scholarly journals Fractional Heat Conduction in an Infinite Medium with a Spherical Inclusion

Entropy ◽  
2013 ◽  
Vol 15 (12) ◽  
pp. 4122-4133 ◽  
Author(s):  
Yuriy Povstenko
Keyword(s):  
Heat Conduction ◽  
Spherical Inclusion ◽  
Infinite Medium ◽  
Fractional Heat Conduction

Time-fractional heat conduction in an infinite medium with a spherical hole under robin boundary condition

2013 ◽  
Vol 16 (2) ◽  
Author(s):  
Yuriy Povstenko
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Linear Combination ◽  
Integral Transforms ◽  
Robin Boundary Condition ◽  
Normal Derivative ◽  
Infinite Medium ◽  
Symmetric Case ◽  
Robin Boundary ◽  
Fractional Heat Conduction

AbstractThe time-fractional heat conduction equation with the Caputo derivative of the order 0 < α ≤ 2 is considered in an infinite medium with a spherical hole in the central symmetric case under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of the values of temperature and the values of its normal derivative at the boundary and the physical condition with the prescribed linear combination of the values of temperature and the values of the heat flux at the boundary. The integral transforms techniques are used. Several particular cases of the obtained solutions are analyzed. The numerical results are illustrated graphically.

scholarly journals Non-linear heat conduction with ramped surface heating ramp surface heating and approximate solution

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 377-389
Author(s):  
Jordan Hristov
Keyword(s):  
Heat Conduction ◽  
Surface Temperature ◽  
Integral Method ◽  
Infinite Medium ◽  
Surface Heating ◽  
Integration Technique ◽  
Solution Approach ◽  
Linear Heat ◽  
Thermal Penetration Depth ◽  
Non Linear

Non-linear heat conduction with a power-law thermal diffusivity and ramped surface temperature has been solved by the double-integration technique of the integral-balance integral method. The case of a semi-infinite medium and infinite ramp of surface temperature has been considered as example demonstrating the versatility of the solution approach. The thermal penetration depth and solution behaviours with finite speeds have been analyzed.

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.

Transient Conduction From Parallel Isothermal Cylinders

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
Rajai S. Alassar
Keyword(s):  
Heat Transfer ◽  
Fourier Series ◽  
Heat Conduction ◽  
Energy Equation ◽  
Transient Heat Conduction ◽  
Infinite Medium ◽  
Basis Functions ◽  
Cylindrical Coordinates ◽  
Transient Conduction ◽  
Isothermal Cylinders

The transient heat conduction from two parallel isothermal cylinders is studied using the naturally fit bipolar cylindrical coordinates system. The energy equation is expanded in a Fourier series using appropriate basis functions to eliminate one of the physical coordinates. The resulting modes of the expansion are solved using a finite difference scheme. It is shown that, as is the case with a single isothermal cylinder in an infinite medium, steady states for two isothermal cylinders are not possible and heat transfer changes indefinitely with time.

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