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
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 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 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
This paper presents two exact explicit solutions for the three dimensional dual-phase lag （DLP） heat conduction equation, during the derivation of which the method of trial and error and the authors＇ previous exper...This paper presents two exact explicit solutions for the three dimensional dual-phase lag （DLP） heat conduction equation, during the derivation of which the method of trial and error and the authors＇ previous experiences are utilized. To the authors＇ knowledge, most solutions of 2D or 3D DPL models available in the literature are obtained by numerical methods, and there are few exact solutions up to now. The exact solutions in this paper can be used as benchmarks to validate numerical solutions and to develop numerical schemes, grid generation methods and so forth. In addition, they are of theoretical significance since they correspond to physically possible situations. The main goal of this paper is to obtain some possible exact explicit solutions of the dual-phase lag heat conduction equation as the benchmark solutions for computational heat transfer, rather than specific solutions for some given initial and boundary conditions. Therefore, the initial and boundary conditions are indeterminate before derivation and can be deduced from the solutions afterwards. Actually, all solutions given in this paper can be easily proven by substituting them into the governing equation.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
In nanoresonators,thermoelastic damping(TED)is a primary energy dissipation mechanism.As a result,when designing nanoresonators,it is critical to limit this type of dissipation.This paper investigates the nonlocal TED...In nanoresonators,thermoelastic damping(TED)is a primary energy dissipation mechanism.As a result,when designing nanoresonators,it is critical to limit this type of dissipation.This paper investigates the nonlocal TED of circular single-layered graphene sheet(SLGS)nanoresonators in axisymmetric out-of-plane vibration utilizing the generalized dual-phase-lag thermoelasticity theory.The nonlocal elasticity and Gurtin-Murdoch surface elasticity theories are employed to capture the small-scale and surface energy effects,respectively.By incorporating these effects into the model,the non-classical equations of the coupled thermoelastic problem are first obtained and then an analytical expression is introduced to predict TED in circular nanoplates.Moreover,the results obtained herein are validated by those of the classical continuum theory which can be found in the open literature.The influences of the aspect ratio,surface elastic modulus,surface residual stress and nonlocal parameter on TED of circular SLGS nanoresonators are investigated using numerical data.The calculated results show the significance of surface and nonlocal effects in nanoplate TED continuum modeling.展开更多
This paper aimed to study the effect of electromagnetic field on general model of the equations of the generalized thermoelasticity reinforcement of the deformation of a micropolar generalized thermoelastic medium.The...This paper aimed to study the effect of electromagnetic field on general model of the equations of the generalized thermoelasticity reinforcement of the deformation of a micropolar generalized thermoelastic medium.The phenomenon is in the context of the couple theory(C-D),Lord-Shulman(L-S)and Green-Lindsay(G-L)as well as the Dual-Phase-Lag(DPL)models.The normal mode technique is used to find the exact expressions components of displacement,force stress,and temperature.The modifications of the considered variables with the horizontal distance are illustrated graphically to show the distance values that reduce to the variables interrupt.Comparisons are made with the results in the absence and presence of electromagnetic field for the general of reinforcement on the total deformation of a micropolar thermoelastic medium.The results obtained are calculated numerically and displayed by the graphs to show the effect of the entered new parameters on the phenomena.展开更多
Dual-phase lag (DPL) model is used to describe the non-Fourier heat conduction in a finite medium where the boundary at x=0 is heated by a rectangular pulsed energy source and the other boundary is tightly contactal w...Dual-phase lag (DPL) model is used to describe the non-Fourier heat conduction in a finite medium where the boundary at x=0 is heated by a rectangular pulsed energy source and the other boundary is tightly contactal with another medium and satisfies the continuous boundary condition. Numerical solution of thes kind of non-Fourier heat conduction is presented in this paper. The results are compared with those predicted by the hyperbolic heat conduction (HHC) equation.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
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
In this paper,the generalized thermoelasticity problem for an infinite fiberreinforced transversely-isotropic thick plate subjected to initial stress is solved.The lower surface of the plate rests on a rigid foundatio...In this paper,the generalized thermoelasticity problem for an infinite fiberreinforced transversely-isotropic thick plate subjected to initial stress is solved.The lower surface of the plate rests on a rigid foundation and temperature while the upper surface is thermally insulated with prescribed surface loading.The normal mode analysis is used to obtain the analytical expressions for the displacements,stresses and temperature distributions.The problem has been solved analytically using the generalized thermoelasticity theory of dual-phase-lags.Effect of phase-lags,reinforcement and initial stress on the field quantities is shown graphically.The results due to the coupled thermoelasticity theory,Lord and Shulman’s theory,and Green and Naghdi’s theory have been derived as limiting cases.The graphs illustrated that the initial stress,the reinforcement and phase-lags have great effects on the distributions of the field quantities.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
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
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.
