The effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids in a generalized thermoplastic half-space are studied by using the Lord-Shulman (L-S) model and the dual-phase-la...The effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids in a generalized thermoplastic half-space are studied by using the Lord-Shulman (L-S) model and the dual-phase-lag (DPL) model. The analytical solutions for the displacements, stresses, temperature, diffusion concentration, and volume fraction field with different values of the magnetic field, the rotation, the gravity, and the initial stress are obtained and portrayed graphically. The results indicate that the effects of gravity, rotation, voids, diffusion, initial stress, and electromagnetic field are very pronounced on the physical properties of the material.展开更多
We build a fractional dual-phase-lag model and the corresponding bioheat transfer equation, which we use to interpret the experiment results for processed meat that have been explained by applying the hyperbolic condu...We build a fractional dual-phase-lag model and the corresponding bioheat transfer equation, which we use to interpret the experiment results for processed meat that have been explained by applying the hyperbolic conduction. Analytical solutions expressed by H-functions are obtained by using the Laplace and Fourier transforms method. The inverse fractional dual-phase-lag heat conduction problem for the simultaneous estimation of two relaxation times and orders of fractionality is solved by applying the nonlinear least-square method. The estimated model parameters are given. Finally, the measured and the calculated temperatures versus time are compared and discussed. Some numerical examples are also given and discussed.展开更多
The problem of a semi-infinite medium subjected to thermal shock on its plane boundary is solved in the context of the dual-phase-lag thermoelastic model. The expressions for temperature, displacement and stress are p...The problem of a semi-infinite medium subjected to thermal shock on its plane boundary is solved in the context of the dual-phase-lag thermoelastic model. The expressions for temperature, displacement and stress are presented. The governing equations are expressed in Laplace transform domain and solved in that domain. The solution of the problem in the physical domain is obtained by using a numerical method for the inversion of the Laplace transforms based on Fourier series expansions. The numerical estimates of the displacement, temperature, stress and strain are obtained for a hypothetical material. The results obtained are presented graphically to show the effect phase-lag of the heat flux and a phase-lag of temperature gradient on displacement, temperature, stress.展开更多
In this study,transient non-Fourier heat transfer in a solid cylinder is analytically solved based on dual-phase-lag for constant axial heat flux condition.Governing equations for the model are expressed in two-dimens...In this study,transient non-Fourier heat transfer in a solid cylinder is analytically solved based on dual-phase-lag for constant axial heat flux condition.Governing equations for the model are expressed in two-dimensional cylindrical coordinates;the equations are nondimensionalized and exact solution for the equations is presented by using the separation of variable method.Results showed that the dual-phase-lag model requires less time to meet the steady temperature compared with single-phase-lag model.On the contrary,thermal wave diffusion speed for the dual-phase-lag model is greater than the single-phase-lag model.Also the effect of relaxation time in dual-phase-lag model has been taken on consideration.展开更多
The present work is devoted to define a generalized Green’s function solution for the dual-phase-lag model in homogeneous materials in a unified manner .The high-order mixed derivative with respect to space and time ...The present work is devoted to define a generalized Green’s function solution for the dual-phase-lag model in homogeneous materials in a unified manner .The high-order mixed derivative with respect to space and time which reflect the lagging behavior is treated in special manner in the dual-phase-lag heat equation in order to construct a general solution applicable to wide range of dual-phase-lag heat transfer problems of general initial-boundary conditions using Green’s function solution method. Also, the Green’s function for a finite medium subjected to arbitrary heat source and arbitrary initial and boundary conditions is constructed. Finally, four examples of different physical situations are analyzed in order to illustrate the accuracy and potentialities of the proposed unified method. The obtained results show good agreement with works of [1-4].展开更多
Nanoscale heat transfer cannot be described by the classical Fourier law due to the very small dimension,and therefore,analyzing heat transfer in nanoscale is of crucial importance for the design and operation of nano...Nanoscale heat transfer cannot be described by the classical Fourier law due to the very small dimension,and therefore,analyzing heat transfer in nanoscale is of crucial importance for the design and operation of nano-devices and the optimization of thermal processing of nano-materials.Recently,time-fractional dualphase-lagging(DPL)equations with temperature jump boundary conditions have showed promising for analyzing the heat conduction in nanoscale.This article proposes a numerical algorithm with high spatial accuracy for solving the timefractional dual-phase-lagging nano-heat conduction equation with temperature jump boundary conditions.To this end,we first develop a