Numerical Study of Melting of an Organic Phase Change Material Inside a Corrugated Annulus

• Published in: International journal of applied and computational mathematics Vol. 11; no. 3
• Main Authors: Ali, Farooq H., Al-amir, Qusay Rasheed, Hamzah, Hameed K.
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.06.2025; Springer Nature B.V
• Subjects: Annuli; Applications of Mathematics; Computational Science and Engineering; Enclosures; Fluid flow; Free convection; Heat transfer; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Melting; Nanoparticles; Nuclear Energy; Nusselt number; Operations Research/Decision Theory; Original Paper; Parameters; Phase change materials; Theoretical; Viscosity; Natural convection; PCM; Annulus enclosure; Corrugated surface; Mg–MgO hybrid nanofluid
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-025-01866-1

In this work, the melting process of octadecane is numerically demonstrated in an annulus enclosure having a corrugated inner surface with a hybrid nanoparticle consisting of Mg–MgO. Finite-elements techniques are employed for solving the heat and flow model, depending on the undulations ( N ) of the inner surface. The influence of Fourier number, viscosity, and conductivity is examined. The heat transfer characteristics, including Nusselt number (Nu) and nanoparticle concentration ( ϕ ), are analyzed at concentration ratio, Rayleigh, Prandtl, and Stefan numbers of 0.05 (0.025Mg + 0.025MgO), 10 8 , 50, and 0.1, respectively. It is found that increasing the undulation number from N  = 4 to N  = 6 can first improve the melting process and thus the thermal performance, whereas a further increase ( N  = 9) can lead to a difficult fluid movement in the region close to undulated surfaces and low thermal performance. The melting process in the enclosure can be clearly defined in three stages according to the dominant transfer mechanism. At low Fourier number (Fo < 0.4), heat transfer is enhanced by increasing the number of undulations ( N ) from 4 to 6, but decreases when it increases to 9. In these three stages, the average Nusselt number behaves differently depending on the time evolution. Without accounting for the little variation in the initial values of (Nu)av for N  = 6 and N  = 9, the second model with N  = 6 exhibits the greatest average Nusselt number values across the whole range of Fourier numbers. In addition, it was found that the thermal convection parameter has a more profound effect on improving thermal performance than the dynamic viscosity parameter. The value of the average Nusselt number decreases with the increase in the Fourier number for three cases ( N  = 4, 6, and 9) and converges very closely after the Fourier value of 0.7.