scholarly journals Fractional heat conduction equation and associated thermal stresses in an infinite solid with spherical cavity

2008 ◽  
Vol 61 (4) ◽  
pp. 523-547 ◽  
Author(s):  
Y. Z. Povstenko
Keyword(s):  
Heat Conduction ◽  
Spherical Cavity ◽  
Heat Conduction Equation ◽  
Thermal Stresses ◽  
Conduction Equation ◽  
Fractional Heat Conduction

Thermoelastic Interaction in an Infinite Long Hollow Cylinder with Fractional Heat Conduction Equation

2017 ◽  
Vol 9 (2) ◽  
pp. 378-392
Author(s):  
Ahmed. E. Abouelregal
Keyword(s):  
Heat Conduction ◽  
Laplace Transform ◽  
Hollow Cylinder ◽  
Heat Conduction Equation ◽  
Thermal Stresses ◽  
Generalized Thermoelasticity ◽  
Constant Heat Flux ◽  
Conduction Equation ◽  
The Laplace Transform ◽  
Fractional Heat Conduction

AbstractIn this work, we introduce a mathematical model for the theory of generalized thermoelasticity with fractional heat conduction equation. The presented model will be applied to an infinitely long hollow cylinder whose inner surface is traction free and subjected to a thermal and mechanical shocks, while the external surface is traction free and subjected to a constant heat flux. Some theories of thermoelasticity can extracted as limited cases from our model. Laplace transform methods are utilized to solve the problem and the inverse of the Laplace transform is done numerically using the Fourier expansion techniques. The results for the temperature, the thermal stresses and the displacement components are illustrated graphically for various values of fractional order parameter. Moreover, some particular cases of interest have also been discussed.

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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