On the convergence of a certain type of nonlinear lumped energy equations

✍ Scribed by A. Salazar; A. Campo

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 120 KB
• Volume: 13
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/(sici)1098-2426(199707)13:4<433::aid-num8>3.0.co;2-m

✦ Synopsis

proposed a simple iterative procedure to solve approximately a forced convection heat-transfer problem inside a tube subjected to nonlinear convective boundary conditions. Their technique relied on solutions of a one-dimensional ordinary differential equation of first order to estimate the behavior of the solution of the two-dimensional parabolic partial differential equation. The recursive steps, proposed by Campo and Lacoa, can be combined in a single fixed-point iteration formula thus facilitating the study of its properties. In this note, we present a short analysis of the convergence of the Campo-Lacoa equation and give alternatives to guarantee and improve the convergence patterns. Our results show that the Picard's iterative method converges for all values of Z in the region of thermal development, e.g., 0 ≤ Z ≤ 1; however, the convergence rate tends to diminish as Z increases. To guarantee convergence for larger values of Z, a damped-Picard's iteration may be adopted. Moreover, to increase the rate of convergence, a Newton's iteration is proposed. A detailed comparison in terms of accuracy and CPU time is provided.