Approximate Analytical Solution To The Classical Graetz Problem Enlisting A Minimal Number Of Eigenvalues: A Historical Disruption
Antonio CampoAbstract
The present study addresses a novel nonlinear interpolation scheme intended for the determination of an approximate, analytical solution to the classical Graetz problem. Convergence of the Graetz infinite series is problematic in the upstream sub-domainner the origin x = 0. To implement the nonlinear interpolation scheme, the required ingredients are: 1) the uniform temperature of the viscous fluid at the inlet, 2) the mean bulk temperature along with the mean bulk temperature gradient of the viscous fluid evaluated at a certain x > 0 with the approximate Graetz two-term series and 3) the mean bulk temperature of the viscous fluid stream along with the mean bulk temperature gradient evaluated at a closer x > 0 with the approximate Nusselt three-term series. Application of a novel nonlinear interpolation scheme generates two power interpolation equations descriptive of the approximate mean bulk temperature sub-distributions of the viscous fluid. The two two power interpolation equations exhibit superlative accuracy in the upstream sub-domain x > 0.