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

In this paper, an exact solution for the equation of two-dimensional transient heat conduction in a hollow sphere made of functionally graded material and piezoelectric layers is developed. Temperature distribution, as function of radial and circumferential directions and time with general thermal and mechanical 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 functionally graded material properties, are assumed to depend on the variable r and they are expressed as power functions of r.

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