A modified fractional order generalized bio-thermoelastic theory with temperature-dependent thermal material properties

Li, Xiaoya; Xue, Zhangna; Tian, Xiaogeng

doi:10.1016/j.ijthermalsci.2018.06.007

Cited by 57 publications

(8 citation statements)

References 55 publications

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“…Abbas [27] studied an infinite medium with a spherical cavity and subjected to a thermal shock by using the fractional-order generalized thermoelasticity. Li et al [28] used a modified fractional-order theory to solve a generalized bio-thermoelastic problem with temperature-dependent thermal properties. Peng and He [29] introduced the diffusion theory into the generalized fractional thermoelastic theory and studied a thermoelastic diffusion problem for an infinite body with a spherical cavity.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis to the fractional order thermoelastic problem of porous structure

Liu

2022

Z Angew Math Mech

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Porous materials have been extensively applied in many areas such as aerospace, electronic communication, petrochemical, bio‐medicine, and so forth, especially, under some extreme heating conditions, study on the coupling problem of deformation field and temperature field in porous media is of great significance to the application and optimal design of the material. On account of this, in the present paper, according to the Lord and Shulman's generalized thermoelastic theory and Ezzat's fractional order theory, the dynamic response of an infinite porous thermoelastic material with a spherical cavity and subjected to a ramp‐type heating is studied. The governing equations of the corresponding problem are formulated and then solved by means of Laplace transform and its numerical inversion. The distributions of the nondimensional temperature, displacement, stress, and volume fraction in the porous structure are obtained and illustrated graphically. In simulation, the effects of the time, the thermal lag factor, and the fractional‐order factor on all the considered variables are examined and discussed in detail.

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Section: Introductionmentioning

confidence: 99%

Dynamic analysis to the fractional order thermoelastic problem of porous structure

Liu

2022

Z Angew Math Mech

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“…In the past decade, many models in viscoelasticity, bioengineering, and heat conduction [32][33][34] have been effectively revised using fractional order calculus. As a result, fractional order should be incorporated into generalized thermoelastic diffusion theory [35].…”

Section: Introductionmentioning

confidence: 99%

Dual‐phase‐lag thermoelastic diffusion analysis of a size‐dependent microplate based on modified fractional‐order heat conduction model

Tian

Peng

2022

Z Angew Math Mech

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With the rapid evolution of small-scale devices, the effect of size dependence on elastic deformation becomes more and more obvious. Furthermore, the physical processes usually involve memory and inheritance for some anomalous diffusion that the constitutive relation does not obey the standard gradient rate. Owing to capturing the memory-dependent effect and the size-dependent effect, the existing thermoelastic diffusion theories cannot be applicable. To further refine the thermoelastic diffusion model for micro/nano structures, a refined nonlocal thermoelastic diffusion model is developed by combining the fractional-order dual-phase-lag (DPL) heat conduction model and fractional-order diffusion model in this paper. In addition, the Tempered-Caputo (TC) definition is an extension of the Caputo definition without the fractional derivative of the singular kernel, which is adopted for the first time to reflect the memory-dependent effects of heat conduction and stress-strain relationship. Then, this new model is applied to investigating the transient response of an elastic microplate subjected to a sinusoidal thermal loading. The corresponding governing equations are formulated and solved by the Laplace transform method and its numerical inversion. In calculation, the influences of the fractional-order parameter, the tempered parameter and the nonlocal parameter on the variations of the considered quantities are presented and discussed in detail. It is expected to provide new insights into thermoelastic diffusion behaviors of structures at the micro/nanoscale.

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“…Fluid flow increased as the porosity parameter was raised. By introducing a one‐layer skin texture parameter with variable thermal properties for numerical evaluation after accurate accuracy of a modified thermoelastic model, Li et al 18 created a generalized thermoelastic theory of modified fraction with variable thermal material properties for anisotropic skin texture. Akram et al 19 used Riccati generalized image equations to investigate two states of the Klein–Fok–Gordon equation that had a significant impact on hereditary memory maintenance.…”

Section: Introductionmentioning

confidence: 99%

Analytical assessment of the time‐space fractional bioheat transfer equation by the radial basis function method for living tissues

et al. 2022

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In recent years, thermal treatment has proven to be helpful, notably in oncology. In fact, ablating the superfluous mass and eliminating the malignant tumor using a different modality such as warmth or cooling is a therapeutic method. In this study, the radial basis function approach was used to answer the time-space fractional heat transfer equations of human body tissue during thermal therapy. To validate the radial basis function technique, it was also compared to the fourthorder Runge-Kutta numerical method. The findings demonstrated that this methodology is extremely accurate and efficient, with an error rate of less than 1%. The effect of time and spatial fractional parameters, blood perfusion coefficient, metabolic coefficient, and internal source coefficient on the temperature profile inside human living tissues has been studied and depicted well.

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A modified fractional order generalized bio-thermoelastic theory with temperature-dependent thermal material properties

Cited by 57 publications

References 55 publications

Dynamic analysis to the fractional order thermoelastic problem of porous structure

Dynamic analysis to the fractional order thermoelastic problem of porous structure

Dual‐phase‐lag thermoelastic diffusion analysis of a size‐dependent microplate based on modified fractional‐order heat conduction model

Analytical assessment of the time‐space fractional bioheat transfer equation by the radial basis function method for living tissues

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