Analysis of solidification in a finite PCM storage with internal fins by employing heat balance integral method

Abstract

Summary Here, a simplified analytical model has been proposed to predict solid fraction, solid–liquid interface, solidification time, and temperature distribution during solidification of phase change material (PCM) in a two‐dimensional latent heat thermal energy storage system (LHTES) with horizontal internal plate fins. Host of boundary conditions such as imposed constant heat flux, end‐wall temperature, and convective air environment on the vertical walls are considered for the analysis. Heat balance integral method was used to obtain the solution. Present model yields closed‐form solution for temperature variation and solid fraction as a function of various modeling parameters. Also, solidification time of PCM, which is useful in optimum design of PCM‐based thermal energy storages, has been evaluated during the analysis. The solidification time was found to be reduced by 93% by reducing the aspect ratio from 8 to 0.125 for constant heat flux boundary condition. While, for constant wall temperature boundary condition, the solidification time reduces by 99% by changing the aspect ratio from 5 to 0.05. In case of convective air boundary surrounding, the solidification time is found to reduce by 88% by reducing the aspect ratio from 8 to 0.125. Based on the analytical solution, correlations have been proposed to predict solidification time in terms of aspect ratio and end‐wall boundary condition.

Semianalytical solution for PCM solidification during the discharging of a planar thermal energy accumulator

“…By replacing the expressions (11) to (13) in Equations (1) to (8) and regrouping the terms with equal powers, a system of equations is obtained. After several mathematical manipulations, the solutions of this system are provided.…”

“…Some exact analytical solutions exist only for pure conduction problems in semi‐infinite or infinite media, which are often subjected to simple initial and boundary conditions. When it is hard to find exact solutions, approximate, analytical and numerical methods can be introduced to solve the Stefan problems.…”

A semi‐analytical solution for time‐varying latent heat thermal energy storage problems

“…Several methods have been used to solve melting/solidification problems such as integral method, enthalpy method, and heat capacity method . On the other hand, different types of numerical methods were utilized such as finite element method (FEM), finite volume method (FVM), and finite difference method (FDM) .…”

“…The most related works that recently published include simulation and analysis of solidification process of a PCM, initiated by flowing cold water, inside a planar LHSU using the perturbation method and analysis of solidification in a finite PCM storage with internal fins by employing heat balance integral method …”

“…The most related works that recently published include simulation and analysis of solidification process of a PCM, initiated by flowing cold water, inside a planar LHSU using the perturbation method 33 and analysis of solidification in a finite PCM storage with internal fins by employing heat balance integral method. 34 In this research, the GDQM is used to discretize four test problems involving different nonlinearities and then the resulted nonlinear set of ordinary differential equations (ODEs) is solved via Runge-Kutta method (RKM). RKM is a reliable method to obtain transient response iteratively.…”