Purpose

The purpose of this paper is to study an expandable or contractible metallic fin and heat transfer process. The fin is assumed to be thin having a rectangular cross section. It is attached to a hot surface with a time-dependent temperature, and its tip extends to a medium (fluid) of an ambient temperature. With the insulated wall constraint at the tip, the tip of the metallic fin has the property of expanding or contracting in time at a specific rate.

Design/methodology/approach

The corresponding physical problem is so formulated that the unsteady heat transfer problem is governed by means of a similarity variable represented by a second-order ordinary differential equation. The system can be reduced to the traditional well-documented steady state fin problem often studied in the literature, if the unsteadiness is turned off from the formulated system.

Findings

The system is then solved analytically for the temperature distribution through the fin. The fin tip temperatures are calculated, and the heat transfer analysis is made with varying physical parameters. And finally, observations are discussed leading to better fin efficiency and heat transfer enhancement.

Originality/value

An expandable or contractible metallic fin and heat transfer process are analyzed for the first time in the literature. Full solutions are presented, whose numerical correspondence is discussed through graphical and tabular forms.

中文翻译：

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矩形轮廓的膨胀/收缩翅片

目的

本文的目的是研究可膨胀或可收缩的金属翅片和热传递过程。假定鳍片是薄的，具有矩形的横截面。它以随时间变化的温度连接到热表面，并且其尖端延伸到环境温度的介质（流体）。由于在末端具有绝缘壁约束，金属翅片的末端具有以特定速率及时膨胀或收缩的特性。

设计/方法/方法

如此公式化相应的物理问题，使得不稳定的传热问题通过由二阶常微分方程表示的相似性变量来控制。如果从制定的系统中消除了不稳定因素，则可以将该系统简化为文献中经常研究的传统的，有据可查的稳态鳍问题。

发现

然后通过散热片分析该系统的温度分布。计算翅片尖端温度，并通过变化的物理参数进行传热分析。最后，讨论了观察结果，以提高散热片效率并增强传热效果。

创意/价值

文献中首次分析了可膨胀或可收缩的金属翅片和传热过程。提出了完整的解决方案，其数字对应关系通过图形和表格形式进行了讨论。