scholarly journals A solution to the problem of time-fractional heat conduction in a multi-layer slab

2015 ◽  
Vol 14 (3) ◽  
pp. 95-102
Author(s):  
Urszula Siedlecka ◽  
◽  
Stanislaw Kukla ◽  
Keyword(s):  
Heat Conduction ◽  
Problem Of Time ◽  
Fractional Heat Conduction

scholarly journals An analytical solution to the problem of time-fractional heat conduction in a composite sphere

2017 ◽  
Vol 65 (2) ◽  
pp. 179-186 ◽  
Author(s):  
S. Kukla ◽  
U. Siedlecka
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Source ◽  
Thermal Contact ◽  
Time Derivative ◽  
Solid Sphere ◽  
Composite Sphere ◽  
Problem Of Time ◽  
Time Space ◽  
Fractional Heat Conduction

Abstract An analytical solution to the problem of time-fractional heat conduction in a sphere consisting of an inner solid sphere and concentric spherical layers is presented. In the heat conduction equation, the Caputo time-derivative of fractional order and the Robin boundary condition at the outer surface of the sphere are assumed. The spherical layers are characterized by different material properties and perfect thermal contact is assumed between the layers. The analytical solution to the problem of heat conduction in the sphere for time-dependent surrounding temperature and for time-space-dependent volumetric heat source is derived. Numerical examples are presented to show the effect of the harmonically varying intensity of the heat source and the harmonically varying surrounding temperature on the temperature in the sphere for different orders of the Caputo time-derivative.

scholarly journals An analysis of heat conduction in polar bear hairs using one-dimensional fractional model

2016 ◽  
Vol 20 (3) ◽  
pp. 785-788 ◽  
Author(s):  
Wei-Hong Zhu ◽  
Shao-Tang Zhang ◽  
Zheng-Biao Li
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Polar Bear ◽  
Thermal Protection ◽  
Polar Bears ◽  
Cold Environment ◽  
Membrane Pore ◽  
One Dimensional ◽  
Fractional Heat Conduction ◽  
Maintain Body Temperature

Hairs of a polar bear are of superior properties such as the excellent thermal protection. The polar bears can perennially live in an extremely cold environment and can maintain body temperature at around 37 ?C. Why do polar bears can resist such cold environment? Its membrane-pore structure plays an important role. In the previous work, we established a 1-D fractional heat conduction equation to reveal the hidden mechanism for the hairs. In this paper, we further discuss solutions and parameters of the equation established and analyze heat conduction in polar bear hairs.

scholarly journals Fractional Heat Conduction Models and Thermal Diffusivity Determination

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Monika Žecová ◽  
Ján Terpák
Keyword(s):  
Heat Conduction ◽  
Thermal Diffusivity ◽  
Numerical Methods ◽  
Fractional Order ◽  
Experimental Verification ◽  
Heat Conduction Equation ◽  
Historical Overview ◽  
One Dimensional ◽  
The One ◽  
Fractional Heat Conduction

The contribution deals with the fractional heat conduction models and their use for determining thermal diffusivity. A brief historical overview of the authors who have dealt with the heat conduction equation is described in the introduction of the paper. The one-dimensional heat conduction models with using integer- and fractional-order derivatives are listed. Analytical and numerical methods of solution of the heat conduction models with using integer- and fractional-order derivatives are described. Individual methods have been implemented in MATLAB and the examples of simulations are listed. The proposal and experimental verification of the methods for determining thermal diffusivity using half-order derivative of temperature by time are listed at the conclusion of the paper.

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.

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