In order to investigate the thermal shock and the heat conduction property of a target under multi-pulsed laser radiation, analytic expressions of both temperature and thermal stress fields in the target are deduced o...In order to investigate the thermal shock and the heat conduction property of a target under multi-pulsed laser radiation, analytic expressions of both temperature and thermal stress fields in the target are deduced on the basis of the non-Fourier conduction law and the thermo-elastic theory. Taking a stainless steel target as an example, we can solve the analytic expressions under appropriate boundary conditions by using the finite difference method and MATLAB software, and then reveal the evolution law of both surplus temperaturt, and thermal stress in the target. The results indicate that the temperature curves in the target irradiated by a multi-pulsed laser take on a delayed character in different sections away from the boundary, which is only affected by its relaxation time. The front of the stress wave is very steep in the non-Fourier numerical solutions, which presents an obvious thermal shock, so it is necessary to consider the non-Fourier effect of semi-infinite body under the high energy laser radiation.展开更多
The conservation equations for heat conduction are established based on the concept of thermal mass.We obtain a general heat conduction law which takes into account the spatial and temporal inertia of thermal mass.The...The conservation equations for heat conduction are established based on the concept of thermal mass.We obtain a general heat conduction law which takes into account the spatial and temporal inertia of thermal mass.The general law introduces a damped thermal wave equation.It reduces to the well-known CV model when the spatial inertia of heat flux and temperature and the temporal inertia of temperature are neglected,which indicates that the CV model only considers the temporal inertia of heat flux.Numerical simulations on the propagation and superposition of thermal waves show that for small thermal perturbation the CV model agrees with the thermal wave equation based on the thermal mass theory.For larger thermal perturbation,however,the physically impossible phenomenon pre-dicted by CV model,i.e.the negative temperature induced by the thermal wave superposition,is eliminated by the general heat conduction law,which demonstrates that the present heat conduction law based on the thermal mass theory is more reasonable.展开更多
A three-dimensional Darcy Forchheimer mixed convective flow of a couple stress hybrid nanofluid flow through a vertical plate by means of the double diffusion Cattaneo-Christov model is presented in this study.The inf...A three-dimensional Darcy Forchheimer mixed convective flow of a couple stress hybrid nanofluid flow through a vertical plate by means of the double diffusion Cattaneo-Christov model is presented in this study.The influence of highorder velocity slip flow,as well as a passive and active control,is also considered.The motive of the research is to develop a computational model,using cobalt ferrite(Co Fe_(2)O_(4))and copper(Cu)nanoparticles(NPs)in the carrier fluid water,to magnify the energy and mass communication rate and boost the efficiency and performance of thermal energy conduction for a variety of commercial and biological purposes.The proposed model becomes more significant,with an additional effect of non-Fick's mass flux and Fourier's heat model to report the energy and mass passage rate.The results are obtained through the computational strategy parametric continuation method.The figures are plotted to reveal the physical sketch of the obtained solution,while the statistical assessment has been evaluated through tables.It has been observed that the dispersion of Cu and Co Fe_(2)O_(4)NPs to the base fluid significantly enhances the velocity and thermal conductivity of water,which is the most remarkable property of these NPs from the industrial point of view.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
In this paper,thermoelastic damping （TED） in a micro-beam resonator with a pair of piezoelectric layers bonded on its upper and lower surfaces is investigated.Equation of motion is derived and the thermoelasticity e...In this paper,thermoelastic damping （TED） in a micro-beam resonator with a pair of piezoelectric layers bonded on its upper and lower surfaces is investigated.Equation of motion is derived and the thermoelasticity equation is governed using two dimensional non-Fourier heat conduction model based on continuum theory frame.Applying Galerkin discretization method and complex-frequency approach to solve the equations of coupled thermoelasticity,we study TED of a clamped-clamped micro-beam resonator.The presented results demonstrate that thickness of the piezoelectric layers and application of DC voltage to them can affect the TED ratio and the critical thickness value of the resonator.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
