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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.

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.

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.

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.

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.

The paper's originality is reflected in the precision of its results, due to the use of a high-accuracy numerical approximation based on collocation spectral methods, and the choice of Chebyshev polynomials basis in both axial and radial directions.

The purpose of this paper is to conduct a numerical study to analyze the melting process along a vertical wavy surface with uniform surface temperature.

The cavity horizontal walls are insulated while the left hot wavy wall and the right cold wall are maintained at temperatures, TH=38.3°C and TC=28.3°C, respectively. The enclosure was filled by solid Gallium initially at temperature TC. A numerical code is developed using an unstructured finite-volume method and an enthalpy porosity technique to solve for natural convection coupled to solid-liquid phase change. The validity of the numerical code used is ascertained by comparing the results with previously published results.

The effect of number of wavy surface undulation and amplitude of the wavy surface on the flow structure and heat transfer characteristics is investigated in detail. The numerical results show that the enhanced total heat transfer rate seems to depend on the amplitude of the wavy surface.

Flow and heat transfer from irregular surfaces are often encountered in many engineering applications to enhance heat transfer such as micro-electronic devices, flat plate solar collectors and flat-plate condensers in refrigerators, etc. Roughened surfaces could be used in latent storage systems where the wall heat flux is known. One of the reasons why a roughened surface is more efficient in heat transfer is its capability to promote fluid motion near the surface; in this way a complex wavy surface is expected to promote a larger heat transfer rate than a flat plate. This complex geometry will promote a correspondingly complicated motion in the fluid near the surface; this motion is described by the nonlinear boundary-layer equations.

The purpose of this paper is to analyse the convective heat transfer of an unsteady pulsed, laminar, incompressible flow in axisymmetric tubes with periodic sections. The flow is supposed to be developing dynamically and thermally from the duct inlet. The wall is heated at constant and uniform temperature.

The problem is written with classical homogeneous boundary conditions. We use a shift operator to impose non‐homogeneous boundary conditions. Consequently, this method introduces source terms in the Galerkin formulation. The momentum equations and the energy equation which govern this problem are numerically solved in space by a spectral Galerkin method especially oriented to this situation. A Crank‐Nicolson scheme permits the resolution in time.

From the temperature field, the heat transfer phenomenon is presented, discussed and compared to those obtained in straight cylindrical pipes. This study showed the existence of zones of dead fluid that locally have a negative influence on heat transfer. Substantial modifications of the thermal convective heat transfer are highlighted at the entry and the minimum duct sections.

Pulsated flows in axisymmetric geometries can be applied to medical industries, mechanical engineering and technological processes.

One of the original features of this study is the choice of Chebyshev polynomials basis in both axial and radial directions for spectral methods, combined with the use of a shift operator to satisfy non‐homogeneous boundary conditions.