Explicit solution for a two-phase fractional Stefan problem with a heat flux condition at the fixed face

Roscani, Sabrina; Tarzia, Domingo A.

doi:10.1007/s40314-018-0600-z

Cited by 7 publications

(4 citation statements)

References 28 publications

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“…Then writing the complete system in term of Caputo derivative [7,8] with 0 < 𝛽𝛽 < 1: 𝑠𝑠 1−𝛽𝛽 . The solutions of (11. 𝑎𝑎 − 12. 𝑏𝑏) were found in [6], not shown here for brevity.…”

Section: Fig 3 Schematic Representation Of Two Generic Heat Diffusion...mentioning

confidence: 86%

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A fractional-order theory of phase transformation in presence of anomalous heat transfer

Nuzzo

2023

Theoretical and Applied Mechanics - AIMETA 2022

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Section: Fig 3 Schematic Representation Of Two Generic Heat Diffusion...mentioning

confidence: 86%

“…The aim of this paper is to exploit the fractional formulation of Fourier's law to reach the solutions found in [6], starting with physical considerations.…”

Section: Introductionmentioning

confidence: 99%

A fractional-order theory of phase transformation in presence of anomalous heat transfer

Nuzzo

2023

Theoretical and Applied Mechanics - AIMETA 2022

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“…However, satisfactory results were obtained following this approach, see e.g. [6,7,15,18,20,24,40] (see also [4,21,26,27,[29][30][31][32]36]).…”

Section: (27)mentioning

confidence: 99%

A Note on Models for Anomalous Phase-Change Processes

Ceretani

2020

Fract Calc Appl Anal

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We review some fractional free boundary problems that were recently considered for modeling anomalous phase-transitions. All problems are of Stefan type and involve fractional derivatives in time according to Caputo's definition. We survey the assumptions from which they are obtained and observe that the problems are nonequivalent though all of them reduce to a classical Stefan problem when the order of the fractional derivatives is replaced by one. We further show that a simple heuristic approach built upon a fractional version of the energy balance and the classical Fourier's law leads to a natural generalization of the classical Stefan problem in which time derivatives are replaced by fractional ones.

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“…More examples of applications of free boundary problems can be found in the areas of geophysics, semiconductor design and cryosurgery (Mackenzie and Robertson, 2000) (see also Friedman (2000)). Stefan problems have been extensively studied (Roscani and Tarzia, 2018) and are nowadays the subject of intense research, from the experimental, numerical and analytical viewpoints (Chen et al, 2015).…”

Section: Typical Assumptions and Simplifications In Agf Designmentioning

confidence: 99%

Improved engineering solutions for thermal design of artificial ground freezing

Sancho Calderón

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Artificial ground freezing is a safe, proven and reliable method for various construction projects in water-bearing, unstable soils and rock, from special civil engineering (e.g. for excavations), to tunnel construction and mine shafts. Essential for the design and control of the freezing process are the thermal calculations. Historically, these have been performed by using analytical methods. However, the project-specific geometrical and geological conditions and the construction sequence have a significant influence on the design, which is difficult to consider using analytical and empirical methods only. A partial solution to more complex design challenges is currently the use of numerical models. An important advantage of numerical modelling, among others, is the use of 3D models, which becomes practically necessary in many present challenges of engineering and allows a suitable representation of the geological structure. Numerical models also make possible the proper combined simulation of the excavation sequence, the ground support and the coupling thermo-hydro-geomechanical approach.It must be stated, however, that the results of numerical calculations are known to be meshdependent, which means that for too "coarse" meshes a correct interpretation of the analysed physical phenomena is not possible. Unfortunately, there are also other factors which significantly influence the accuracy of numerical calculations.The research work of Diego Sancho Calderón starts at this point, reviewing the analytical and numerical approaches. He selected different freezing problems, which he investigated and analysed. Based on the performed verification, he was able to define the limitations and applicability of both analytical and numerical methods. In my opinion, the presented results are a step forward in the scientific research of artificial ground freezing. Furthermore, the presented adjustment of the Sanger & Sayles formula and the code of good practice for thermal numerical modelling are of great practical importance for construction projects using the artificial ground freezing technique.It was a great pleasure for me to assist and support Diego in his work and I would like to thank him for the opportunity to be a part of this very important research.

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Explicit solution for a two-phase fractional Stefan problem with a heat flux condition at the fixed face

Cited by 7 publications

References 28 publications

A fractional-order theory of phase transformation in presence of anomalous heat transfer

A fractional-order theory of phase transformation in presence of anomalous heat transfer

A Note on Models for Anomalous Phase-Change Processes

Improved engineering solutions for thermal design of artificial ground freezing

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