Modelling of a Phase Change Material Melting Process Heated from below Using Spectral Collocation Methods
Résumé
Purpose – Mathematical and numerical models are developed to study the melting of a Phase
Change Material (PCM) inside a 2D cavity. The bottom of the cell is heated at constant
and uniform temperature or heat flux, assuming that the rest of the cavity is completely
adiabatic. The paper used suitable numerical methods to follow the interface temporal evolution
with a good accuracy. The purpose of this paper is to show how the evolution of the latent energy
absorbed to melt the PCM depends on the temperature imposed on the lower wall of the cavity.
Design/methodology/approach – The problem is written with non-homogeneous boundary
conditions. Momentum and energy equations are numerically solved in space by a spectral
collocation method especially oriented to this situation. A Crank-Nicolson scheme permits the
resolution in time.
Findings – The results clearly show the evolution of multicellular regime during the process
of fusion and the kinetics of phase change depends on the boundary condition imposed on the
bottom cell wall. Thus the charge and discharge processes in energy storage cells can be
controlled by varying the temperature in the cell PCM. Substantial modifications of the thermal
convective heat and mass transfer are highlighted during the transient regime. This model is
particularly suitable to follow with a good accuracy the evolution of the solid/liquid interface in
the process of storage/release energy.
Research limitations/implications – The time-dependent physical properties that induce
non-linear coupled unsteady terms in Navier-Stokes and energy equations are not taken into account in
the present model. The present model is actually extended to these coupled situations. This problem
requires smoother geometries. One can try to palliate this disadvantage by constructing smoother
approximations of non-smooth geometries. The augmentation of polynomials developments orders
increases strongly the computing time. When the external heat flux or temperature imposed at the
PCM is much greater than the temperature of the PCM fusion, one must choose carefully some data to
assume the algorithms convergence.
Practical implications – Among the areas where this work can be used, are: buildings where the
PCM are used in insulation and passive cooling; thermal energy storage, the PCM stores energy
by changing phase, solid to liquid (fusion); cooling and transport of foodstuffs or pharmaceutical
or medical sensitive products, the PCM is used in the food industry, pharmaceutical and medical,
to minimize temperature variations of food, drug or sensitive materials; and the textile industry,
PCM materials in the textile industry are used in microcapsules placed inside textile fibres. The PCM
intervene to regulate heat transfer between the body and the outside.
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