“…An increase in the magnitudes of the field variables within the nanobeam has been noticed as the values of the non-local variable grow. Consequently, the results of this study could be useful for future research into many different nanostructure-based systems, such as dampening mechanisms and different ways of designing nanoscale devices 29 , 74 . Figure 6 Variation of tangential displacement versus non-local parameter .…”
Accurately characterizing the thermomechanical parameters of nanoscale systems is essential for understanding their performance and building innovative nanoscale technologies due to their distinct behaviours. Fractional thermal transport models are commonly utilized to correctly depict the heat transfer that occurs in these nanoscale systems. The current study presents a novel mathematical thermoelastic model that incorporates a new fractional differential constitutive equation for heat conduction. This heat equation is useful for understanding the effects of thermal memory. An application of a fractional-time Atangana–Baleanu (AB) derivative with a local and non-singular kernel was utilized in the process of developing the mathematical model that was suggested. To deal with effects that depend on size, nonlocal constitutive relations are introduced. Furthermore, in order to take into consideration, the viscoelastic behaviour of the material at the nanoscale, the fractional Kelvin–Voigt model is utilized. The proposed model is highly effective in properly depicting the unusual thermal conductivity phenomena often found in nanoscale devices. The study also considered the mechanical deformation, temperature variations, and viscoelastic characteristics of the functionally graded (FG) nanostructured beams. The consideration was made that the material characteristics exhibit heterogeneity and continuous variation across the thickness of the beam as the nanobeam transitions from a ceramic composition in the lower region to a metallic composition in the upper region. The complicated thermomechanical features of simply supported viscoelastic nanobeams that were exposed to harmonic heat flow were determined by the application of the model that was constructed. Heterogeneity, nonlocality, and fractional operators are some of the important variables that contribute to its success, and this article provides a full study and illustration of the significance of these characteristics. The results that were obtained have the potential to play a significant role in pushing forward the design and development of tools, materials, and nanostructures that have viscoelastic mechanical characteristics and graded functions.
“…An increase in the magnitudes of the field variables within the nanobeam has been noticed as the values of the non-local variable grow. Consequently, the results of this study could be useful for future research into many different nanostructure-based systems, such as dampening mechanisms and different ways of designing nanoscale devices 29 , 74 . Figure 6 Variation of tangential displacement versus non-local parameter .…”
Accurately characterizing the thermomechanical parameters of nanoscale systems is essential for understanding their performance and building innovative nanoscale technologies due to their distinct behaviours. Fractional thermal transport models are commonly utilized to correctly depict the heat transfer that occurs in these nanoscale systems. The current study presents a novel mathematical thermoelastic model that incorporates a new fractional differential constitutive equation for heat conduction. This heat equation is useful for understanding the effects of thermal memory. An application of a fractional-time Atangana–Baleanu (AB) derivative with a local and non-singular kernel was utilized in the process of developing the mathematical model that was suggested. To deal with effects that depend on size, nonlocal constitutive relations are introduced. Furthermore, in order to take into consideration, the viscoelastic behaviour of the material at the nanoscale, the fractional Kelvin–Voigt model is utilized. The proposed model is highly effective in properly depicting the unusual thermal conductivity phenomena often found in nanoscale devices. The study also considered the mechanical deformation, temperature variations, and viscoelastic characteristics of the functionally graded (FG) nanostructured beams. The consideration was made that the material characteristics exhibit heterogeneity and continuous variation across the thickness of the beam as the nanobeam transitions from a ceramic composition in the lower region to a metallic composition in the upper region. The complicated thermomechanical features of simply supported viscoelastic nanobeams that were exposed to harmonic heat flow were determined by the application of the model that was constructed. Heterogeneity, nonlocality, and fractional operators are some of the important variables that contribute to its success, and this article provides a full study and illustration of the significance of these characteristics. The results that were obtained have the potential to play a significant role in pushing forward the design and development of tools, materials, and nanostructures that have viscoelastic mechanical characteristics and graded functions.
“…As a result, the materials of the nonlocal thermomaterial should be considered nonlocal thermosolids to refine the fields of temperature and deformation using Eringen's nonlocal model [9][10][11]. Soleiman et al [12] examined the thermomechanical behaviour of functionally graded nanoscale beams under the fractional heat transfer model using a two-parameter Mittag-Leffler function. Fahmy proposed unique boundary element solutions to thermoelastic nanostructure problems [13,14].…”
This paper provides a new fractional boundary element method (BEM) solution for nonlinear nonlocal thermoelastic problems with anisotropic fibrous polymer nanoparticles. This comprehensive BEM solution comprises two solutions: the anisotropic fibrous polymer nanoparticles problem solution and the nonlinear nonlocal thermoelasticity problem. The nonlinear nonlocal thermoelasticity problem solution separates the displacement field into complimentary and specific components. The overall displacement is obtained using the boundary element methodology, which solves a Navier-type problem, and the specific displacement is derived using the local radial point interpolation method (LRPIM). The new modified shift-splitting (NMSS) technique, which minimizes memory and processing time requirements, was utilized to solve BEM-created linear systems. The performance of NMSS was evaluated. The numerical results show how fractional and graded parameters influence the thermal stresses of nonlinear nonlocal thermoelastic issues involving anisotropic fibrous polymer nanoparticles. The numerical findings further reveal that the BEM results correlate very well with the finite element method (FEM) and analytical results, demonstrating the validity and correctness of the proposed methodology.
“…For over four decades, considerable attention has focused on generalized thermoelasticity theories, which posit a finite speed for thermal signals [25][26][27][28][29][30][31][32][33][34]. These theories, in contrast to the classical coupled thermoelasticity (CT) theory based on a parabolic heat equation and infinite heat propagation speed, employ a hyperbolic heat equation.…”
Understanding the biothermal response of skin tissue exposed to electromagnetic (EM) radiation and variable thermal fields is crucial for mitigating risks associated with such exposures. This knowledge can empower the development of safe and efficacious evidence‐based treatments for various skin conditions within the medical field. This study employs the fourth‐order Moore–Gibson–Thomson (MGT) concept to establish a theoretical framework for biothermal analysis. This investigation aims to elucidate the biothermal response of skin tissues to EM radiation. The developed model facilitates the prediction of thermal reactions within human skin and the subsequent evaluation of bioheat transfer efficiency in biological tissues. The proposed model is implemented on a one‐dimensional representation of a skin layer and incorporates the effects of an induced electric field and a time‐harmonic heat source. Additionally, a linear dependence of metabolic heat generation on tissue temperature is considered. By employing Laplace transforms, the analytical solutions for tissue temperature are presented. The derived analytical solutions are compared with established theories to assess the accuracy of the proposed model. The results reveal that the modified MGT bioheat transfer model predicts lower temperatures compared to the conventional Pennes model, attributable to the incorporation of the thermal relaxation time constant.
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