Exact Axisymmetric Thermal Analysis of Functionally Graded Disks with Continuously Hyperbolically Varying Thickness

Abstract

An exact thermal analysis of radially functionally graded (FG) disks with continuously varying thickness is performed by steady-state 1-D Fourier heat conduction equation at specific surface temperatures. By employing a simple-power material grading pattern together with the convergent/divergent hyperbolic disk profiles, the differential equation is obtained in the form of Euler-Cauchy type. Analytical solution of the differential equation gives the temperature field and heat flux distributions in the radial direction in a closed form. A numerical study is conducted to visualize both the temperature and heat flux variations with respect to the disk profile parameter for hyperbolic disks made of SUS-304 /ZrO2 (Stainless steel/Zirconium oxide) metal-ceramic pairs. Those exact expressions are also used to study parametrically the effects of both the inhomogeneity and profile parameters on the temperature field of the disks made of hypothetic FG metal-ceramic pairs. It is revealed that heat conduction behavior of such disks is strictly affected from the variation of both inhomogeneity and disk profile parameters.