fourth-order accurate and unconditionally stable compact finite difference scheme for solving this time-fractional DPL model.We then present a fast numerical solver based on the divide-and-conquer strategy for the obtained finite difference scheme in order to reduce the huge computational work and storage.Finally,the algorithm is tested by two examples to verify the accuracy of the scheme and computational speed.And we apply the numerical algorithm for predicting the temperature rise in a nano-scale silicon thin film.Numerical results confirm that the present difference scheme provides min{2−α,2−β}order accuracy in time and fourth-order accuracy in space,which coincides with the theoretical analysis.Results indicate that the mentioned time-fractional DPL model could be a tool for investigating the thermal analysis in a simple nanoscale semiconductor silicon device by choosing the suitable fractional order of Caputo derivative and the parameters in the model.展开更多
The present article represents an analysis of reflection of P-wave and SV-wave on the boundary of an isotropic and homogeneous generalized thermoelastic half-space when the boundary is stress-free as well as isotherma...The present article represents an analysis of reflection of P-wave and SV-wave on the boundary of an isotropic and homogeneous generalized thermoelastic half-space when the boundary is stress-free as well as isothermal. The modulus of elasticity is taken as a linear function of reference temperature. The basic governing equations are applied under four theories of the generalized thermoelasticity： Lord-Shulman （L-S） theory with one relaxation time, Green-Naghdi （G-N） theory without energy dissipation and Tzou theory with dual-phase-lag （DPL）, as well as the coupled thermoelasticity （CTE） theory. It is shown that there exist three plane waves, namely, a thermal wave, a P-wave and an SV-wave. The reflection from an isothermal stress-free surface is studied to obtain the reflection amplitude ratios of the reflected waves for the incidence of P- and SV-waves. The amplitude ratios variations with the angle of incident are shown graphically. Also the effects of reference temperature of the modulus of elasticity and dual-phase lags on the reflection amplitude ratios are discussed numerically.展开更多
The aim of this paper is to present the backward substitution method for solving a class of fractional dual-phase-lag models of heat transfer.The proposed method is based on the Fourier series expansion along the spat...The aim of this paper is to present the backward substitution method for solving a class of fractional dual-phase-lag models of heat transfer.The proposed method is based on the Fourier series expansion along the spatial coordinate over the orthonormal basis formed by the eigenfunctions of the corresponding Sturm-Liouville problem.This Fourier expansion of the solution transforms the original fractional par-tial differential equation into a sequence of multi-term fractional ordinary differential equations.These fractional equations are solved by the use of the backward substi-tution method.The numerical examples with temperature-jump boundary condition and parameters of the tissue confirm the high accuracy and efficiency of the proposed numerical scheme.展开更多
The dual-phase-lag heat transfer model is employed to study the reflection phenomena of P and SV waves from a surface of a semi-infinite magnetothermoelastic solid.The ratios of reflection coefficients to that of inci...The dual-phase-lag heat transfer model is employed to study the reflection phenomena of P and SV waves from a surface of a semi-infinite magnetothermoelastic solid.The ratios of reflection coefficients to that of incident coefficients are obtained for P-and SV-wave cases.The results for partition of the energy for various values of the angle of incidence are computed numerically under the stress-free and rigidly fixed thermally insulated boundaries.The reflection coefficients are depending on the angle of incidence,magnetic field,phase lags and other material constants.Results show that the sum of energy ratios is unity at the interface.The results are discussed and depicted graphically.展开更多
The thermoelastic diffusion problem of an isotropic half-space is presented.The Green-Naghdi model with and without energy dissipation is proposed.Novel multi single/dual-phase-lag models are presented to investigate ...The thermoelastic diffusion problem of an isotropic half-space is presented.The Green-Naghdi model with and without energy dissipation is proposed.Novel multi single/dual-phase-lag models are presented to investigate the thermoelastic diffusion behavior of the medium.The simple Green-Naghdi type Ⅱ and Ⅲ and their modified models are all examined here.The exact solution of thermodiffusion governing equations has been obtained considering the initial and boundary conditions.The validity of results is acceptable by comparing all variables.Benchmark results are reported to help other investigators in their future comparisons.展开更多
文摘The effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids in a generalized thermoplastic half-space are studied by using the Lord-Shulman (L-S) model and the dual-phase-lag (DPL) model. The analytical solutions for the displacements, stresses, temperature, diffusion concentration, and volume fraction field with different values of the magnetic field, the rotation, the gravity, and the initial stress are obtained and portrayed graphically. The results indicate that the effects of gravity, rotation, voids, diffusion, initial stress, and electromagnetic field are very pronounced on the physical properties of the material.
