Exact Thermal Analysis of Functionally Graded Cylindrical and Spherical Vessels

Thermal analyses of radially functionally graded (FG) thick-walled a spherical vessel and an infinite cylindrical vessel or a circular annulus are conducted analytically by the steady-state 1-D Fourier heat conduction theory under Dirichlet’s boundary conditions. By employing simple-power material grading pattern the differential equations are obtained in the form of Euler-Cauchy types. Analytical solution of the differential equations gives the temperature field and the heat flux distribution in the radial direction in a closed form. Three different physical metal-ceramic pairs first considered to study the effect of the aspect ratio, which is defined as the inner radius to the outer radius of the structure, on the temperature and heat flux variation along the radial coordinate. Then a parametric study is performed with hypothetic inhomogeneity indexes for varying aspect ratios.