Study of the usability of sinusoidal function heat flux based on enthalpy-porosity technique for PCM-related application
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Study of the usability of sinusoidal function heat flux based on enthalpy‑porosity technique for PCM‑related applications Tarek Bouzennada1 · Farid Mechighel1 · Abdelkader Filali2 · Lioua Kolsi3,4 Received: 25 September 2019 / Accepted: 10 December 2019 © Akadémiai Kiadó, Budapest, Hungary 2020
Abstract The present study summarizes a two-dimensional (2D) numerical simulation of a phase change material (PCM) melting/ solidification processes in a square cavity. The objectives of this study are to study and compare the effect of the application of different applied thermal boundary conditions such as constant or variable thermal flux during the melting and solidification processes of a PCM. Here, the convective heat transfer is taken into account according to the Boussinesq approximation. The commercial code COMSOL Multiphysics is used, and the “Voller model” based on the enthalpy-porosity technique is applied on a fixed computational grid. Results presented in terms of solid–liquid fraction, flow structure, isotherms, and stored and released thermal energy have shown that the melting time for the applied variable heat flux is reduced compared to that of constant heat applied flux. In addition, it was found that the PCM melting time was shorter than the solidification time. Therefore, the use of variable (sinusoidal) heat flux conditions can be useful in engineering applications such as thermal energy storage applications (PCM life cycle test, solar energy where a variable heat flow is involved due to the change of day). Keywords PCM · Mushy region · Melting · Solidification · Convective flow · Thermal energy storage List of symbols cp Specific heat (J kg−1 K−1) g Gravitational acceleration (m s2) k Thermal conductivity, W m−1 K−1 P Pressure (Pa) Q Heat flux (W m−2) * Tarek Bouzennada tarek.bouzennada@univ‑annaba.org * Lioua Kolsi [email protected] Farid Mechighel farid.mechighel@univ‑annaba.dz Abdelkader Filali [email protected] 1
Mechanics, Materials and Industrial Maintenance laboratory LR3MI, Mechanical Engineering Department, Faculty of Engineering Sciences, Badji Mokhtar - Annaba University, P.B. 12, 23000 Annaba, Algeria
2
Chemical Engineering Department, Imperial College London, South Kensington, London SW7 2AZ, UK
3
Mechanical Engineering Department, College of Engineering, Ha’il University, Ha’il City, Saudi Arabia
4
Laboratoire de Métrologie et des Systèmes Énergétiques, École Nationale d’Ingénieurs, University of Monastir, Monastir, Tunisia
T Temperature (K) Tm Melting point (K) Tl Liquid temperature (K) Ts Solid temperature (K) T̄ Average value of temperature (K) Tin Initial temperature (K) ΔT Transition temperature range (K) t Time (s) V⃗ Liquid velocity (m s−1) u Velocity in x-direction (m s−1) v Velocity in y-direction (m s−1) h Sensible enthalpy (kJ kg−1) H Total enthalpy (kJ kg−1) ΔH Latent heat (kJ kg−1) href Enthalpy reference (kJ kg−1) L Characteristic length (m) Gr Grashof number D Smoothed delta Dirac function ⃗ a Source term of porosity f
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