT_{solidus}Tsolidus​ and TliquidusT_{liquidus}Tliquidus​ are the phase change limits,
• λ\lambdaλ is the latent heat of fusion,
• TmeltT_{melt}Tmelt​ is the melting temperature.

If your PCM melts over a temperature range rather than at a single melting point, using the effective PCM temperature or enthalpy-based approaches can be more accurate.

Mehran Sharifi First i would like to thank you for your interaction

The formula that you introduced for the exergy calculation is exactely the one i shared in my question. Indeed, i'm using the enthalpy based approach included in Ansys Fluent software. I'm confused about the PCM temperature Tp included in the formula, is it correct to replace it by the average temperature of the PCM or i should apply the formula in each control volume and then integrate. If i should use the last suggestion how to do it correctely in Fluent.

Best regards.

In a phase change material the temperature of the phase-changing material is set by the boiling point vs pressure relationship, e.g. water at 1 Bar.a = 100C, at 10 Bar.a = 180 C. When a liquid is changing phase the liquid's temperature is effectively constant because mixing is very rapid. A melting solid-phase is more difficult and is extremely uncommon apart from on start-up of molten salt heating systems!

can you share the reference you pulled the equation from?

@Jack Broughton - in thermal energy storage, solid-liquid PCMs are quite common and appears to be the primary design focus here.

Nicholas Robert Jankowski hello sir

Here's the DOI of the article: Article Preparation and thermal characterization of composite PCMs w...