EIGENVALUES AND THREE-TERM APPROXIMATION OF FOURIER SERIES SOLUTION OF HEAT CONDUCTION TRANSIENTS, VALID FOR 0.02<FO<∞ AND ALL BI
 
A. Ostrogorsky (DOI: 10.24874/jsscm.2017.11.01.11)
 
Abstract
 
For transient conduction/diffusion driven by convection boundary conditions, in plates, cylinders and spheres, a set of correlations is presented providing explicit one-, two- and three-term approximations of Fourier series solution. The correlations yield eigenvalues (λ1, λ2 and λ3) and coefficients (A1 ,A2 and A3) with less than 0.6 % error. The correlations are more precise than tables or charts available in textbooks, and do not require interpolation between given values or curves.