scholarly journals Time-fractional heat conduction in a finite composite cylinder with heat source

2020 ◽  
Vol 19 (2) ◽  
pp. 85-94
Author(s):  
Stanisław Kukla ◽  
Urszula Siedlecka
Keyword(s):  
Heat Conduction ◽  
Heat Source ◽  
Composite Cylinder ◽  
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 Understanding the thermal problem of variable gradient functionally graded plate based on hybrid numerical method under linear heat source

2021 ◽  
Vol 13 (5) ◽  
pp. 168781402110178
Author(s):  
Jianhui Tian ◽  
Guoquan Jing ◽  
Xingben Han ◽  
Guangchu Hu ◽  
Shilin Huo
Keyword(s):  
Heat Conduction ◽  
Temperature Distribution ◽  
Heat Source ◽  
Numerical Method ◽  
Functionally Graded ◽  
Thermal Problem ◽  
Linear Heat ◽  
Hybrid Numerical Method ◽  
Linear Heat Source ◽  
Gradient Parameter

The thermal problem of functionally graded materials (FGM) under linear heat source is studied by a hybrid numerical method. The accuracy of the analytical method and the efficiency of the finite element method are taken into account. The volume fraction of FGM in the thickness direction can be changed by changing the gradient parameters. Based on the weighted residual method, the heat conduction equation under the third boundary condition is established. The temperature distribution of FGM under the action of linear heat source is obtained by Fourier transform. The results show that the closer to the heat source it is, the greater the influence of the heat source is and the influence of the heat source is local. The temperature change trend of the observation points is consistent with the heat source, showing a linear change. The results also show that the higher the value of gradient parameter is, the higher the temperature of location point is. The temperature distribution of observation points is positively correlated with gradient parameter. When the gradient parameter value exceeds a certain value, it has a little effect on the temperature change in the model and the heat conduction in the model tends to be pure metal heat conduction, the optimal gradient parameters combined the thermal insulation property of ceramics and the high strength toughness of metals are obtained.

Calculating the multi-domain transient heat conduction with heat source problem by virtual boundary meshfree Galerkin method

2018 ◽  
Vol 74 (1) ◽  
pp. 465-479 ◽  
Author(s):  
Dong-Sheng Yang ◽  
Jing Ling ◽  
Hong-Ying Wang ◽  
Ting-Yi Chen ◽  
Yun-Dan Du ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Heat Source ◽  
Galerkin Method ◽  
Transient Heat Conduction ◽  
Virtual Boundary
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