Simplistic solution of the Graetz problem in the upstream sub-region x → 0 using nonlinear interpolation of the three-term, mean bulk temperature series for the downstream sub-region x → ∞: A historical perspective

The present paper addresses an approximate, analytical solution of the Graetz problem confined to the upstream sub-region x -> 0, which is known to belong to the Leveque solution. Inspired in the defective three-term Graetz series due to Nusselt as the motivation, the computational procedure focuses on a peculiar nonlinear interpolation of three data points. The three data points are: 1) the mean bulk temperature at the entrance x = 0, 2) the mean bulk temperature at a given downstream location extracted from the three-term Graetz series and 3) the mean bulk temperature derivative at the same downstream location. Relying on the accurate mean bulk temperature distribution suited for the downstream sub-region x -> infinity, it is demonstrated that the relative errors of the the mean bulk temperatures supplied by the nonlinear interpolation are smaller than those provided by the Leveque solution. (C) 2020 Elsevier Ltd. All rights reserved.