Effects of Total Thermal Balance on the Thermal Energy Absorbed or Released by a High-Temperature Phase Change Material

Abstract

Front tracking and enthalpy methods used to study phase change processes are based on a local thermal energy balance at the liquid–solid interface where mass accommodation methods are also used to account for the density change during the phase transition. Recently, it has been shown that a local thermal balance at the interface does not reproduce the thermodynamic equilibrium in adiabatic systems. Total thermal balance through the entire liquid–solid system can predict the correct thermodynamic equilibrium values of melted (solidified) mass, system size, and interface position. In this work, total thermal balance is applied to systems with isothermal–adiabatic boundary conditions to estimate the sensible and latent heat stored (released) by KNO3 and KNO3/NaNO3 salts which are used as high-temperature phase change materials. Relative percent differences between the solutions obtained with a local thermal balance at the interface and a total thermal balance for the thermal energy absorbed or released by high-temperature phase change materials are obtained. According to the total thermal balance proposed, a correction to the liquid–solid interface dynamics is introduced, which accounts for an extra amount of energy absorbed or released during the phase transition. It is shown that melting or solidification rates are modified by using a total thermal balance through the entire system. Finally, the numerical and semi-analytical methods illustrate that volume changes and the fraction of melted (solidified) solid (liquid) estimated through a local thermal balance at the interface are not invariant in adiabatic systems. The invariance of numerical and semi-analytical solutions in adiabatic systems is significantly improved through the proposed model.

Effects of Volume Changes on the Thermal Performance of PCM Layers Subjected to Oscillations of the Ambient Temperature: Transient and Steady Periodic Regimes

“…The FEM was applied to find the spacial dependence of the temperature field in each phase [ 32 ]. Equation ( 4 ) was solved through the methodology described in Ref.…”

“…Equation ( 4 ) was solved through the methodology described in Ref. [ 32 ], but using the linear Lagrange shape functions at each element as follows: Here and represent the nodal coordinates of any given element. The temperature field within each element is given by: where, and is the time dependent part of the temperature at each node.…”

“…Equations ( 13 ), ( 16 ), and ( 18 ) were solved for the dynamical variables , , and by using an explicit finite difference scheme with a first order approximation to the time derivatives. The position of each interface and the thickness of the PCM layer in the next time level were used to solve the heat equation through the FEM previously mentioned [ 32 ].…”

Thermophysical Characterization of Paraffin Wax Based on Mass-Accommodation Methods Applied to a Cylindrical Thermal Energy-Storage Unit

“…The authors, however, did not consider the volume changes of the system during the phase transition, since equal densities in the liquid and solid phase were assumed. Effects on the energy stored, charging times, and melting fractions produced by considering volume changes during phase transitions at constant pressure have been addressed on planar configurations [16][17][18][19]. The authors did not take into account the effects of supercooling (superheating) and natural convection during the solidification (melting) process, despite considering high temperature gradients.…”