To better describe the phenomenon of non-Fourier heat conduction, the fractional Cattaneo heat equation is introduced from the generalized Cattaneo model with two fractional derivatives of different orders. The anomal...To better describe the phenomenon of non-Fourier heat conduction, the fractional Cattaneo heat equation is introduced from the generalized Cattaneo model with two fractional derivatives of different orders. The anomalous heat conduction under the Neumann boundary condition in a semi-infinity medium is investigated. Exact solutions are obtained in series form of the H-function by using the Laplace transform method. Finally, numerical examples are presented graphically when different kinds of surface temperature gradient are given. The effects of fractional parameters are also discussed.展开更多
This paper consists of two parts. (1) For a hollow sphere with sudden temperature changes on its inner and outer surfaces, the hyperbolic heat conduction equation is employed to describe this extreme thermal case and...This paper consists of two parts. (1) For a hollow sphere with sudden temperature changes on its inner and outer surfaces, the hyperbolic heat conduction equation is employed to describe this extreme thermal case and an analytical expression of its temperature distribution is obtained. According to the expression, the non-Fourier heat conduction behavior that will appear in the hollow sphere is studied and some qualitative conditions that will result in distinct non-Fourier behavior in the medium is ultimately attained. (2) A novel experiment to observe non-Fourier heat conduction behavior in porous material (mainly ordinary duplicating paper) heated by a microsecond laser pulse is presented. The conditions for observing distinct non-Fourier heat conduction behavior in the experimental sample agree well with the theoretical results qualitatively.展开更多
The two-dimensional(2D) motion of the Jeffrey fluid by the curved stretching sheet coiled in a circle is investigated. The non-Fourier heat flux model is used for the heat transfer analysis. Feasible similarity variab...The two-dimensional(2D) motion of the Jeffrey fluid by the curved stretching sheet coiled in a circle is investigated. The non-Fourier heat flux model is used for the heat transfer analysis. Feasible similarity variables are used to transform the highly nonlinear ordinary equations to partial differential equations(PDEs). The homotopy technique is used for the convergence of the velocity and temperature equations. The effects of the involved parameters on the physical properties of the fluid are described graphically.The results show that the curvature parameter is an increasing function of velocity and temperature, and the temperature is a decreasing function of the thermal relaxation time.Besides, the Deborah number has a reverse effect on the pressure and surface drag force.展开更多
The non-Fourier effect in heat conduction and the coupling effect between temperature and strain rate, became the most significant effects in the nano-scale beam. In the present study, a generalized solution for the g...The non-Fourier effect in heat conduction and the coupling effect between temperature and strain rate, became the most significant effects in the nano-scale beam. In the present study, a generalized solution for the generalized thermoelastic vibration of a bounded nano-beam resonator induced by ramp type of heating is developed and the solutions take into account the above two effects. The Laplace transforms and direct method are used to determine the lateral vibration, the temperature, the displacement, the stress and the energy of the beam. The effects of the relaxation time and the ramping time parameters have been studied with some comparisons.展开更多
Non-Fourier heat conduction induced by ultrafast heating of metals with a high-energy density beam was analyzed. The non-Fourier effects during high heat flux heating were illustrated by comparing the transient temp...Non-Fourier heat conduction induced by ultrafast heating of metals with a high-energy density beam was analyzed. The non-Fourier effects during high heat flux heating were illustrated by comparing the transient temperature response to different heat flux and material relaxation times. Based on the hyperbolic heat conduction equation for the non-Fourier heat conduction law, the equation was solved using a hybrid method combining an analytical solution and numerical inversion of the Laplace transforms for a semi- infinite body with the heat flux boundary. Analysis of the temperature response and distribution led to a crite- rion for the applicability of the non-Fourier heat conduction law. The results show that at a relatively large heat flux, such as greater than 108 W/cm2, the heat-affected zone in the metal material experiences a strong thermal shock as the non-Fourier effects cause a large step increase in the surface temperature. The results provide a method for analyzing transient heat conduction problems using a high-energy density beam, such as electron beam deep penetration welding.展开更多
