Behavior of the solution of a Stefan problem by changing thermal coefficients of the substance

Olguín, Mariela C.; Medina, Mario A.; Sanziel, María Cristina; Tarzia, Domingo A.

doi:10.1016/j.amc.2007.01.104

Cited by 5 publications

(4 citation statements)

References 16 publications

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“…In fact, the resultant mathematical model is a strongly nonlinear moving boundary (MB) problem (Liu et al, 2012;Zhao et al, 2020;Jiao et al, 2021), owing to the effect of TPG. This threshold problem is really distinct from the classical Stefan MB problem (Voller et al, 2004;Olguín et al, 2007) in the heat conduction theory, although its governing equation has the same form as the heat conduction governing equation of the Stefan problem. Their main difference is that for the Stefan problem, the MB velocity is proportional to the first derivative of the potential (temperature) with respect to distance from the MB (Voller et al, 2004;Olguín et al, 2007).…”

Section: Introductionmentioning

confidence: 96%

“…This threshold problem is really distinct from the classical Stefan MB problem (Voller et al, 2004;Olguín et al, 2007) in the heat conduction theory, although its governing equation has the same form as the heat conduction governing equation of the Stefan problem. Their main difference is that for the Stefan problem, the MB velocity is proportional to the first derivative of the potential (temperature) with respect to distance from the MB (Voller et al, 2004;Olguín et al, 2007). However, for the MB problem of the non-Darcian flow with the TPG, it has been proved theoretically that the MB velocity is proportional to the second derivative of the potential (pressure) with respect to distance from the MB (Liu et al, 2012;Liu et al, 2019a;Liu, 2019).…”

Section: Introductionmentioning

confidence: 96%

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A Fundamental Moving Boundary Problem of 1D Commingled Preferential Darcian Flow and Non-Darcian Flow Through Dual-Layered Porous Media

Wang

Ding

et al. 2022

Front. Energy Res.

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In consideration of vertical formation heterogeneity, a basic nonlinear model of 1D commingled preferential Darcian flow and non-Darcian flow with the threshold pressure gradient (TPG) in a dual-layered formation is presented. Non-Darcian flow in consideration of the TPG happens in the low-permeability tight layer, and the Darcian kinematic equation holds in the other high-permeability layer. The similarity transformation method is applied to analytically solve the model. Moreover, the existence and uniqueness of the analytical solution are proved strictly. Through analytical solution results, some significant conclusions are obtained. The existence of the TPG in the low-permeability tight layer can intensify the preferential Darcian flow in the high-permeability layer, and the intensity of the preferential Darcian flow is very sensitive to the dimensionless layer thickness ratio. The effect of the layer permeability ratio and layer elastic storage ratio on the production sub-rate is more sensitive than that of the layer thickness ratio. In addition, it is strictly demonstrated that moving boundary conditions caused by the TPG should be incorporated into the model. When the moving boundary is neglected, the preferential Darcian flow in the high-permeability layer will be exaggerated. Eventually, solid theoretical foundations are provided here, which are very significant for solving non-Darcian seepage flow problems in engineering by numerical simulation validation and physical experiment design. Furthermore, they are very helpful for better understanding the preferential flow behavior through the high-permeability paths (such as fractures) in the water flooding development of heterogeneous low-permeability reservoirs; then, the efficient profile control technology can be further developed to improve oil recovery.

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Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 96%

A Fundamental Moving Boundary Problem of 1D Commingled Preferential Darcian Flow and Non-Darcian Flow Through Dual-Layered Porous Media

Wang

Ding

et al. 2022

Front. Energy Res.

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“…Stefan problem is presented regularly in different fields of applied science and has been examined by several researchers. [11][12][13][14] The investigations of the phase change model with periodic boundary conditions (PBC) are substantial for practical applications of the TES system. Several studies considering half-plane have been presented in the open literature.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of thermal energy storage system inside a spherical capsule under periodic boundary conditions

2022

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In this work, inward solidification process of a spherical capsule subjected to a periodic boundary condition is numerically studied. The temperature transforming technique is utilized to solve the 1D phase change model and an inhouse model developed in C++. The interface position and the transient temperature profiles are evaluated with respect to the different oscillation amplitudes and oscillation frequencies of the periodically oscillating surface temperature.The results demonstrate that in the situation where the amplitude is 30, the elapsed time for total solidification is dropped by 23.7% compared to the case without oscillation. It is also found that there is a 21.8% reduction in the time for total solidification when the frequency is changed from ω = π/64 to ω = 0.

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“…1. This paper is organized as follows: Section 2 describes the mathematical modeling and simulation used to support the thermal control process model using a phase change simulation for Stefan problems coupled as well as Navier-Stokes equations [1,2].…”

Section: Introductionmentioning

confidence: 99%

Distributed Parallel Performance of Compression Molding Model for Some Characteristics Identification of Tire Tread Block

Alias*,

Darwis,

Yusniman

et al. 2019

IJEAT

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A control process based on the mathematical modeling of phase change simulations was used to address process limitations of tire tread manufacturing process. The objective of this model was to predict and monitor expected characteristic identifications respect to space and time. This paper proposes a high-performance control process for visualizing the temperature behavior of a compression molding process using pressure, density, elasticity, crack propagation, volume, space, and time during tire tread block manufacturing operations. The control process modeling of tire tread blocks at the liquid-solid interface enabled the use of large sparse computations for solving the real time molding process of a Rubber Compression Molding Machine (RCMM) LWB VRE 1000 type at the Malaysia Rubber Board Research Center (LGM). The modeling simulation emphasized parallel algorithms, domain decomposition, and parallel processing techniques on Distributed Parallel Computer Architecture (DPCS). This study identified alternative numerical methods and their parallelization by comparing numerical analysis and parallel performance indicators using tables, graphs, and multidimensional visualizations. The multidimensional visualization of characteristics using the high-performance control process model accurately illustrated the heating and cooling profile of the compression molding process.

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Behavior of the solution of a Stefan problem by changing thermal coefficients of the substance

Cited by 5 publications

References 16 publications

A Fundamental Moving Boundary Problem of 1D Commingled Preferential Darcian Flow and Non-Darcian Flow Through Dual-Layered Porous Media

A Fundamental Moving Boundary Problem of 1D Commingled Preferential Darcian Flow and Non-Darcian Flow Through Dual-Layered Porous Media

Numerical simulation of thermal energy storage system inside a spherical capsule under periodic boundary conditions

Distributed Parallel Performance of Compression Molding Model for Some Characteristics Identification of Tire Tread Block

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