Journal ArticleDOI
Comparison of finite element techniques for solidification problems
A. J. Dalhuijsen,A. Segal +1 more
Reads0
Chats0
TLDR
In this article, the authors compared the accuracies of the computed temperatures of a liquid in a corner region under freezing conditions with various fixed-grid finite element techniques using the analytical solution for this problem as a reference.Abstract:
The accuracies of the computed temperatures of a liquid in a corner region under freezing conditions are compared for various fixed-grid finite element techniques using the analytical solution for this problem as a reference.
In the finite element formulation of the problem different time-stepping schemes are compared: the implicit Euler-backward algorithm combined with an iterative scheme and two three-time-level methods—the Lees algorithm and a Dupont algorithm, which are both applied as non-iterative schemes.
Furthermore, different methods for handling the evolution of latent heat are examined: an approximation method suggested by Lemmon and one suggested by Del Giudice, both using the enthalpy formulation as well as a fictitious heat-flow method presented by Rolph and Bathe.
Results of calculations performed with the consistent heat-capacity matrix are compared with those performed with a lumped heat-capacity matrix.read more
Citations
More filters
Journal ArticleDOI
Review on thermal energy storage with phase change materials and applications
TL;DR: The use of a latent heat storage system using phase change materials (PCMs) is an effective way of storing thermal energy and has the advantages of high energy storage density and the isothermal nature of the storage process.
Journal ArticleDOI
Eral source-based method for solidification phase change
TL;DR: In this paper, a linearization of the discretized source term is proposed to deal efficiently with a wide range of latent heat evolution mechanisms (i.e., liquid fraction temperature relationships).
Journal ArticleDOI
Fixed grid techniques for phase change problems: A review
TL;DR: In this paper, the major fixed grid formulations and solution methods for conduction controlled phase change problems are categorised using a two phase model of a solid/liquid phase change, the basic enthalpy equation is derived.
Journal ArticleDOI
Heat transfer enhancement of phase change materials for thermal energy storage applications: A critical review
Nasiru I. Ibrahim,Fahad A. Al-Sulaiman,Saidur Rahman,Saidur Rahman,Bekir Sami Yilbas,Ahmet Z. Sahin +5 more
TL;DR: In this paper, the authors present a review on various techniques of heat transfer enhancement in latent heat thermal energy storage (LHTES) systems, which can be achieved through either geometric configuration and/or thermal conductivity enhancement.
Journal ArticleDOI
Meshfree explicit local radial basis function collocation method for diffusion problems
B. arler,R. Vertnik +1 more
TL;DR: A simple explicit local version of the classical meshless radial basis function collocation (Kansa) method, structured on multiquadrics radial basis functions, which outperforms the classical finite difference method in terms of accuracy.
References
More filters
Book
The Finite Element Method for Elliptic Problems
Philippe G. Ciarlet,J. T. Oden +1 more
TL;DR: The finite element method has been applied to a variety of nonlinear problems, e.g., Elliptic boundary value problems as discussed by the authors, plate problems, and second-order problems.
Book
Numerical solution of differential equations
TL;DR: The program for the sixth Symposium on applied mathematics of the American Mathematical Society, on the subject of algebraic geometry, is being arranged by the Society's Applied Mathematics Committee as mentioned in this paper.
Journal ArticleDOI
Finite element solution of non‐linear heat conduction problems with special reference to phase change
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.
Journal ArticleDOI
Numerical solution of phase-change problems
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.
Journal ArticleDOI
Maximum principle and uniform convergence for the finite element method
TL;DR: In this paper, it was shown that the Dirichlet boundary value problem converges uniformly to the exact solution u if u ϵ W1,p (Ω), with p > n, and that ∥u−u h ∥ L ∞(Ω) = O(h) if uϵ W2,p(ϵ), with 2p > n.