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. PCMs have been widely used in latent heat thermal-storage systems for heat pumps, solar engineering, and spacecraft thermal control applications. The uses of PCMs for heating and cooling applications for buildings have been investigated within the past decade. There are large numbers of PCMs that melt and solidify at a wide range of temperatures, making them attractive in a number of applications. This paper also summarizes the investigation and analysis of the available thermal energy storage systems incorporating PCMs for use in different applications.

Review on thermal energy storage with phase change materials and applications

The major methods of mathematical modelling of solidification and melting problems are reviewed in this paper. Different analytical methods, nowadays still used as standard references to validate numerical models, are presented. Various mathematical formulations to numerically solve solidification and melting problems are categorized. Relative merits and disadvantages of each formulation are analysed. Recent advances in modelling solidification and melting problems associated with convective motion of liquid phase are discussed. Based on this comprehensive survey, basic guidelines are outlined to choose a correct mathematical formulation for solving solidification and melting problems.

https://iopscience.iop.org/article/10.1088/0965-0393/4/4/004/pdf

Mathematical modelling of solidification and melting: a review

The study of travelling waves or fronts has become an essential part of the mathematical analysis of nonlinear diffusion-convection-reaction processes. Whether or not a nonlinear second-order scalar reaction-convection-diffusion equation admits a travelling-wave solution can be determined by the study of a singular nonlinear integral equation. This article is devoted to demonstrating how this correspondence unifies and generalizes previous results on the occurrence of travelling-wave solutions of such partial differential equations. The detailed comparison with earlier results simultaneously provides a survey of the topic. It covers travelling-wave solutions of generalizations of the Fisher, Newell-Whitehead, Zeldovich, KPP and Nagumo equations, the Burgers and nonlinear Fokker-Planck equations, and extensions of the porous media equation.

/pdf/travelling-waves-in-nonlinear-diffusion-convection-reaction-g8nh2uaqi8.pdf

Travelling Waves in Nonlinear Diffusion-Convection Reaction

Role of oxygen gradients in shaping redox relationships between the human intestine and its microbiota

A chemomechanical mathematical model is presented to simulate the response of concrete exposed to external sulfate solutions. The model is based on the diffusion-reaction approach, and several mechanisms for the reaction of calcium aluminates with sulfates to form expansive ettringite are considered. Fick’s second law is assumed for diffusion of the sulfate ions. A second-order chemical reaction between reacting calcium aluminates and ingressing sulfates depletes the sulfate concentration. The products of the second-order reaction between the aluminates and sulfates are chosen among several competing mechanisms, and a rule-of-mixtures approach is used to relate the expansive nature of the products with the prescribed specific gravity of the compounds. It is furthermore assumed that the crystallization pressure of products of reaction results in a bulk expansion of the solid. The constitutive response of the matrix and the expansive stresses are calculated from the imposed volumetric strain. Microcracks are initiated when the strength of the matrix is reached, leading to changes in the diffusivity and a reduction in the elastic properties of the matrix. The variation of diffusivity is linked to the scalar damage parameter due to cracking of the matrix. Due to the changes in the diffusivity, the problem is treated as a moving boundary problem, and a methodology is proposed to adapt the solution of the 1D case to the 2D problem of a prismatic specimen. Theoretical expansion-time responses are obtained and compared with a variety of data available in the literature.

Modeling of damage in cement-based materials subjected to external sulfate attack. I: Formulation

/pdf/a-moving-boundary-problem-arising-from-the-diffusion-of-148xc2s4kq.pdf

A moving boundary problem arising from the diffusion of oxygen in absorbing tissue

Isotherm Migration Method in two dimensions

/pdf/a-method-for-solving-moving-boundary-problems-in-heat-flow-3sbqbespdh.pdf

A Method for Solving Moving Boundary Problems in Heat Flow using Cubic Splines or Polynomials

https://bura.brunel.ac.uk/bitstream/2438/1980/1/TR_70.pdf

John Crank

Papers

A moving boundary problem arising from the diffusion of oxygen in absorbing tissue

Isotherm Migration Method in two dimensions

A Method for Solving Moving Boundary Problems in Heat Flow using Cubic Splines or Polynomials

Isotherm migration along orthogonal flow lines in two dimensions

On an implicit scheme for the isotherm migration method along orthogonal flow lines in two dimensions