Fractal nonlocal thermoelasticity of thin elastic nanobeam with apparent negative thermal conductivity

El-Nabulsi, Rami Ahmad; Anukool, Waranont

doi:10.1080/01495739.2022.2041517

Cited by 21 publications

(3 citation statements)

References 95 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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“…Theoretical applications of fractal analysis that have been of interest to various studies include the physical phenomena of hierarchical structure, thermal conductivity in micro-channels, diffusion, dynamics of the atmosphere and ocean, petroleum and nuclear engineering, meteorology, material design, and thermo-elasticity [25][26][27][28][29][30][31][32][33] . Through a porous structure, Sheng et al 34 investigated a fractal model, and Miao et al 35 looked into another fractal model of shale.…”

Section: Introductionmentioning

confidence: 99%

An instrumental insight for a periodic solution of a fractal Mathieu–Duffing equation

El‐Dib

Elgazery

Alyousef

2023

Journal of Low Frequency Noise, Vibration and Active Control

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The primary goal of the present study is to investigate how to obtain a periodic solution for a fractal Mathieu–Duffing oscillator. To achieve this, the fractal oscillator in the fractal space has been transformed into a damping Mathieu–Duffing equation in the continuous space by employing a new modification of He’s definition of the fractal derivative. The required analytical periodic solution has been based on the rank upgrade technique (RUT) presented. The RUT successfully generates a periodic solution without sacrificing the damping coefficient by creating an alternate equation, aside from any challenges in managing the impact of the linear damping component. The homotopy perturbation method (HPM) has been used to find the required periodic solution for the alternate equation. A comparison of the numerical solutions of the original equation and the alternative equation showed good agreement. The stability behavior in the non-resonance case as well as in the sub-harmonic resonance case has also been discussed. Further, another method, “the non-perturbative approach”, that deals with the obtained equation has been introduced.

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“…The fractal studying is an interesting idea that has distinctive applications in assorted areas, for instance, the physical phenomena of the hierarchical structure, diffusion, thermal conductivity within branched networks, meteorology, fluids flow resistance in micro-channels, ocean and atmosphere dynamics, nuclear and petroleum engineering, thermo elasticity, and materials design [30][31][32][33][34][35][36][37][38]. As a result of these important applications, the study of fractals was a fertile field for many scientists.…”

Section: Introductionmentioning

confidence: 99%

An innovative technique to solve a fractal damping Duffing-jerk oscillator

El‐Dib

Elgazery

Khattab

et al. 2023

Commun. Theor. Phys.

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The idea of the present article is to look into the nonlinear dynamics and vibration of a damping Duffing-jerk oscillator in fractal space exhibiting the non-perturbative approach. Using a new analytical technique, namely, the modification of He's a fractal derivative that converts the fractal derivative to the traditional derivative in continuous space, this study provides an effective and easy-to-apply procedure that is dependent on He's fractal derivative approach. The analytic approximate solution has significant match with the results of the numerical simulation as the fractal parameter is very closer to unity, which proves the reliability of the method. Stability behavior is discussed and illustrated graphically. These new powerful analytical tools are developed in an attempt to obtain effective analytical tools, valid for any fractal nonlinear problems.

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Fractal nonlocal thermoelasticity of thin elastic nanobeam with apparent negative thermal conductivity

Cited by 21 publications

References 95 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

An instrumental insight for a periodic solution of a fractal Mathieu–Duffing equation

An innovative technique to solve a fractal damping Duffing-jerk oscillator

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