基金supported by the National Natural Science Foundation of China(Grant Nos.11102102,11472161,and 91130017)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2014AQ015)the Independent Innovation Foundation of Shandong University,China(Grant No.2013ZRYQ002)
文摘We build a fractional dual-phase-lag model and the corresponding bioheat transfer equation, which we use to interpret the experiment results for processed meat that have been explained by applying the hyperbolic conduction. Analytical solutions expressed by H-functions are obtained by using the Laplace and Fourier transforms method. The inverse fractional dual-phase-lag heat conduction problem for the simultaneous estimation of two relaxation times and orders of fractionality is solved by applying the nonlinear least-square method. The estimated model parameters are given. Finally, the measured and the calculated temperatures versus time are compared and discussed. Some numerical examples are also given and discussed.
文摘The problem of a semi-infinite medium subjected to thermal shock on its plane boundary is solved in the context of the dual-phase-lag thermoelastic model. The expressions for temperature, displacement and stress are presented. The governing equations are expressed in Laplace transform domain and solved in that domain. The solution of the problem in the physical domain is obtained by using a numerical method for the inversion of the Laplace transforms based on Fourier series expansions. The numerical estimates of the displacement, temperature, stress and strain are obtained for a hypothetical material. The results obtained are presented graphically to show the effect phase-lag of the heat flux and a phase-lag of temperature gradient on displacement, temperature, stress.
文摘In this study,transient non-Fourier heat transfer in a solid cylinder is analytically solved based on dual-phase-lag for constant axial heat flux condition.Governing equations for the model are expressed in two-dimensional cylindrical coordinates;the equations are nondimensionalized and exact solution for the equations is presented by using the separation of variable method.Results showed that the dual-phase-lag model requires less time to meet the steady temperature compared with single-phase-lag model.On the contrary,thermal wave diffusion speed for the dual-phase-lag model is greater than the single-phase-lag model.Also the effect of relaxation time in dual-phase-lag model has been taken on consideration.
文摘The present work is devoted to define a generalized Green’s function solution for the dual-phase-lag model in homogeneous materials in a unified manner .The high-order mixed derivative with respect to space and time which reflect the lagging behavior is treated in special manner in the dual-phase-lag heat equation in order to construct a general solution applicable to wide range of dual-phase-lag heat transfer problems of general initial-boundary conditions using Green’s function solution method. Also, the Green’s function for a finite medium subjected to arbitrary heat source and arbitrary initial and boundary conditions is constructed. Finally, four examples of different physical situations are analyzed in order to illustrate the accuracy and potentialities of the proposed unified method. The obtained results show good agreement with works of [1-4].
基金supported by the National Natural Science Foundation of China(Grant No.12001307)by the Natural Science Foundation of Shandong Province(Grant No.ZR2020QA033).
