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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.

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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.

Understanding the factors that contribute to the growth of sediment delta lobes in river systems has significant benefit towards protecting civil and social infrastructure from severe weather events. To develop this understanding, this paper aims to construct a three‐dimensional numerical model of a sediment delta depositing on to a two‐dimensional bedrock basement entering an ocean at a constant sea‐level.

The approach used adapts and applies techniques and schemes previously used in building numerical heat transfer models of melting systems. Particular emphasis is placed on modifying fixed grid enthalpy like schemes.

The resulting model provides important insight on the features that control the partition of sediment delta deposition between the land and ocean domains. The model also illustrates how tectonic subsidence may control the rate of delta growth.

This is the first numerical heat transfer inspired model of a three‐dimensional sediment delta deposit over both land and ocean domains. The problem has scientific merit in that it represents a melting‐like moving boundary problem with two distinct moving boundaries and a space/time dependent latent heat. Further, this work is a necessary first step towards building a comprehensive understanding of how to restore delta systems to protect civil and social infrastructure.

The purpose of this paper is the study of the electro-vortex flow (EVF) as well as heating and melting processes for mini industrial direct current electric arc furnace (DC EAF).

A mini DC EAF was designed, manufactured and installed to study the industrial processes of heating and melting a small amount of melt, being 4.6 kg of steel in the case under study. Numerical modelling of metal melting was performed using the enthalpy and porosity approach at equal values and non-equal values of the solidus and liquidus temperatures of the metal. The EVF of the liquid phase of metal was computed using the large eddy simulation model of turbulence. Melt temperature measurements were made using an infrared camera and a probe with a thermocouple sensor. The melt speed was estimated by observing the movement of particles at the top surface of melt.

The thermal flux for metal heating and melting, which is supplied through an arc spot at the top surface of metal, is estimated using the thermal balance of the furnace at melting point. The melting time was estimated using numerical modelling of heating and melting of metal. The process started at room temperature and finished once whole volume of metal was molten. The evolution of the solid/melt phase boundary as well as evolution of EVF patterns of the melt was studied.

Numerical studies of heating and melting processes in metal were performed in the case of intensive liquid phase turbulent circulation due to the Lorentz force in the melt, which results from the interaction of electrical current with a self-magnetic field.

The axisymmetric steady‐state convective‐diffusive thermal field problem associated with direct‐chill, semi‐continuously cast billets has been solved using the dual reciprocity boundary element method. The solution is based on a formulation which incorporates the one‐phase physical model, Laplace equation fundamental solution weighting, and scaled augmented thin plate splines for transforming the domain integrals into a finite series of boundary integrals. Realistic non‐linear boundary conditions and temperature variation of all material properties are included. The solution is verified by comparison with the results of the classical finite volume method. Results for a 0.500[m] diameter Al 4.5 per cent Cu alloy billet at typical casting conditions are given.

To present a novel moving boundary problem related to the shoreline movement in a sedimentary basin and demonstrate that numerical techniques from heat transfer, in particular enthalpy methods, can be adapted to solve this problem.

The problem of interest involves tracking the movement (on a geological time scale) of the shoreline of a sedimentary ocean basin in response to sediment input, sediment transport (via diffusion), variable ocean base topography, and changing sea level. An analysis of this problem shows that it is a generalized Stefan melting problem; the distinctive feature, a latent heat term that can be a function of both space and time. In this light, the approach used in this work is to explore how previous analytical solutions and numerical tools developed for the classical Stefan melting problem (in particular fixed grid enthalpy methods) can be adapted to resolve the shoreline moving boundary problem.

For a particular one‐dimensional case, it is shown that the shoreline problem admits a similarity solution, similar to the well‐known Neumann solution of the Stefan problem. Through the definition of a compound variable (the sum of the fluvial sediment and ocean depths) a single domain‐governing equation, mimicking the enthalpy formulation of a one‐phase melting problem, is derived. This formulation is immediately suitable for numerical solution via an explicit time integration fixed grid enthalpy solution. This solution is verified by comparing with the analytical solution and a limiting geometric solution. Predictions for the shoreline movement in a constant depth ocean are compared with shoreline predictions from an ocean undergoing tectonic subsidence.

