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 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
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
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 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 (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.
