Efficient numerical method for two-dimensional phase change problems
01 Nov 1984-International Journal of Heat and Mass Transfer (Pergamon)-Vol. 27, Iss: 11, pp 2077-2084
TL;DR: In this article, the fine balance of the horizontal and vertical sweeps of the standard alternating direction implicit method is efficiently incorporated in the numerical scheme for two-dimensional phase change problems, isolating the nonlinearity associated with the moving interface and accurately tracking the interface movement along both the coordinate axes.
About: This article is published in International Journal of Heat and Mass Transfer.The article was published on 1984-11-01. It has received 24 citations till now. The article focuses on the topics: Alternating direction implicit method & Numerical analysis.
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TL;DR: In this paper, the authors introduce the basic concepts of macroscopic and microscopic phenomena which enter normally into any solidification process, and the latest developments in numerical techniques which are used to solve the continuity equations are briefly presented together with the advantages and inconvenience.
Abstract: Modelling of heat flow has become a standard practice in many solidification processes. Effort is currently being made to couple heat flow calculations to related macroscopic phenomena such as mould filling, fluid flow, macrosegregation, or thermal stresses. If these macroscopic aspects are important in predicting formation of macroscopic defects or optimising process conditions, then microstructural features such as phase appearance, morphology, grain size, spacings, or microdefects are certainly no less important in determining the ultimate mechanical properties of the solidified product. The aim of the present paper is to introduce the basic concepts of macroscopic and microscopic phenomena which enter normally into any solidification process. At the macroscopic level, i.e. at the scale of the whole process (casting, weldment, … ), the latest developments in numerical techniques which are used to solve the continuity equations are briefly presented together with the advantages and inconvenience...
459 citations
TL;DR: In this article, a two-dimensional model for the phase change, conduction based heat transfer problem around a tube immersed in the pcm is presented, where the energy equation is written in the enthalpy form, and the heat and flow problems are coupled by an energy balance on the fluid element flowing inside the tube.
94 citations
TL;DR: In this article, phase change materials based on epoxy resin paraffin wax with the melting point 27°C were used as a new energy storage system and the thermophysical properties of the prepared composite have been characterized by using a new transient hot plate apparatus.
61 citations
TL;DR: In this article, an iterative implicit algorithm using the boundary element method (BEM) with time-dependent Green's functions and convolution integrals was developed for the calculation of the motion of the solid-liquid interface and the timedependent temperature field during solidification of a pure metal.
Abstract: The problem of interest in this paper is the calculation of the motion of the solid–liquid interface and the time-dependent temperature field during solidification of a pure metal. An iterative implicit algorithm has been developed for this purpose using the boundary element method (BEM) with time-dependent Green's functions and convolution integrals.
The BEM approach requires discretization of only the surface of the solidifying body. Thus, the numerical method closely follows the physics of the problems and is intuitively very appealing.
The formulation and the numerical scheme presented here are general and can be applied to a broad range of moving boundary problems. Emphasis is given to two-dimensional problems. Comparison with existing semi-analytical solutions and other numerical solutions from the literature reveals that the method is fast, accurate and without major time step limitations.
56 citations
Journal Article•
TL;DR: In this article, the effect of weld pool surface deformation on weld joint penetration under the arc pressure has been studied in stationary gas tungsten arc welding (CTAW), by considering the four driving forces for weld pool convection: electromagnetic force, buoyancy force, aerodynamic drag force, and surface tension force.
Abstract: The effect of weld pool surface deformation on weld joint penetration under the arc pressure has been studied in stationary gas tungsten arc welding (CTAW), by considering the four driving forces for weld pool convection: electromagnetic force, buoyancy force, aerodynamic drag force, and surface tension force at the weld pool surface. In the numerical simulation, difficulties associated with the irregular shape of the deformed weld pool surface and the moving liquid-solid interface have been successfully overcome by adopting a boundaryfitted coordinate system, which eliminates the analytical complexity there. This method also has the capacity to handle the time-dependent changing solution domain of the moving boundary problem and could be applied effectively to this transient weld pool development problem with the phase change condition and moving boundary, such as at the deformed weld pool surface and the liquidsolid interface.
44 citations
References
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Book•
31 Dec 1959
TL;DR: In this paper, a classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems, including boundary value maximization.
Abstract: This classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems.
21,807 citations
TL;DR: In this article, the authors present a general approach to transient heat conduction problems with non-linear physical properties and boundary conditions using an unconditionally stable central algorithm which does not require iteration.
Abstract: The paper presents a generally applicable approach to transient heat conduction problems with non-linear physical properties and boundary conditions. An unconditionally stable central algorithm is used which does not require iteration.
Several examples involving phase change (where latent heat effects are incorporated as heat capacity variations) and non-linear radiation boundary conditions are given which show very good accuracy.
Simple triangular elements are used throughout but the formulation is generally valid and not restricted to any single type of element.
506 citations
TL;DR: A three-time level implicit scheme, which is unconditionally stable and convergent, is employed for the numerical solution of phase change problems, on the basis of an analytical approach consisting in the approximation of the latent heat effect by a large heat capacity over a small temperature range as discussed by the authors.
500 citations
TL;DR: In this article, the enthalpy model for multidimensional phase change problems in media having a distinct phase change temperature is demonstrated, and subsequent numerical applications of the model are carried out.
Abstract: The basis of the enthalpy model for multidimensional phase change problems in media having a distinct phase change temperature is demonstrated, and subsequent numerical applications of the model are carried out. It is shown that the mathematical representation of the enthalpy model is equivalent to the conventional conservation equations in the solid and liquid regions and at the solid-liquid interface. The model is employed in conjunction with a fully implicit finite-difference scheme to solve for solidification in a convectively cooled square container. The implicit scheme was selected because of its ability to accommodate a wide range of the Stefan number Ste. After its accuracy had been established, the solution method was used to obtain results for the local and surface-integrated heat transfer rates, boundary temperatures, solidified fraction, and interface position, all as functions of time. The results are presented with SteFo (Fo = Fourier number) as a correlating parameter, thereby facilitating their use for all Ste values in the range investigated. At low values of the Biot number, the surface-integrated heat transfer rate was relatively constant during the entire solidification period, which is a desirable characteristic for phase change thermal energy storage.
385 citations
01 Jan 1975
TL;DR: In this article, the enthalpy model for multidimensional phase change problems in media having a distinct phase change temperature is demonstrated, and subsequent numerical applications of the model are carried out.
Abstract: The basis of the enthalpy model for multidimensional phase change problems in media having a distinct phase change temperature is demonstrated, and subsequent numerical applications of the model are carried out. It is shown that the mathematical representation of the enthalpy model is equivalent to the conventional conservation equations in the solid and liquid regions and at the solid-liquid interface. The model is employed in conjunction with a fully implicit finite-difference scheme to solve for solidification in a convectively cooled square container. The implicit scheme was selected because of its ability to accommodate a wide range of the Stefan number Ste. After its accuracy had been established, the solution method was used to obtain results for the local and surface-integrated heat transfer rates, boundary temperatures, solidified fraction, and interface position, all as functions of time. The results are presented with SteFo (Fo = Fourier number) as a correlating parameter, thereby facilitating their use for all Ste values in the range investigated. At low values of the Biot number, the surface-integrated heat transfer rate was relatively constant during the entire solidification period, which is a desirable characteristic for phase change thermal energy storage.
372 citations