On the asymptotic solution of the Graetz‐Nusselt problem for short x → 0 and large x → ∞ with partial usage of finite differences

The principal goal of this article is to present two asymptotic solutions for the classical Graetz‐Nusselt problem. The method of lines (MOL) has been adopted for solving the governing partial differential energy equation in two independent variables in an asymptotic manner. Two temperature subfields are determined semianalytically: one for small x (x → 0) and the other for large x (x → ∞). Later, the two asymptotic mean Nusselt number subdistributions, Nu _X→0(x) and Nu _X→∞(x), blend themselves into a generalized correlation equation for the mean Nusselt number distribution Nu (x) covering the entire x‐domain. The simplicity of the MOL procedure, combined with the high quality asymptotic mean Nusselt number subdistributions, provides an alternative methodology for solving the Graetz‐Nusselt problem without using higher level mathematics. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004.