The Experts below are selected from a list of 20823 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 the fractional heat Conduction Equation in a ball under robin boundary condition
Open Mathematics, 2014Co-Authors: Yuriy PovstenkoAbstract:The central symmetric time-fractional heat Conduction Equation with Caputo derivative of order 0 < α ≤ 2 is considered in a ball under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of values of temperature and values of its normal derivative at the boundary, and the physical condition with the prescribed linear combination of values of temperature and values of the heat flux at the boundary, which is a consequence of Newton’s law of convective heat exchange between a body and the environment. The integral transform technique is used. Numerical results are illustrated graphically.
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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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the neumann boundary problem for axisymmetric fractional heat Conduction Equation in a solid with cylindrical hole and associated thermal stress
Meccanica, 2012Co-Authors: Yuriy PovstenkoAbstract:The theory of thermoelasticity based on the heat Conduction Equation with the Caputo time-fractional derivative of order α is used to study thermal stress in an infinite medium with a cylindrical hole. Two types of Neumann boundary conditions are considered: the constant value of the normal derivative of the temperature and constant heat flux at the surface of a cavity. The solution is obtained applying Laplace and Weber integral transforms. Numerical results are illustrated graphically.
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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.
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.
H Han - 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.
Shijun Liao - One of the best experts on this subject based on the ideXlab platform.
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General boundary element method for non-linear heat transfer problems governed by hyperbolic heat Conduction Equation
Computational Mechanics, 1997Co-Authors: Shijun LiaoAbstract:The general Boundary Element Method (BEM) for strongly non-linear problems proposed by Liao (1995) is further applied to solve a two-dimensional unsteady non-linear heat transfer problem in the time domain, governed by the hyperbolic heat Conduction Equation (HHCE) with the temperature-dependent thermal conductivity coefficients which are different in the x and y directions. This paper confirms that the general BEM can be used to solve even those non-linear unsteady heat transfer problems whose governing Equations do not contain any linear terms in spatial domain.
Raimondas Ciegis - One of the best experts on this subject based on the ideXlab platform.
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numerical solution of hyperbolic heat Conduction Equation
Mathematical Modelling and Analysis, 2009Co-Authors: Raimondas CiegisAbstract:Abstract Hyperbolic heat Conduction problem is solved numerically. The explicit and implicit Euler schemes are constructed and investigated. It is shown that the implicit Euler scheme can be used to solve efficiently parabolic and hyperbolic heat Conduction problems. This scheme is unconditionally stable for both problems. For many integration methods strong numerical oscillations are present, when the initial and boundary conditions are discontinuous for the hyperbolic problem. In order to regularize the implicit Euler scheme, a simple linear relation between time and space steps is proposed, which automatically introduces sufficient amount of numerical viscosity. Results of numerical experiments are presented.