Summary
The second-order statistics (i.e., mean and variance) of the temperature and thermal stresses are analytically obtained in an annular disc with spatially random heat transfer coefficients (HTCs) on the upper and lower surfaces. This annular disc is assumed to have arbitrary variations in the HTCs solely in the radial direction and is subjected to deterministic axisymmetrical heating at the lateral surfaces. The stochastic temperature field is analyzed by considering the annular disc to be multilayered with spatially constant, but random HTCs in each layer. The Vodicka's method, which is a type of integral transform method, and a perturbation method are employed to obtain the analytical solutions for the statistics. The autocorrelation coefficients of the random HTCs and cross-correlation coefficients between the HTCs on different surfaces are expressed in exponential function forms as a homogeneous Markov random field of discrete space. Numerical calculations are performed for annular discs similar to an annular fin, which comprise two types of distributions of the means of the HTCs. The effects of the magnitude of the means of HTCs, spatial variations in the means of HTCs and correlation strengths of the HTCs on the standard deviations of the temperature and thermal stresses are discussed.