Analytical solution for the time-fractional heat conduction equation in spherical coordinate system by the method of variable separation

2011 ◽  
Vol 27 (6) ◽  
pp. 994-1000 ◽  
Author(s):  
Ting-Hui Ning ◽  
Xiao-Yun Jiang
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Coordinate System ◽  
Heat Conduction Equation ◽  
Spherical Coordinate System ◽  
Conduction Equation ◽  
Variable Separation ◽  
Spherical Coordinate ◽  
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.

scholarly journals Remark on a constrained variational principle for heat conduction

2013 ◽  
Vol 17 (3) ◽  
pp. 951-952 ◽  
Author(s):  
Zhao-Ling Tao ◽  
Guo-Hua Chen
Keyword(s):  
Heat Conduction ◽  
Variational Principle ◽  
Heat Conduction Equation ◽  
Inverse Method ◽  
Separation Of Variables ◽  
Conduction Equation ◽  
Variable Separation

The heat conduction equation is re-studied by the semi-inverse method combined with separation of variables; a new variational principle for the heat conduction equation is obtained. Equivalence of the existed two in literature is shown. The significance of variable separation is confirmed once more.

A re-examination of the strain field around a simple pile

1994 ◽  
Vol 31 (2) ◽  
pp. 303-308 ◽  
Author(s):  
V. Silvestri ◽  
C. Tabib
Keyword(s):  
Analytical Solution ◽  
Coordinate System ◽  
Shear Strain ◽  
Key Words ◽  
Strain Field ◽  
Technical Note ◽  
Spherical Coordinate System ◽  
Spherical Coordinate ◽  
Streaming Motion

This technical note describes the analysis of the strain field around a simple pile. The analytical solution is obtained by using a spherical coordinate system of reference. It is shown that the expressions for the various strains are very simple. Streaming motions and octahedral shear strain contours are presented in graphical forms. Key words : simple pile, streaming motion, strain field.

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