Thermal transport equations in porous media from product-like fractal measure

El-Nabulsi, Rami Ahmad

doi:10.1080/01495739.2021.1919585

Cited by 38 publications

(2 citation statements)

References 82 publications

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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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“…In fact, this new concept was introduced recently by Li and Ostoja-Starzewski in order to describe dynamics in anisotropic and continuum media [42][43][44] and was motivated by Tarasov fractal calculus arguments [45,46]. It is considered a successful approach, which has proved to have several successful implications in sciences and engineering at different scales [47][48][49][50][51][52][53][54][55][56][57][58]. In the Li and Ostoja-Starzewski approach (LOSA henceforth), the dynamic equations of motion hold mathematical forms involving integer-order integrals, whereas their local forms are expressed through partial differential equations with integerorder derivatives except that they contain coefficients involving fractal dimensions.…”

Section: Introductionmentioning

confidence: 99%

Emergence of lump-like solitonic waves in Heimburg–Jackson biomembranes and nerves fractal model

El-Nabulsi

2022

J. R. Soc. Interface.

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The aim of this study is to extend the soliton propagation model in biomembranes and nerves constructed by Heimburg and Jackson for the case of fractal dimensions. Our analyses are based on the product-like fractal measure concept introduced by Li and Ostoja-Starzewski in their attempt to explore anisotropic fractal elastic media and electromagnetic fields. The mathematical model presented in the paper is formulated for only a part of a single nerve cell (an axon). The analytical and numerical envelop soliton of this equation are reported. The results obtained prove the emergence of lump-type solitonic waves in nerves and biomembranes. In particular, these waves decay algebraically to the background wave in space direction. This scenario is viewed as a particular class of rational localized waves which are solutions of the integrable Ishimori I equation and the (2 + 1) Kadomtsev–Petviashvili I equation. The effects of fractal dimensions are discussed and were found to be significant to some extents.

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Modeling of combustion and turbulent jet diffusion flames in fractal dimensions

El-Nabulsi

Anukool

2022

Continuum Mech. Thermodyn.

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Thermal transport equations in porous media from product-like fractal measure

Cited by 38 publications

References 82 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

Emergence of lump-like solitonic waves in Heimburg–Jackson biomembranes and nerves fractal model

Modeling of combustion and turbulent jet diffusion flames in fractal dimensions

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