Review on numerical algorithms for melting and solidification studies and their implementation in general purpose computational fluid dynamic software

•A comprehensive theory of evolution of melting and solidification enthalpy models.•A detailed discussion on the porosity models used for simulating the velocity reduction to zero during solidification process.•Comprehensive discussion on the error and stability issues of the numerical schemes used in CFD for melting and solidification.•Detailed discussion on error introduced due to the difference between the complex physics of solidification and melting and numerical results.•Challenges and future directions in research for simulation of solidification and melting. Phase change materials (PCMs) have gained much attention due to their high ratio of energy density to mass and their near isothermal behaviour during melting and solidification. Recently, the simulation of solidification and melting has been carried out using CFD solvers in various fields including electronic cooling circuits, building envelopes, and other heating, air conditioning and ventilation systems. This article reviews the evolution of the numerical algorithms on solidification and melting through commercial computational fluid dynamic (CFD) software. A guideline for using appropriate melting and solidification algorithm are is required for obtaining accurate and stable solutions. This review work bridges that gap. Errors and stability issues of the numerical schemes for melting and solidification are presented in this work. Also, the error that occurs due to the difference between the complex physics of solidification and melting and their numerical results is addressed in this work. CFD simulation avoids costly experiments, ensures the fastest parametric studies, and also generates the result for almost all points in the domain without disturbing the domain. Thus, the modelling and simulation of PCM-employed thermal energy models using CFD software helps to minimize the time for design and execution as well as the expenditure on the construction of any real-time thermal systems. In this article the algorithm of various types of solvers for melting and solidification, using CFD software and their applications reported by various researchers are discussed in detail. Also, the challenges in micro-scale modelling and future directions in the simulation of solidification and melting are discussed in this review work.