The present paper paper,we estimate the theory of thermoelasticity a thin slim strip under the variable thermal conductivity in the fractional-order form is solved.Thermal stress theory considering the equation of hea...The present paper paper,we estimate the theory of thermoelasticity a thin slim strip under the variable thermal conductivity in the fractional-order form is solved.Thermal stress theory considering the equation of heat conduction based on the time-fractional derivative of Caputo of orderis applied to obtain a solution.We assumed that the strip surface is to be free from traction and impacted by a thermal shock.The transform of Laplace(LT)and numerical inversion techniques of Laplace were considered for solving the governing basic equations.The inverse of the LT was applied in a numerical manner considering the Fourier expansion technique.The numerical results for the physical variables were calculated numerically and displayed via graphs.The parameter of fractional order effect and variation of thermal conductivity on the displacement,stress,and temperature were investigated and compared with the results of previous studies.The results indicated the strong effect of the external parameters,especially the timefractional derivative parameter on a thermoelastic thin slim strip phenomenon.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 effect of laser, as a heat source, on a one-dimensional finite living tissue was stud- ied in this paper. The dual phase lagging （DPL） non-Fourier heat conduction model was used for thermal analysis. The thermal...The effect of laser, as a heat source, on a one-dimensional finite living tissue was stud- ied in this paper. The dual phase lagging （DPL） non-Fourier heat conduction model was used for thermal analysis. The thermal conductivity was assumed temperature- dependent, resulting in a nonlinear equation. The obtained equations were solved using the approximate-analytical Adomian decomposition method （ADM）. It was concluded that the nonlinear analysis was important in nomFourier heat conduction problems. Moreover, a good agreement between the present nonlinear model and experimental result was obtained.展开更多
This paper investigates the problem of a 2-D plate containing internal cracks at arbitrary angles to the heating surface under thermal shock.The finite difference method is applied to solve the temperature distributio...This paper investigates the problem of a 2-D plate containing internal cracks at arbitrary angles to the heating surface under thermal shock.The finite difference method is applied to solve the temperature distribution and a difference scheme of the oblique crack is developed.For the first time,a non-Fourier heat transfer analysis method of a 2-D plate with inner cracks at arbitrary direction angles is established.Specifically,for a strip with an inner crack paralleling to the surface,numerical results are compared with the analytical solutions by rotating the boundary,and perfect agreement is obtained.Numerical experiments are further presented to investigate the influence of crack orientation angle and multi-crack distribution on non-Fourier heat conduction.展开更多
基金supported by the Chinese Natural Science Fund (No.10572020)
文摘In order to investigate the thermal shock and the heat conduction property of a target under multi-pulsed laser radiation, analytic expressions of both temperature and thermal stress fields in the target are deduced on the basis of the non-Fourier conduction law and the thermo-elastic theory. Taking a stainless steel target as an example, we can solve the analytic expressions under appropriate boundary conditions by using the finite difference method and MATLAB software, and then reveal the evolution law of both surplus temperaturt, and thermal stress in the target. The results indicate that the temperature curves in the target irradiated by a multi-pulsed laser take on a delayed character in different sections away from the boundary, which is only affected by its relaxation time. The front of the stress wave is very steep in the non-Fourier numerical solutions, which presents an obvious thermal shock, so it is necessary to consider the non-Fourier effect of semi-infinite body under the high energy laser radiation.
基金Supported by the National Natural Science Foundation of China(Grant No.50606018)
文摘The conservation equations for heat conduction are established based on the concept of thermal mass.We obtain a general heat conduction law which takes into account the spatial and temporal inertia of thermal mass.The general law introduces a damped thermal wave equation.It reduces to the well-known CV model when the spatial inertia of heat flux and temperature and the temporal inertia of temperature are neglected,which indicates that the CV model only considers the temporal inertia of heat flux.Numerical simulations on the propagation and superposition of thermal waves show that for small thermal perturbation the CV model agrees with the thermal wave equation based on the thermal mass theory.For larger thermal perturbation,however,the physically impossible phenomenon pre-dicted by CV model,i.e.the negative temperature induced by the thermal wave superposition,is eliminated by the general heat conduction law,which demonstrates that the present heat conduction law based on the thermal mass theory is more reasonable.
