The Neumann boundary problem for axisymmetric fractional heat conduction equation in a solid with cylindrical hole and associated thermal stress

Meccanica ◽  
2011 ◽  
Vol 47 (1) ◽  
pp. 23-29 ◽  
Author(s):  
Yuriy Povstenko
Keyword(s):  
Heat Conduction ◽  
Thermal Stress ◽  
Boundary Problem ◽  
Heat Conduction Equation ◽  
Neumann Boundary ◽  
Cylindrical Hole ◽  
Conduction Equation ◽  
Fractional Heat Conduction

scholarly journals Time-Fractional Heat Conduction in a Plane with Two External Half-Infinite Line Slits under Heat Flux Loading

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 689 ◽  
Author(s):  
Yuriy Povstenko ◽  
Tamara Kyrylych
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Graphical Representation ◽  
Integral Transform ◽  
Conduction Equation ◽  
Infinite Plane ◽  
Conservation Of Energy ◽  
Infinite Line ◽  
Fractional Heat Conduction

The time-fractional heat conduction equation follows from the law of conservation of energy and the corresponding time-nonlocal extension of the Fourier law with the “long-tail” power kernel. The time-fractional heat conduction equation with the Caputo derivative is solved for an infinite plane with two external half-infinite slits with the prescribed heat flux across their surfaces. The integral transform technique is used. The solution is obtained in the form of integrals with integrand being the Mittag–Leffler function. A graphical representation of numerical results is given.

Time-fractional heat conduction in a two-layer composite slab

2016 ◽  
Vol 19 (4) ◽  
Author(s):  
Yuriy Povstenko
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Composite Body ◽  
Composite Slab ◽  
Layer Composite ◽  
Fractional Heat Conduction

AbstractThe heat conduction equation is considered in a composite body consisting of two regions: 0 <

Reconstruction of the Robin boundary condition and order of derivative in time fractional heat conduction equation

2018 ◽  
Vol 13 (1) ◽  
pp. 5 ◽  
Author(s):  
Rafał Brociek ◽  
Damian Słota
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Fractional Order ◽  
Heat Conduction Equation ◽  
Robin Boundary Condition ◽  
Conduction Equation ◽  
Additional Information ◽  
Bee Colony ◽  
Robin Boundary ◽  
Fractional Heat Conduction

This paper describes an algorithm for reconstruction the boundary condition and order of derivative for the heat conduction equation of fractional order. This fractional order derivative was applied to time variable and was defined as the Caputo derivative. The heat transfer coefficient, occurring in the boundary condition of the third kind, was reconstructed. Additional information for the considered inverse problem is given by the temperature measurements at selected points of the domain. The direct problem was solved by using the implicit finite difference method. To minimize functional defining the error of approximate solution an Artificial Bee Colony (ABC) algorithm and Nelder-Mead method were used. In order to stabilize the procedure the Tikhonov regularization was applied. The paper presents examples to illustrate the accuracy and stability of the presented algorithm.

The Method of Fundamental Solutions for the Moving Boundary Problem of the One-Dimension Heat Conduction Equation

2014 ◽  
Vol 1039 ◽  
pp. 59-64 ◽  
Author(s):  
Xin Jiang ◽  
Xiao Gang Wang ◽  
Yue Wei Bai ◽  
Chang Tao Pang
Keyword(s):  
Heat Conduction ◽  
Boundary Problem ◽  
Heat Conduction Equation ◽  
Moving Boundary ◽  
Numerical Solutions ◽  
Fundamental Solutions ◽  
Metal Wire ◽  
Moving Boundary Problem ◽  
Conduction Equation ◽  
Temperature Function

The melting of the material is regarded as the moving boundary problem of the heat conduction equation. In this paper, the method of fundamental solution is extended into this kind of problem. The temperature function was expressed as a linear combination of fundamental solutions which satisfied the governing equation and the initial condition. The coefficients were gained by use of boundary condition. When the metal wire was melting, process of the moving boundary was gained through the conversation of energy and the Prediction-Correlation Method. A example was given. The numerical solutions agree well with the exact solutions. In another example, numerical solutions of the temperature distribution of the metal wire were obtained while one end was heated and melting.

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