The Experts below are selected from a list of 15564 Experts worldwide ranked by ideXlab platform
Yuriy Povstenko - One of the best experts on this subject based on the ideXlab platform.
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thermoelasticity based on time fractional Heat Conduction Equation in spherical coordinates
2015Co-Authors: Yuriy PovstenkoAbstract:The fundamental solutions to the first and second Cauchy problems and to the source problem are obtained for axisymmetric time-fractional Heat Conduction Equation in an infinite plane in polar coordinates. Radial Heat Conduction in a cylinder and in an infinite solid with a cylindrical cavity is investigated. The Dirichlet boundary problems with the prescribed boundary value of temperature and the physical Neumann boundary problems with the prescribed boundary value of the Heat flux are solved using the integral transform technique. The associated thermal stresses are studied. The numerical results are illustrated graphically. Figures show the characteristic features of temperature and stress distribution and represent the whole spectrum of order of time-derivative.
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Fundamental Solutions to Robin Boundary-Value Problems for the Time-Fractional Heat-Conduction Equation in a Half Line
Journal of Mathematical Sciences, 2013Co-Authors: Yuriy PovstenkoAbstract:The time-fractional Heat-Conduction Equation with the Caputo derivative of the order 0 < α ≤ 2 is considered in a half line. Two types of Robin boundary condition are examined: the mathematical condition with prescribed linear combination of the values of temperature and the values of its normal derivative and the physical condition with prescribed linear combination of the values of temperature and the values of Heat flux on the boundary of the domain. These two types of Robin boundary condition coincide only for the classical Heat-Conduction Equation.
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nonaxisymmetric solutions of the time fractional Heat Conduction Equation in a half space in cylindrical coordinates
Journal of Mathematical Sciences, 2012Co-Authors: Yuriy PovstenkoAbstract:UDC 539.3 Nonaxisymmetric solutions of the time-fractional Heat Conduction Equation with source term in cylindrical coordinates are obtained for a half-space. The solutions are found using the Laplace transform with respect to time, the Hankel transform with respect to the radial coordinate, the finite Fourier transform with respect to the angular coordinate, and the sine or cosine Fourier transform with respect to the bulk coordinate. Numerical results are illustrated graphically.
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Different kinds of boundary condition for time-fractional Heat Conduction Equation
Proceedings of the 13th International Carpathian Control Conference (ICCC), 2012Co-Authors: Yuriy PovstenkoAbstract:Different kinds of boundary conditions (Dirichlet, Neumann, Robin) for time-fractional Heat Conduction Equation are discussed. The fundamental solutions to time-fractional Heat Conduction Equation with the Caputo derivative of the order 0 < α < 2 is considered in a half-plane under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of the values of temperatute and the values of its normal derivative and the physical condition with the prescribed linear combination of the values of temperature and the values of the Heat flux at the boundary of the domain.
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theory of thermoelasticity based on the space time fractional Heat Conduction Equation
Physica Scripta, 2009Co-Authors: Yuriy PovstenkoAbstract:The space-time-nonlocal generalization of the Fourier law and the space-time-fractional Heat Conduction Equation are discussed. A theory of thermoelasticity based on such an Equation is considered. The proposed theory interpolates classical thermoelasticity and a thermoelasticity without energy dissipation introduced by Green and Naghdi.
Xiaoyun Jiang - One of the best experts on this subject based on the ideXlab platform.
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analytical solution for the time fractional Heat Conduction Equation in spherical coordinate system by the method of variable separation
Acta Mechanica Sinica, 2011Co-Authors: Tinghui Ning, Xiaoyun JiangAbstract:In this paper, using the fractional Fourier law, we obtain the fractional Heat Conduction Equation with a time-fractional derivative in the spherical coordinate system. The method of variable separation is used to solve the timefractional Heat Conduction Equation. The Caputo fractional derivative of the order 0 < α ≤ 1 is used. The solution is presented in terms of the Mittag-Leffler functions. Numerical results are illustrated graphically for various values of fractional derivative.