基金Deanship of Scientific Research at King Khalid University for funding this work through Large Groups Project under grant number(RGP.2/155/43)。
文摘A three-dimensional Darcy Forchheimer mixed convective flow of a couple stress hybrid nanofluid flow through a vertical plate by means of the double diffusion Cattaneo-Christov model is presented in this study.The influence of highorder velocity slip flow,as well as a passive and active control,is also considered.The motive of the research is to develop a computational model,using cobalt ferrite(Co Fe_(2)O_(4))and copper(Cu)nanoparticles(NPs)in the carrier fluid water,to magnify the energy and mass communication rate and boost the efficiency and performance of thermal energy conduction for a variety of commercial and biological purposes.The proposed model becomes more significant,with an additional effect of non-Fick's mass flux and Fourier's heat model to report the energy and mass passage rate.The results are obtained through the computational strategy parametric continuation method.The figures are plotted to reveal the physical sketch of the obtained solution,while the statistical assessment has been evaluated through tables.It has been observed that the dispersion of Cu and Co Fe_(2)O_(4)NPs to the base fluid significantly enhances the velocity and thermal conductivity of water,which is the most remarkable property of these NPs from the industrial point of view.
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In this paper,thermoelastic damping （TED） in a micro-beam resonator with a pair of piezoelectric layers bonded on its upper and lower surfaces is investigated.Equation of motion is derived and the thermoelasticity equation is governed using two dimensional non-Fourier heat conduction model based on continuum theory frame.Applying Galerkin discretization method and complex-frequency approach to solve the equations of coupled thermoelasticity,we study TED of a clamped-clamped micro-beam resonator.The presented results demonstrate that thickness of the piezoelectric layers and application of DC voltage to them can affect the TED ratio and the critical thickness value of the resonator.
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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11102102, 11072134, and 91130017)the Natural Science Foundation of Shandong Province, China (Grant No. ZR2009AQ014)the Independent Innovation Foundation of Shandong University, China (Grant No. 2010ZRJQ002)
文摘To better describe the phenomenon of non-Fourier heat conduction, the fractional Cattaneo heat equation is introduced from the generalized Cattaneo model with two fractional derivatives of different orders. The anomalous heat conduction under the Neumann boundary condition in a semi-infinity medium is investigated. Exact solutions are obtained in series form of the H-function by using the Laplace transform method. Finally, numerical examples are presented graphically when different kinds of surface temperature gradient are given. The effects of fractional parameters are also discussed.
基金Supported by the Chinese Academy of Sciences (No. KJ 951-B1-704), the National Natural Science Foundation of China (No. 59736130) and the State Key Fundamental Research Plan of China (No. G2000026305).
文摘This paper consists of two parts. (1) For a hollow sphere with sudden temperature changes on its inner and outer surfaces, the hyperbolic heat conduction equation is employed to describe this extreme thermal case and an analytical expression of its temperature distribution is obtained. According to the expression, the non-Fourier heat conduction behavior that will appear in the hollow sphere is studied and some qualitative conditions that will result in distinct non-Fourier behavior in the medium is ultimately attained. (2) A novel experiment to observe non-Fourier heat conduction behavior in porous material (mainly ordinary duplicating paper) heated by a microsecond laser pulse is presented. The conditions for observing distinct non-Fourier heat conduction behavior in the experimental sample agree well with the theoretical results qualitatively.
