206 Optimization Problem of Two Dimensional Distribution of Material Composition in Functionally Graded Hollow Sphere Using GA

2000 ◽  
Vol 2000.75 (0) ◽  
pp. _2-11_-_2-12_
Author(s):  
Masashi MORIKAWA ◽  
Ryuusuke KAWAMURA ◽  
Yoshinobu TANIGAWA
Keyword(s):  
Hollow Sphere ◽  
Optimization Problem ◽  
Functionally Graded ◽  
Material Composition ◽  
Two Dimensional ◽  
Dimensional Distribution

Solution for Equation of Two-Dimensional Transient Heat Conduction in Functionally Graded Material Hollow Sphere With Piezoelectric Internal and External Layers

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
M. Jabbari ◽  
S. M. Mousavi ◽  
M. A. Kiani
Keyword(s):  
Heat Conduction ◽  
Functionally Graded Material ◽  
Hollow Sphere ◽  
Transient Heat Conduction ◽  
Functionally Graded ◽  
Transient Temperature ◽  
Two Dimensional ◽  
Power Functions ◽  
Legendre Series ◽  
Graded Material

In this paper, an exact solution for the equation of two-dimensional transient heat conduction in a hollow sphere made of functionally graded material (FGM) and piezoelectric layers is developed. Transient temperature distribution, as a function of radial and circumferential directions and time with general thermal boundary conditions on the inside and outside surfaces, is analytically obtained for different layers, using the method of separation of variables and Legendre series. The results are the sum of transient and steady-state solutions that depend upon the initial condition for temperature and heat source, respectively. The FGM properties are assumed to depend on the variable r and they are expressed as power functions of r.

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