Calculation of non-steady-state thermal conduction for low Fourier numbers (Fo<0.001)

Abstract

Assuming that for small Fourier numbers heat transfer is determined by the specific heat of a heated layer of thickness $\delta = \sqrt {a \cdot \tau }$, an equation is derived for the temperature field, whose solution is satisfied in finite quadratures and has a fairly simple form. The results of calculations made using the proposed dependence are compared with the accurate solutions obtained by A. V. Lykov. This suggests that acceptable calculation accuracy may be achieved for Fo<0.001 and Bi<20. In this case the values of the dimensionless temperature do not depend on the shape of the body, and the proposed dependence can be used for calculations of plates, cylinders, or spheres.