文摘The two-dimensional(2D) motion of the Jeffrey fluid by the curved stretching sheet coiled in a circle is investigated. The non-Fourier heat flux model is used for the heat transfer analysis. Feasible similarity variables are used to transform the highly nonlinear ordinary equations to partial differential equations(PDEs). The homotopy technique is used for the convergence of the velocity and temperature equations. The effects of the involved parameters on the physical properties of the fluid are described graphically.The results show that the curvature parameter is an increasing function of velocity and temperature, and the temperature is a decreasing function of the thermal relaxation time.Besides, the Deborah number has a reverse effect on the pressure and surface drag force.
文摘The non-Fourier effect in heat conduction and the coupling effect between temperature and strain rate, became the most significant effects in the nano-scale beam. In the present study, a generalized solution for the generalized thermoelastic vibration of a bounded nano-beam resonator induced by ramp type of heating is developed and the solutions take into account the above two effects. The Laplace transforms and direct method are used to determine the lateral vibration, the temperature, the displacement, the stress and the energy of the beam. The effects of the relaxation time and the ramping time parameters have been studied with some comparisons.
基金Supported by the National Defense Science Foundation of China and the Special Fund of Colleges and Universities for Doctoral Study
文摘Non-Fourier heat conduction induced by ultrafast heating of metals with a high-energy density beam was analyzed. The non-Fourier effects during high heat flux heating were illustrated by comparing the transient temperature response to different heat flux and material relaxation times. Based on the hyperbolic heat conduction equation for the non-Fourier heat conduction law, the equation was solved using a hybrid method combining an analytical solution and numerical inversion of the Laplace transforms for a semi- infinite body with the heat flux boundary. Analysis of the temperature response and distribution led to a crite- rion for the applicability of the non-Fourier heat conduction law. The results show that at a relatively large heat flux, such as greater than 108 W/cm2, the heat-affected zone in the metal material experiences a strong thermal shock as the non-Fourier effects cause a large step increase in the surface temperature. The results provide a method for analyzing transient heat conduction problems using a high-energy density beam, such as electron beam deep penetration welding.
文摘The present paper paper,we estimate the theory of thermoelasticity a thin slim strip under the variable thermal conductivity in the fractional-order form is solved.Thermal stress theory considering the equation of heat conduction based on the time-fractional derivative of Caputo of orderis applied to obtain a solution.We assumed that the strip surface is to be free from traction and impacted by a thermal shock.The transform of Laplace(LT)and numerical inversion techniques of Laplace were considered for solving the governing basic equations.The inverse of the LT was applied in a numerical manner considering the Fourier expansion technique.The numerical results for the physical variables were calculated numerically and displayed via graphs.The parameter of fractional order effect and variation of thermal conductivity on the displacement,stress,and temperature were investigated and compared with the results of previous studies.The results indicated the strong effect of the external parameters,especially the timefractional derivative parameter on a thermoelastic thin slim strip phenomenon.
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.
文摘The effect of laser, as a heat source, on a one-dimensional finite living tissue was stud- ied in this paper. The dual phase lagging （DPL） non-Fourier heat conduction model was used for thermal analysis. The thermal conductivity was assumed temperature- dependent, resulting in a nonlinear equation. The obtained equations were solved using the approximate-analytical Adomian decomposition method （ADM）. It was concluded that the nonlinear analysis was important in nomFourier heat conduction problems. Moreover, a good agreement between the present nonlinear model and experimental result was obtained.
基金supported by Aeronautical Science Foundation of China(No.20160953008)。
文摘This paper investigates the problem of a 2-D plate containing internal cracks at arbitrary angles to the heating surface under thermal shock.The finite difference method is applied to solve the temperature distribution and a difference scheme of the oblique crack is developed.For the first time,a non-Fourier heat transfer analysis method of a 2-D plate with inner cracks at arbitrary direction angles is established.Specifically,for a strip with an inner crack paralleling to the surface,numerical results are compared with the analytical solutions by rotating the boundary,and perfect agreement is obtained.Numerical experiments are further presented to investigate the influence of crack orientation angle and multi-crack distribution on non-Fourier heat conduction.
