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New correlation for transient laminar natural convection heat transfer in a differentially heated square cavity between air and a PCM layer

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Abstract

This paper proposes a new correlation to evaluate the heat transfer coefficient between a vertical wall containing a phase change material (PCM) and air in a square enclosure. This correlation was determined in order to simulate the transient process during PCM discharge and its effect on the heat transfer inside the cavity without using complex CFD models. A 2D CFD model based on the resolution of Navier–Stokes and energy equations inside the air and the PCM was previously validated. It was used to generate numerical data in order to build the proposed heat transfer correlation. The new correlation is \({\text{Nu}}={0.186\cdot {{\text{Ra}}}^{0.28}\theta }^{0.271}{{\text{Ste}}}^{0.022}\) valid for: \({10}^{5}\le {\text{Ra}} \le { 4.3 10}^{7}, 0.05 \le \theta \le 1 {\text{and}} 0.05 \le {\text{ste}} \le 0.6\). The accuracy of the proposed correlation versus the correlations established without phase change is analysed through a simplified model considering only the PCM layer and replacing the air cavity by a flux condition with an appropriate heat transfer coefficient. The relative error being lower than 1%, the new correlation shows a better agreement with the CFD results than existing correlations.

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Abbreviations

c :

Specific heat (kJ kg−1 K−1)

e :

PCM thickness (m)

L :

Cavity side length (m)

f :

PCM liquid fraction (%)

g :

Gravitational acceleration (m s−2)

H :

Latent heat (kJ kg−1)

HTC:

Heat transfer coefficient (W m−2 K−1)

Nu:

Nusselt number (−)

P :

Pressure (Pa)

PCM:

Phase change material

Ra:

Rayleigh number (−)

Ste:

Stefan number (−)

Fo:

Fourier number (−)

t :

Time (s)

T :

Temperature (K)

U,V :

Velocity components (m s−1)

x,y :

Cartesian coordinates (m)

X :

Length ratio (−)

Y :

Height ratio (−)

β :

Thermal expansion coefficient (K−1)

ρ :

Density (kg m−3)

μ :

Dynamic viscosity (kg m−1 s−1)

ν :

Kinematic viscosity (m2 s−1)

λ :

Thermal conductivity (W m−1 K−1)

θ :

Dimensionless temperature (−)

α :

Thermal diffusivity(m2s−1)

C :

Cold

g :

Gas

H :

Hot

l :

Liquid

s :

Solid

m :

Melting

W :

PCM/air interface

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Acknowledgements

This study is a part of the RAFRIBAT project financially supported by the pars grant from the HASSAN II Academy of Sciences and Techniques, Morocco.

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Authors and Affiliations

  1. LGCGM, Univ Rennes, 3 Rue du Clos Courtel, BP 90422, 35704, Rennes, CEDEX 7, France

    Paul Byrne & Amina Meslem

  2. Laboratory of Processes for Sustainable Energy & Environment (ProcEDE), Cadi Ayyad University, Marrakech, Morocco

    Hassan Chehouani & Brahim Benhamou

  3. Pole Cristal, 49 Av. René Cassin, 22100, Dinan, France

    Abdelouhab Labihi

Authors
  1. Abdelouhab Labihi
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  2. Hassan Chehouani
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  3. Brahim Benhamou
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Contributions

AL and HC: writing, simulation and interpretation of the results. BB: revision and supervision the work. AM and PB: writing, revision and supervision the work.

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Correspondence to Abdelouhab Labihi.

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Labihi, A., Chehouani, H., Benhamou, B. et al. New correlation for transient laminar natural convection heat transfer in a differentially heated square cavity between air and a PCM layer. J Therm Anal Calorim 149, 4033–4047 (2024). https://doi.org/10.1007/s10973-024-12982-3

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