Stochastic heat conduction analysis of a functionally graded annular disc with spatially random heat transfer coefficients

The mean and variance of the temperature are analytically obtained in a functionally graded annular disc with spatially random heat transfer coefficients (HTCs) on the upper and lower surfaces. This annular disc has arbitrary variations in the HTCs (i.e., arbitrary thermal interaction with the surroundings) and gradient material composition only along the radial direction and is subjected to deterministic axisymmetrical heating at the lateral surfaces. The stochastic temperature field is analysed by considering the annular disc to be multilayered with spatially constant material properties and spatially constant but random HTCs in each layer. A type of integral transform method and a perturbation method are employed in order to obtain the analytical solutions for the statistics. The correlation coefficients of the random HTCs are expressed in the form of a linear function with respect to the radial distance as a non-homogeneous random field of discrete space. Numerical calculations are performed for functionally graded annular discs composed of stainless steel and ceramic, which comprise two types of material composition distributions. The effects of the magnitude of the means of HTCs, volume fraction distributions of the constitutive materials and correlation strengths of the HTCs on the standard deviation of the temperature are discussed.