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Cyclic phase change involves the successive freezing and melting of a region driven by a boundary temperature that cycles above and below the solid/liquid phase change temperature. In this paper, a recently proposed fixed grid phase change enthalpy method is modified and applied to cyclic solid/liquid phase change problems. The basic approach is demonstrated on application to a one‐dimensional, heat conduction controlled phase change. Then the method is used to investigate a cyclic phase change problem that involves fluid flow. The interaction of the melting and freezing with the phase change leads to some interesting predictions for the location and shape of the solid/liquid interface. The results also indicate that melting cycles are more effective than freezing cycles.

The present paper describes the applicability of hybrid transfinite element modelling/analysis formulations for non‐linear heat conduction problems involving phase change. The methodology is based on application of transform approaches and classical Galerkin schemes with finite element formulations to maintain the modelling versatility and numerical features for computational analysis. In addition, in conjunction with the above, the effects due to latent heat are modelled using enthalpy formulations to enable a physically realistic approximation to be effectively dealt computationally for materials exhibiting phase change within a narrow band of temperatures. Pertinent details of the approach and computational scheme adapted are described in technical detail. Numerical test cases of comparative nature are presented to demonstrate the applicability of the proposed formulations for numerical modelling/analysis of non‐linear heat conduction problems involving phase change.

A method has been developed for conjugate heat transfer analysis of fluid flow inside parallel channels formed by a phase change material (PCM) separated from the fluid by a wall. The phase change in the PCM is two dimensional and a hybrid analysis consisting of an analytical solution in one direction and a finite‐difference method in another direction is used to solve for the temperature in the PCM. The heat transfer fluid (HTF) inlet temperature is given and the heat transfer between the HTF and the PCM is treated as a conjugate problem that requires no iterations to obtain a solution. The numerical results are found to be stable, convergent, and accurate. Application of the method to the solution of heat extraction from a phase‐change energy storage unit is given in detail and the numerical results are shown to be accurate, based on an energy conservation analysis, to within 3%.

A phase‐change temperature‐based formulation including general latent heat effects is presented. These effects are taken into account by means of an explicit “phase‐change function” (or liquid fraction‐temperature relationship in a more specific context) defined analytically or based on experimental measurements. The behaviour of different functions is studied and compared. The finite element equations of this formulation are also described. Finally, a numerical example is analysed to illustrate the performance of the proposed methodology.

Two common fixed grid enthalpy methods used in the numerical modelling of phase change problems are the apparent heat capacity and the source based methods. In this paper, a general enthalpy method that includes as subsets both apparent heat capacity and source based methods, is derived. Following this, an optimal enthalpy scheme is identified. The superiority of the optimal scheme over the apparent heat capacity and the source based schemes is illustrated by solving sample phase change problems.

The homographic approximation, in which the Heaviside step function is replaced by a continuous smooth curve, is applied to the enthalpy method for heat transfer problems with isothermal phase change. Both the finite difference and finite element implementations, based on the basic enthalpy, the apparent heat capacity and the source term formulations, are considered. A 1‐D Stefan problem of melting a solid is used as a test problem. The accuracy of the numerical solutions is measured globally using L2 error norms and comparison is made between the solutions using homographic approximation and those using linear approximation. The advantages of using homographic approximation are examined.

Thermal solidification processes are an important concern in today’s manufacturing technology. Because of the complex geometric nature of real‐world problems, analytical techniques with closed‐form solutions are scarce and/or not feasible. As a consequence, various numerical techniques have been employed for the numerical simulations. Of interest in the present paper are thermal solidification problems involving single or multiple arbitary phases. In order to effectively handle such problems, the finite element method is employed in conjunction with adaptive time stepping approaches to accurately and effectively track the various phase fronts and describe the physics of phase front interactions and thermal behaviour. In conjunction with the enthalpy method which is employed to handle the latent heat release, a fixed‐grid finite element technique and an automatic time stepping approach which uses the norm of the temperature distribution differences between adjacent time step levels to control the error are employed with the scale of the norm being automatically selected. Several numerical examples, including single and multiple phase change problems, are described.

A rigorous Finite Element (FE) formulation based on an enthalpy technique is developed for solving coupled nonlinear heat conduction/mass diffusion problems with phase change. The FE formulation consists of a fully coupled heat conduction and solute diffusion formulation, with solid‐liquid phase change, where the effects of pressure and convection are neglected. A full enthalpy method is employed eliminating singularities which result from abrupt changes in heat capacity at the phase interfaces. The FE formulation is based on the fixed grid technique where the elements are two dimensional, four noded quadrilaterals with the primary variables being enthalpy and average solute concentration. Temperature and solid mass fraction are calculated on a local level at each integration point of an element. A fully consistent Newton‐Raphson method is used to solve the global coupled equations and an Euler backward difference scheme is used for the temporal discretization. The solution of the enthalpy‐temperature relationship is carried out at the integration points using a Newton‐Raphson method. A secant method employing the regula falsi technique takes into account sudden jumps or sharp changes in the enthalpy‐temperature behaviour which occur at the phase zone interfaces. The Euler backward difference integration rule is used to calculate the solid mass fraction and its derivatives. A practical example is analysed and results are presented.

In the original effective heat capacity method the latent heat effect is approximated by a large effective heat capacity over a small temperature range. This method is simple in concept and easy to implement. However, it is so sensitive to the choice of the phase change temperature interval and the chosen time integration scheme that non‐convergence always occurs when it is implemented with implicit time integration schemes. Presents the cause and cure of non‐convergence in effective heat capacity methods and discusses sample results.

The conservation element and solution element (CE/SE) method, an accurate and efficient explicit numerical method for resolving moving discontinuities in fluid mechanics problems, is used for the first time to solve phase change problems. Several isothermal phase change cases are studied and comparisons are made to existing analytical solutions. The CE/SE method is found to be accurate and robust for the numerical modeling of phase change problems.