Comparison of methods for calculating the non-stationary temperature field in thick-walled cylindrical structures
Various approaches to the calculation of the propagation of thermal disturbances in structures having the shape of a hollow cylinder with a large wall thickness are considered. A formula describing the temperature field from a nonstationary linear source in a material array is derived in the form of an infinite series in degrees of a dimensionless radial coordinate using the method of self - similar solutions. The results of calculations for this equation are compared with the dependence previously obtained by the author using a finite - difference approximation of the data for the numerical solution of the original Fourier differential equation for the case of cylindrical symmetry. It is shown that for large values of the dimensionless radial coordinate corresponding to small moments of time, the compared variants are equivalent.