A study of the fractal foam drainage model in a microgravity space

Wang, Kang‐Le

doi:10.1002/mma.7428

Cited by 40 publications

(7 citation statements)

References 48 publications

(49 reference statements)

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“…2), it becomes invalid, so we need to give a modification of it. Recently, the fractal and fractional calculus are adopted to model many complex phenomenon arising in the extreme conditions such as the un-smooth boundary [16][17][18][19][20][21], microgravity space [22,23], fractal media [24], porous media [25] and so on [26][27][28]. Inspired by these research results, here we apply the fractal calculus to Eq.…”

Section: Fig 2 Schematic Of a Porous Finmentioning

confidence: 99%

A new fractal model of the convective-radiative fins with temperature-dependent thermal conductivity

Wang

Shi

2023

THERM SCI

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In this paper, the convective-radiative fins of rectangular profile with temperature-dependent thermal conductivity are considered. By studying the conventional heat transfer equation, its modified fractal form, which can describe the problem in the porous medium, is presented based on He?s fractal derivative for the first time. The fractal two-scale transform method together with the Taylor series are applied to deal with fractal model, and an analytical approximate solution is obtained. The impact of the different fractal orders on the thermal behavior of the fins is also elaborated in detail. In addition, a comparison between our solution and the existing one is given to prove the correctness of the proposed method, which shows that the proposed method is easy but effective, and are expected to shed a bright light on practical applications of fractal calculus.

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Section: Fig 2 Schematic Of a Porous Finmentioning

confidence: 99%

A new fractal model of the convective-radiative fins with temperature-dependent thermal conductivity

Wang

Shi

2023

THERM SCI

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“…Fractal calculus is very simple but extremely effective in dealing with phenomena in hierarchical or porous media. The use of fractal calculus can have important application significance in microgravity space [2], mathematical iterative solution [3] and foam surface tension [4]. The traditional sandwich cushioning material is similar to a honeycomb.…”

Section: Introductionmentioning

confidence: 99%

Cushioning Performance of Hilbert Fractal Sandwich Packaging Structures under Quasi-Static Compressions

Xu¹,

Song²,

Wang³

2023

Computer Modeling in Engineering &Amp; Sciences

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The sandwich structure of cushioning packaging has an important influence on the cushioning performance. Mathematical fractal theory is an important graphic expression. Based on Hilbert fractal theory, a new sandwich structure was designed. The generation mechanism and recurrence formula of the Hilbert fractal were expressed by Lin's language, and the second-order Hilbert sandwich structure was constructed from thermoplastic polyurethane. The constitutive model of the hyperelastic body was established by using the finite element method. With the unit mass energy absorption as the optimization goal, the fractal sandwich structure was optimized, and the best result was obtained when the order was 2.5 and the unit layer thickness was 0.75 mm. The Hilbert sandwich structure was compared with the rice-shaped sandwich structure commonly used in industry, and the Hilbert fractal structure had better energy absorption. This has practical significance for the development and application of new cushioning packaging structures. KEYWORDSHilbert fractal; sandwich structure; static compression; buffer packaging Abbreviation List TPU Thermoplastic polyurethane 3D Three-dimensional EA Total energy absorption SEA m Energy absorption per unit mass SEA v Energy absorption per unit volume n O r d e r t Unit layer thickness

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“…In recent years, the local fractional calculus (LFC) 1,2 is a very hot topic and has been widely employed to demonstrate very complex scientific and engineering problems, such as objects move in microgravity space, 3,4 and fluids flow in porous media or with unsmooth boundaries. Some complex fractal problems [5][6][7][8] can also been successfully modeled by LFC.…”

Section: Introductionmentioning

confidence: 99%

A novel perspective to the local fractional Zakharov–Kuznetsov‐modified equal width dynamical model on Cantor sets

Wang

2022

Math Methods in App Sciences

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In this work, the local fractional Zakharov-Kuznetsov-modified equal width dynamical (LFZKMEWD) model is investigated on Cantor sets by using the local fractional derivative (LFD). The fractal variational wave method (FVWM) is employed to obtain the exact traveling wave solutions of the nondifferentiable type for the LFZKMEW model. The numerical example illustrates the FVWM is efficient and straightforward. The properties of exact traveling wave solutions are also elaborated by some figures.

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A study of the fractal foam drainage model in a microgravity space

Cited by 40 publications

References 48 publications

A new fractal model of the convective-radiative fins with temperature-dependent thermal conductivity

A new fractal model of the convective-radiative fins with temperature-dependent thermal conductivity

Cushioning Performance of Hilbert Fractal Sandwich Packaging Structures under Quasi-Static Compressions

A novel perspective to the local fractional Zakharov–Kuznetsov‐modified equal width dynamical model on Cantor sets

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