The Heat Conduction in Nanosized Structures

Sládek, J.; Sládek, V.; Repka, Miroslav�

doi:10.1134/s102995992105012x

Cited by 10 publications

(6 citation statements)

References 19 publications

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“…Making use the 1 st and 2 nd law of thermodynamics, one can show that the rate of density of the Gibbs free energy for classical heat conduction process is given as (Sladek et al, 2022) , , 0…”

Section: Heat Conduction Equation Within Higher-grade Theorymentioning

confidence: 99%

“…The integration constants B are specified for two kinds of boundary value problems (Sladek et al, 2022):…”

Section: Illustration Of Size-effectsmentioning

confidence: 99%

“…Instead, it depends on whether 2 T  varies rapidly on the distance scale of a phonon mean free path. Since the constitutive law in nonlocal theory is given by functional relationship between the heat flux and temperature gradient, the gradients of T  play a role inside the area of nonlocality (Sladek et al, 2022).…”

Section: Introductionmentioning

confidence: 99%

“…microstructural-length scale parameter. Now, application of the variation principle to 2D stationary heat conduction problems with the functional corresponding to the Gibbs free energy density (2) yields the governing equation(Sladek et al, 2022) chosen, we have the general solution of the considered 1D problem is given as…”

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confidence: 99%

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Higher-grade theory of heat conduction and size effects

Sládek¹,

Sladek²

2023

Engineering Mechanics

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It is experimentally evident that size-dependent effects are observed in small samples of nano/microscale dimensions. On the other hand, the classical theory of heat conduction is scale invariant. Incorporation of higher-order gradients of primary field variables into constitutive relationships yields a qualitative explanation of size-effects. Study of stationary heat conduction in bi-layer is rather simple 1D problem which can be solved analytically even within the higher-grade theory despite the high-order differential equations. Having known the exact solution, one can get a reliable analysis of size-effects with avoiding any numerical uncertainties. The influence of boundary conditions, material coefficients and geometrical dimensions on the temperature distribution in bi-layer is studied and discussed in this paper.

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Section: Heat Conduction Equation Within Higher-grade Theorymentioning

confidence: 99%

“…The integration constants B are specified for two kinds of boundary value problems (Sladek et al, 2022):…”

Section: Illustration Of Size-effectsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Higher-grade theory of heat conduction and size effects

Sládek¹,

Sladek²

2023

Engineering Mechanics

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“…Recently, several studies have been established to deal with the thermoelastic behavior of materials and structures using the modified theories and models by considering different environmental circumstances [33][34][35][36][37][38][39][40]. The contribution of this study is to present a new system of thermo-optical equations that characterize the propagation behavior of photo-and thermal carriers in semiconductors under the intense femtosecond laser pulse excitation.…”

mentioning

confidence: 99%

Thermomagnetic behavior of a semiconductor material heated by pulsed excitation based on the fourth-order MGT photothermal model

Abouelregal

Sedighi

Eremeyev

2022

Continuum Mech. Thermodyn.

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This article proposes a photothermal model to reveal the thermo-magneto-mechanical properties of semiconductor materials, including coupled diffusion equations for thermal conductivity, elasticity, and excess carrier density. The proposed model is developed to account for the optical heating that occurs through the semiconductor medium. The Moore-Gibson-Thompson (MGT) equation of the fourth-order serves as the theoretical framework to establish the photothermal model. It is well-known that the optical and heat transfer properties of such materials behave as random functions of photoexcited-carrier density; therefore, the current model is remarkably more reliable compared to the earlier closed-form theories which are limited to a single form. The constructed theoretical framework is able to investigate the magneto-photothermoelastic problems in a semiconductor medium due to laser pulse excitation as a case study. Some parametric studies are used to exhibit the impact of thermal parameters, electromagnetic fields, laser pulses and thermoelectric coupling factors on the thermomagnetic behavior of physical variables. Finally, several numerical examples have been presented to draw the distributions of the examined field variables.

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