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.
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.
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 (50576097) the National Defense Basic Research Program of China (DEDP 1003)
文摘This paper presents two exact explicit solutions for the three dimensional dual-phase lag （DLP） heat conduction equation, during the derivation of which the method of trial and error and the authors＇ previous experiences are utilized. To the authors＇ knowledge, most solutions of 2D or 3D DPL models available in the literature are obtained by numerical methods, and there are few exact solutions up to now. The exact solutions in this paper can be used as benchmarks to validate numerical solutions and to develop numerical schemes, grid generation methods and so forth. In addition, they are of theoretical significance since they correspond to physically possible situations. The main goal of this paper is to obtain some possible exact explicit solutions of the dual-phase lag heat conduction equation as the benchmark solutions for computational heat transfer, rather than specific solutions for some given initial and boundary conditions. Therefore, the initial and boundary conditions are indeterminate before derivation and can be deduced from the solutions afterwards. Actually, all solutions given in this paper can be easily proven by substituting them into the governing equation.
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].
文摘In nanoresonators,thermoelastic damping(TED)is a primary energy dissipation mechanism.As a result,when designing nanoresonators,it is critical to limit this type of dissipation.This paper investigates the nonlocal TED of circular single-layered graphene sheet(SLGS)nanoresonators in axisymmetric out-of-plane vibration utilizing the generalized dual-phase-lag thermoelasticity theory.The nonlocal elasticity and Gurtin-Murdoch surface elasticity theories are employed to capture the small-scale and surface energy effects,respectively.By incorporating these effects into the model,the non-classical equations of the coupled thermoelastic problem are first obtained and then an analytical expression is introduced to predict TED in circular nanoplates.Moreover,the results obtained herein are validated by those of the classical continuum theory which can be found in the open literature.The influences of the aspect ratio,surface elastic modulus,surface residual stress and nonlocal parameter on TED of circular SLGS nanoresonators are investigated using numerical data.The calculated results show the significance of surface and nonlocal effects in nanoplate TED continuum modeling.
文摘This paper aimed to study the effect of electromagnetic field on general model of the equations of the generalized thermoelasticity reinforcement of the deformation of a micropolar generalized thermoelastic medium.The phenomenon is in the context of the couple theory(C-D),Lord-Shulman(L-S)and Green-Lindsay(G-L)as well as the Dual-Phase-Lag(DPL)models.The normal mode technique is used to find the exact expressions components of displacement,force stress,and temperature.The modifications of the considered variables with the horizontal distance are illustrated graphically to show the distance values that reduce to the variables interrupt.Comparisons are made with the results in the absence and presence of electromagnetic field for the general of reinforcement on the total deformation of a micropolar thermoelastic medium.The results obtained are calculated numerically and displayed by the graphs to show the effect of the entered new parameters on the phenomena.
文摘Dual-phase lag (DPL) model is used to describe the non-Fourier heat conduction in a finite medium where the boundary at x=0 is heated by a rectangular pulsed energy source and the other boundary is tightly contactal with another medium and satisfies the continuous boundary condition. Numerical solution of thes kind of non-Fourier heat conduction is presented in this paper. The results are compared with those predicted by the hyperbolic heat conduction (HHC) equation.
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In this paper,the generalized thermoelasticity problem for an infinite fiberreinforced transversely-isotropic thick plate subjected to initial stress is solved.The lower surface of the plate rests on a rigid foundation and temperature while the upper surface is thermally insulated with prescribed surface loading.The normal mode analysis is used to obtain the analytical expressions for the displacements,stresses and temperature distributions.The problem has been solved analytically using the generalized thermoelasticity theory of dual-phase-lags.Effect of phase-lags,reinforcement and initial stress on the field quantities is shown graphically.The results due to the coupled thermoelasticity theory,Lord and Shulman’s theory,and Green and Naghdi’s theory have been derived as limiting cases.The graphs illustrated that the initial stress,the reinforcement and phase-lags have great effects on the distributions of the field quantities.
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.
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.
