On the asymptotic solution of the Graetz‐Nusselt problem for short x → 0 and large x → ∞ with partial usage of finite differences
On the asymptotic solution of the Graetz‐Nusselt problem for short x → 0 and large x → ∞ with partial usage of finite differences
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关于短 x → 0 和大 x → ∞ 的 Graetz-Nusselt 问题的渐进解，部分使用有限差分
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发表时间：
2004
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通讯作者：
A. Campo
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作者：
A. Campo
本文的主要目标是提出经典 Graetz-Nusselt 问题的两个渐近解。采用线法（MOL）以渐近方式求解两个自变量的控制偏微分能量方程。以半解析方式确定两个温度子场：一个用于小 x (x → 0)，另一个用于大 x (x → ∞)。随后，两个渐近平均努塞尔数子分布 NuX→0(x) 和 NuX→∞(x) 将自身混合成覆盖整个 x 域的平均努塞尔数分布 Nu(x) 的广义相关方程。 MOL 过程的简单性与高质量渐近平均努塞尔数子分布相结合，提供了一种无需使用高级数学即可解决 Graetz-Nusselt 问题的替代方法。 © 2004 Wiley periodicals, Inc. 数值方法偏微分方程，2004 年。
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, NuX→0(x) and NuX→∞(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.