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the time fractional Heat Conduction Equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems
Physica A-statistical Mechanics and Its Applications, 2010Co-Authors: Xiaoyun JiangAbstract:In this paper a time fractional Fourier law is obtained from fractional calculus. According to the fractional Fourier law, a fractional Heat Conduction Equation with a time fractional derivative in the general orthogonal curvilinear coordinate system is built. The fractional Heat Conduction Equations in other orthogonal coordinate systems are readily obtainable as special cases. In addition, we obtain the solution of the fractional Heat Conduction Equation in the cylindrical coordinate system in terms of the generalized H-function using integral transformation methods. The fractional Heat Conduction Equation in the case 0<α≤1 interpolates the standard Heat Conduction Equation (α=1) and the Localized Heat Conduction Equation (α→0). Finally, numerical results are presented graphically for various values of order of fractional derivative.
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The time fractional Heat Conduction Equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems
Physica A: Statistical Mechanics and its Applications, 2010Co-Authors: Xiaoyun JiangAbstract:In this paper a time fractional Fourier law is obtained from fractional calculus. According to the fractional Fourier law, a fractional Heat Conduction Equation with a time fractional derivative in the general orthogonal curvilinear coordinate system is built. The fractional Heat Conduction Equations in other orthogonal coordinate systems are readily obtainable as special cases. In addition, we obtain the solution of the fractional Heat Conduction Equation in the cylindrical coordinate system in terms of the generalized H-function using integral transformation methods. The fractional Heat Conduction Equation in the case 0
Y Yuan - One of the best experts on this subject based on the ideXlab platform.
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the boundary element method for the solution of the backward Heat Conduction Equation
Journal of Computational Physics, 1995Co-Authors: H Han, D B Ingham, Y YuanAbstract:In this paper we consider the numerical solution of the one-dimensional, unsteady Heat Conduction Equation in which Dirichlet boundary conditions are specified at two space locations and the temperature distribution at a particular time, say T0, is given. The temperature distribution for all times, t < T0, is now required and this backward Heat Conduction problem is a well-known improperly posed problem. In order to solve this problem the minimal energy technique has been introduced in order to modify the boundary element method and this results in a stable approximation to the solution and the accuracy of the numerical results are very encouraging.
Cemil Kocar - One of the best experts on this subject based on the ideXlab platform.
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exact solution of the Heat Conduction Equation in eccentric spherical annuli
International Journal of Thermal Sciences, 2013Co-Authors: Ayhan Yilmazer, Cemil KocarAbstract:Abstract In this study, an analytical solution to the Heat Conduction Equation in an annulus between eccentric spheres with isothermal boundaries and with Heat generation is obtained using Green's function method. Deriving Green's function in bispherical coordinates for eccentric spherical annuli, an exact solution of Heat Equation for eccentric spheres with constant surface temperatures is expressed in terms of Green's function and source distribution. The solution is general and can easily be applicable to any space dependent Heat source. Results are presented as temperature distributions and local Nusselt numbers for sources having practical and theoretical importance: uniform source, impulse source, shell source. Analytical results are compared with the results of the Computational Fluids Dynamics (CFD) solver Fluent and perfect agreement is observed.
Bin Zheng - One of the best experts on this subject based on the ideXlab platform.
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Exact traveling wave solution for nonlinear Heat Conduction Equation
2010 International Conference On Computer Design and Applications, 2010Co-Authors: Bin Zheng, Qinghua FengAbstract:In this paper, we derive exact traveling wave solutions of nonlinear Heat Conduction Equation by a presented method. The method appears to be efficient in seeking exact solutions of no-nlinear Equations.
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traveling wave solution for the nonlinear Heat Conduction Equation
International Conference on Mathematical methods Computational techniques and Intelligent systems, 2010Co-Authors: Bin ZhengAbstract:In this paper, we derive exact traveling wave solutions of the nonlinear Heat Conduction Equation by a presented method. The method appears to be efficient in seeking exact solutions of nonlinear Equations.
