Some analytical solutions for engineering thermophysics

Analytical solutions proposed by Cai Ruixian for two groups of basic equations in engineering thermophysics presented and analyzed in more detail. They are the explicit analytical solution of inviscid compressible flow of perfect gas and the one-dimensional algebraic explicit analytical solution of unsteady non-Fourier heat conduction in a sphere. The new method of variable separation with addition is used, in which the dependent variable is supposed to be the sum (instead of product) of several one-dimensional functions. Preliminary criterion to consider the existence of non-Fourier heat wave effect is proposed based on the analytical solutions: when the radius of the sphere reaches the same order of magnitude as the mean free path or even smaller, the heat wave has to be considered.