文摘Nanoscale heat transfer cannot be described by the classical Fourier law due to the very small dimension,and therefore,analyzing heat transfer in nanoscale is of crucial importance for the design and operation of nano-devices and the optimization of thermal processing of nano-materials.Recently,time-fractional dualphase-lagging(DPL)equations with temperature jump boundary conditions have showed promising for analyzing the heat conduction in nanoscale.This article proposes a numerical algorithm with high spatial accuracy for solving the timefractional dual-phase-lagging nano-heat conduction equation with temperature jump boundary conditions.To this end,we first develop a fourth-order accurate and unconditionally stable compact finite difference scheme for solving this time-fractional DPL model.We then present a fast numerical solver based on the divide-and-conquer strategy for the obtained finite difference scheme in order to reduce the huge computational work and storage.Finally,the algorithm is tested by two examples to verify the accuracy of the scheme and computational speed.And we apply the numerical algorithm for predicting the temperature rise in a nano-scale silicon thin film.Numerical results confirm that the present difference scheme provides min{2−α,2−β}order accuracy in time and fourth-order accuracy in space,which coincides with the theoretical analysis.Results indicate that the mentioned time-fractional DPL model could be a tool for investigating the thermal analysis in a simple nanoscale semiconductor silicon device by choosing the suitable fractional order of Caputo derivative and the parameters in the model.
基金funded by the Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah,under grant No.(363/130/1431)
文摘The present article represents an analysis of reflection of P-wave and SV-wave on the boundary of an isotropic and homogeneous generalized thermoelastic half-space when the boundary is stress-free as well as isothermal. The modulus of elasticity is taken as a linear function of reference temperature. The basic governing equations are applied under four theories of the generalized thermoelasticity： Lord-Shulman （L-S） theory with one relaxation time, Green-Naghdi （G-N） theory without energy dissipation and Tzou theory with dual-phase-lag （DPL）, as well as the coupled thermoelasticity （CTE） theory. It is shown that there exist three plane waves, namely, a thermal wave, a P-wave and an SV-wave. The reflection from an isothermal stress-free surface is studied to obtain the reflection amplitude ratios of the reflected waves for the incidence of P- and SV-waves. The amplitude ratios variations with the angle of incident are shown graphically. Also the effects of reference temperature of the modulus of elasticity and dual-phase lags on the reflection amplitude ratios are discussed numerically.
基金The work was supported by the Natural Science Foundation of China(No.12072103)the Fundamental Research Funds for the Central Universities(No.B200202126)+4 种基金the Natural Science Foundation of Jiangsu Province(No.BK20190073)the State Key Laboratory of Acoustics,Chinese Academy of Sciences(No.SKLA202001)the State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University(No.KF2020-22)the Key Laboratory of Intelligent Materials and Structural Mechanics of Hebei Province(No.KF2021-01)the China Postdoctoral Science Foundation(Nos.2017M611669 and 2018T110430).
文摘The aim of this paper is to present the backward substitution method for solving a class of fractional dual-phase-lag models of heat transfer.The proposed method is based on the Fourier series expansion along the spatial coordinate over the orthonormal basis formed by the eigenfunctions of the corresponding Sturm-Liouville problem.This Fourier expansion of the solution transforms the original fractional par-tial differential equation into a sequence of multi-term fractional ordinary differential equations.These fractional equations are solved by the use of the backward substi-tution method.The numerical examples with temperature-jump boundary condition and parameters of the tissue confirm the high accuracy and efficiency of the proposed numerical scheme.
文摘The dual-phase-lag heat transfer model is employed to study the reflection phenomena of P and SV waves from a surface of a semi-infinite magnetothermoelastic solid.The ratios of reflection coefficients to that of incident coefficients are obtained for P-and SV-wave cases.The results for partition of the energy for various values of the angle of incidence are computed numerically under the stress-free and rigidly fixed thermally insulated boundaries.The reflection coefficients are depending on the angle of incidence,magnetic field,phase lags and other material constants.Results show that the sum of energy ratios is unity at the interface.The results are discussed and depicted graphically.
文摘The thermoelastic diffusion problem of an isotropic half-space is presented.The Green-Naghdi model with and without energy dissipation is proposed.Novel multi single/dual-phase-lag models are presented to investigate the thermoelastic diffusion behavior of the medium.The simple Green-Naghdi type Ⅱ and Ⅲ and their modified models are all examined here.The exact solution of thermodiffusion governing equations has been obtained considering the initial and boundary conditions.The validity of results is acceptable by comparing all variables.Benchmark results are reported to help other investigators in their future comparisons.
