On the boundary immobilization and variable space grid methods for transient heat conduction problems with phase change: Discussion and refinement

Sadoun, Nacer; Si‐Ahmed, El‐Khider; Colinet, Pierre; Legrand, Jack

doi:10.1016/j.crme.2012.03.003

Cited by 19 publications

(14 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Stefan () began the study of this specific type of system by tracking the heat conduction front, present in phase change problems in ice‐water systems. Since then, many studies have focused on obtaining both analytical solutions (Barry & Caunce, ; Cherniha & Kovalenko, ; Natale, Santillan Marcus, & Tarzia, ; Salva & Tarzia, ; Voller & Falcini, ), and numerical solutions (Caldwell & Chan, ; Kutluay, Bahadir, & Özdeş, ; Mitchell & O'Brien, ; Mitchell, Vynnycky, Gusev, & Sazhin, ; Sadoun, Si‐Ahmed, Colinet, & Legrand, ; Sadoun, Si‐Ahmed, & Legrand, ; Savovic & Caldwell, ). The works of Caldwell and Kwan () bring together the most common numerical methods for solving Stefan problems.…”

Section: Introductionmentioning

confidence: 99%

Modeling of soybean hydration as a Stefan problem: Boundary immobilization method

Nicolin

Silva

Jorge

et al. 2018

J Food Process Engineering

View full text Add to dashboard Cite

In the present work, the mathematical modeling of the soybean hydration process is presented, considering the increase in the grain radius by Stefan problem approach. The boundary immobilization method was used in the model to take into account the spatial mesh variation caused by the diffusion of moisture in the grains. The results provided by the model show its quality when compared with experimental data, both for the adequacy of the predictions for moisture data over time and for the adequacy of grain radius increase predictions over time, for five different temperatures. The presented methodology showed improvements on results already reported in the literature. Practical applications The approach presented in this article allows one to fit diffusivity values for soybean hydration by taking into account a phenomenon commonly observed in this process: the increase of the grains during water absorption. Thus, it is expected the diffusivities to be more realistic and precise, improving the project of equipment. Since the model proposed provide the increase of the grains along the hydration process, an estimation of the increase of a higher amount of the grains could be obtained as well. Such estimation is relevant due to the considerable increase that grains suffer after absorbing water.

show abstract

Section: Introductionmentioning

confidence: 99%

Modeling of soybean hydration as a Stefan problem: Boundary immobilization method

Nicolin

Silva

Jorge

et al. 2018

J Food Process Engineering

View full text Add to dashboard Cite

show abstract

“…One method largely employed is known as the “Variable Space Grid Method” (VSGM). With the use of VSGM, several works stand out in the analysis of numerical accuracy in face of the analytical solution previously known, of Stefan problems . A second method widely used to solve Stefan problems numerically is known as Boundary Immobilization Method (BIM).…”

Section: Introductionmentioning

confidence: 99%

“…The method is based on a modification on the diffusion equation proposed by Landau which fixes the moving boundary of the system. BIM was already used to solve Stefan problems numerically in several types of contexts such as heat or mass transfer problems …”

Section: Introductionmentioning

confidence: 99%

“…With the use of VSGM, several works stand out in the analysis of numerical accuracy in face of the analytical solution previously known, of Stefan problems. [9][10][11][12][13][14] A second method widely used to solve Stefan problems numerically is known as Boundary Immobilization Method (BIM). The method is based on a modification on the diffusion equation proposed by Landau [15] which fixes the moving boundary of the system.…”

Section: Introductionmentioning

confidence: 99%

“…BIM was already used to solve Stefan problems numerically in several types of contexts such as heat or mass transfer problems. [11,13,14,[16][17][18][19][20] Moving boundary problems do not come up solely in heat transfer phenomena. Barry and Caunce [21] stress that moving boundary problems also arise when the diffusion process of moisture causes an increase in size of grains and polymers, as well as when the diffusion governs the process of solids placement in problems of deformational porous mediums.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effects of variable diffusivity on soybean hydration modelling as a Stefan problem

Nicolin

Jorge

2016

Can J Chem Eng

View full text Add to dashboard Cite

The diffusion of moisture in soybean grains is usually followed by two physical facts related to the presence of water: the increase in grain size due to water accumulation and the increase in permeability, as more water is absorbed. In order to increase the physical meaning of the proposed model those two phenomenological facts were inserted in the classical Fick's Second Law of Diffusion. The increase of the grains was taken into account by considering the radius of the grains as a moving boundary of the diffusion system (characterizing a Stefan problem). The increase in permeability was taken into account by considering an exponential dependence of the diffusivity with the moisture content. The behaviour of the main parameters was analyzed with the temperatures. The moisture profiles were calculated for the moving boundary problem as well as the behaviour of the radius of the grains as a function of time. The results showed good agreement with experimental reality of soybean hydration process.

show abstract

A variable time‐step method for a space fractional diffusion moving boundary problem: An application to planar drug release devices

Garshasbi

Sanaei

2020

Int J Numerical Modelling

View full text Add to dashboard Cite

In this article, we consider an anomalous diffusion model in a planar polymeric matrix as a space fractional diffusion problem with moving boundary conditions. An iterative implicit finite difference method with variable timesteps is established to solve the proposed problem. The stability and consistency of the numerical method are proved and the estimation of the numerical error is conducted. The numerical results are compared with the scaleinvariant and homotopy perturbation solutions when the diffusion coefficient is a constant. Furthermore, the numerical results for a test case with timedependent diffusion coefficient are reported.

show abstract

On the boundary immobilization and variable space grid methods for transient heat conduction problems with phase change: Discussion and refinement

Cited by 19 publications

References 42 publications

Modeling of soybean hydration as a Stefan problem: Boundary immobilization method

Modeling of soybean hydration as a Stefan problem: Boundary immobilization method

Effects of variable diffusivity on soybean hydration modelling as a Stefan problem

A variable time‐step method for a space fractional diffusion moving boundary problem: An application to planar drug release devices

Contact Info

Product

Resources

About