Integral Solution of Two-Region Solid–Liquid Phase Change in Annular Geometries and Application to Phase Change Materials–Air Heat Exchangers

Abstract

A mathematical model based on the integral method is developed to solve the problem of conduction-controlled solid–liquid phase change in annular geometries with temperature gradients in both phases. The inner and outer boundaries of the annulus were subject to convective, constant temperature or adiabatic boundary conditions. The developed model was validated by comparison with control volume-based computational results using the temperature-transforming phase change model, and an excellent agreement was achieved. The model was used to conduct parametric studies on the effect of annuli geometry, thermophysical properties of the phase change materials (PCM), and thermal boundary conditions on the dynamics of phase change. For an initially liquid PCM, it was found that increasing the radii ratio increased the total solidification time. Also, increasing the Biot number at the cooled (heated) boundary and Stefan number of the solid (liquid) PCM, decreased (increased) the solidification time and resulted in a greater (smaller) solid volume fraction at steady state. The application of the developed method was demonstrated by design and analysis of a PCM–air heat exchanger for HVAC systems. The model can also be easily employed for design and optimization of annular PCM systems for all associated applications in a fraction of time needed for computational simulations.

The Impact of a Mobile Shading System and a Phase-Change Heat Store on the Thermal Functioning of a Transparent Building Partition

“…In the considered solution of using phase change materials with transparent partitions and shading systems, a complex mechanism of heat exchange between individual elements of the building’s window was taken into account. The temperature distribution in the 1-dimensional discrete system of the composite window with a phase change pillow according to papers [ 24 , 26 , 42 , 44 ] was calculated according to the Equations (3) and (4), as shown in Figure 2 . where R (i−1; i ) —heat resistance between points i−1 and i, ϱ i —density of point i, C wi —specific heat of the material at point i, T t i —t temperature of point i at time t, Δt—time step, Δx 2 i —square of the thickness of the element I and λ i —thermal conductivity coefficient i.…”

Phase Change Material Melting Process in a Thermal Energy Storage System for Applications in Buildings

“…Figures [23][24][25][26][27] show the distribution of the liquid fractions throughout the melting process with 10% (1050 s), 30% (1990 s), 50% (2800 s), 70% (3650 s) and 90% (4690 s) of the volume of the PCM being melted, respectively. In the step referring to Figure 23, with a range of a 0 to 100% liquid fraction, the following characteristics were observed: In the z = 0 and 100 mm sections, the PCM fractions near the fins were found with values around 50%; in the regions referring to the lower half of the annular and close to the external surface of the inner tube, the local liquid fraction values close to 100% were obtained.…”

“…The energy accumulated in a PCM latent thermal system can be used in a liquid desiccant air-conditioning system to control a room's temperature and relative humidity (or absolute humidity). Many other PCM applications in buildings have been reported in the literature, such as a PCM-air heat exchanger system for the heating, ventilation, and air conditioning of buildings [25]; latent heat thermal energy storage using PCM [26]; and solar radiation in PCM cells [27].…”

“…Figures[23][24][25][26][27] show the distribution of the liquid fractions throughout the melting process with 10% (1050 s), 30% (1990 s), 50% (2800 s), 70% (3650 s) and 90% (4690 s) of the volume of the PCM being melted, respectively.…”