The immediate limitation in the work presented here is that “off‐shore” sediment transport is handled in by a “first order” approach. More sophisticated models that take a better accounting of “off shore” transport (e.g. erosion by wave motion) need to be developed.

There is a range of rich problems involving the evolution of the earth's surface. Many of the key transport processes are closely related to heat and mass transport. This paper illustrates that this similarity can be exploited to develop predictive models for earth surface processes. Such models are essential in understanding the formation of the earth's surface and could have a significant impact on natural resource (oil reserves) and land (river restoration) management.

For the most part the solution methods developed in this work are extensions of the standard numerical techniques used in heat transfer. The novelty of the work presented rests in the nature of the problems solved, not the method used. The particular novel feature is the time and space dependence of the latent heat function; a feature that leads to interesting analytical and numerical results.

When a multi component alloy solidifies the redistribution of solute components leads to the formation of macrosegregation patterns. Blending ideas from a number of recent publications the purpose of this paper is to provide a “best practice” on how grid convergence of a given macrosegregation simulation can be measured and determined.

The best practice is arrived at by considering a benchmark problem consisting of a 2D-casting simulation of an idealized Al-4.5%Cu alloy in a side cooled square (76×76 mm) cavity. The model for this simulation is based on a mixture treatment of the relevant heat and mass transfer equations. Simulations are made using three increasingly refined grid sizes.

The best practice to determine grid resolution involves two steps: first, a visual evaluation of predicted segregation images leading to the evaluation of solute profiles along selected transects; and second, the construction of a cumulative distribution function (CDF) of the predicted segregation field. On application to the benchmark problem, it is concluded that current computer resources are insufficient to grid resolve macrosegregation patterns but that the CDF provides a useful signal of the nature of macrosegregation in a given system.

The benchmark is chosen to be representative. Exact convergence behavior, however, may depend on the system chosen.

In addition to establishing a best practice for measuring grid resolution of macrosegregation simulations the work also highlights, even in the absence of complete grid convergence, how the recently proposed CDF treatment can inform solidification modeling and process understanding.

To study the effects of velocity correction schemes for a temperature transforming model (TTM) for convection controlled solid‐liquid phase‐change problem.

The effects of three different solid velocity correction schemes, the ramped switch‐off method (RSOM), the ramped source term method (RSTM) and the variable viscosity method (VVM), on a TTM for numerical simulation of convection controlled solid‐liquid phase‐change problems are investigated in this paper. The comparison is accomplished by analyzing numerical simulation and experimental results of a convection/diffusion phase‐change problem in a rectangular cavity. Model consistency of the discretized TTM is also examined in this paper. The simulation results using RSOM, RSTM and VVM in TTM are compared with experimental results.

In order to efficiently use the discretized TTM model and obtain convergent and reasonable results, a grid size must be chosen with a suitable time step (which should not be too small). Applications of RSOM and RSTM‐TTM yield identical results which are more accurate than VVM.

This paper provides generalized guidelines about the solid velocity correction scheme and criteria for selection of time step/grid size for the convection controlled phase change problem.

Explains that segregation processes during the solidification of a binary alloy occur at two distinct length scales: on the microscopic length scale of the crystal interface, in the two‐phase mushy zone, segregation is controlled by solid state mass diffusion; and, on the macroscopic scale of the process, segregation is controlled by the convective transport of the molten metal. Concludes that developing models that can capture both these scales is a challenge. Introduces a bi‐level grid, and uses a macro grid on the scale of the process for the solution of equations describing macroscopic heat and mass transport. Details how each node point in the macro grid is associated with a micro grid on which equations describing the microscopic phenomena in the mushy region are solved. In this way, develops a dual‐scale model of segregation during the solidification of a binary alloy. On investigating the unidirectional solidification of a binary alloy, demonstrates that this dual‐scale model is able to capture both the macro and micro‐scales in a single numerical treatment.