Purpose

This paper aims to seek purely analytical results relying on the physical parameters including the temperature jump parameter.

Design/methodology/approach

The exponential fin profiles and heat transfer enhancement influenced by a temperature jump at the base are the main targets of this paper.

Findings

The introduced temperature slip at the base penetrates through the surface of the fin and reorganizes the distribution of temperature all over the surface. The overall impact of the temperature jump on the fin efficiency is such that it acts to lower the fin efficiency. However, the efficiency of the exponential fin is increasing for growing shape exponential fins as compared to the rectangular and decaying ones. Hence, exponential fins amenable to certain temperature jump has significance in technological cooling processes. Finally, the optimum dimensions regarding the base fin thickness and the fin length of the exponential profiles are assessed by means of optimizing the base heat transfer rate given a cross-sectional area.

Originality/value

Exact solutions are provided for optimum exponential type fins subjected to a temperature jump. The optimum dimensions regarding the base fin thickness and the fin length of the exponential profiles are assessed.

中文翻译：

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受温度跳跃影响的最佳指数翅片轮廓的热性能

目的

本文旨在寻求依赖于包括温度跳跃参数在内的物理参数的纯解析结果。

设计/方法/方法

受底部温度跳跃影响的指数翅片轮廓和传热增强是本文的主要目标。

发现

在底部引入的温度滑移穿过翅片的表面并重新组织整个表面的温度分布。温度跳变对翅片效率的总体影响使得它起到降低翅片效率的作用。然而，与矩形和衰减的指数翅片相比，指数翅片的效率对于生长形状的指数翅片正在增加。因此，适应一定温度跳跃的指数翅片在技术冷却过程中具有重要意义。最后，在给定横截面积的情况下，通过优化基础传热率来评估指数分布的基础翅片厚度和翅片长度的最佳尺寸。

原创性/价值

为经受温度跳跃的最佳指数型翅片提供了精确的解决方案。评估了关于指数轮廓的基本翅片厚度和翅片长度的最佳尺寸。