Purpose

The purpose of this study is to analyze the free convection phenomena arising from a temperature disparity between a cold circular cylinder and a heated corrugated cylinder.

Design/methodology/approach

Numerical simulations were used to analyze the convection patterns. The inner cylinder, made of a thermally conductive solid material, was heated through its inner surface, while the space between the cylinders was filled with air. The governing equations for velocity, pressure and temperature were solved using a Galerkin finite element method-based solver for partial differential equations.

Findings

The study explored various parameters affecting the dynamic and thermal structure of the flow, including the Rayleigh number (10³ ≤ Ra ≤ 10⁶), the number of corrugations of the inner cylinder (3 ≤ N ≤ 18), the thermal conductivity of the hollow cylinder (1 ≤ K ≤ 200) and the angle of inclination of the inner cylinder (0° ≤ φ ≤ 90°). Results indicated a notable sensitivity of flow intensity to changes in the Rayleigh number and the inner cylinder’s inclination angle φ. Particularly, for Ra = 10⁶, the average heat transfer rate increased by 203% with a K ratio increment from 1 to 100 but decreased by 16.3% as the number of corrugations increased from 3 to 18.

Originality/value

This research contributes to understanding the complex interplay between geometry, thermal properties and flow dynamics in natural convection systems involving cylindrical geometries. The findings offer useful insights for improving the transfer of heat procedures in real-world situations.

中文翻译：

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波纹空心圆柱体圆形腔内自然对流传热的有限元法 (FEM) 分析

 目的

本研究的目的是分析冷圆柱体和加热波纹圆柱体之间的温差引起的自由对流现象。

设计/方法论/途径

数值模拟用于分析对流模式。内筒由导热固体材料制成，通过其内表面加热，而筒之间的空间充满空气。使用基于伽辽金有限元法的偏微分方程求解器求解速度、压力和温度的控制方程。

 发现

该研究探索了影响流动动态和热结构的各种参数，包括瑞利数（10 ³ ≤ Ra ≤ 10 ⁶ ）、内筒波纹数（3 ≤ N ≤ 18）、内筒的导热系数空心圆柱体（ 1≤K≤200 ）和内圆柱体的倾斜角度（0° ≤φ≤90 °）。结果表明，流动强度对瑞利数和内筒倾斜角 的变化具有显着的敏感性。特别是，当Ra = 10 ^{6 时}，随着K比从1增加到100，平均传热率增加了203%，但随着波纹数量从3增加到18，平均传热率下降了16.3%。

 原创性/价值

这项研究有助于理解涉及圆柱形几何形状的自然对流系统中几何形状、热性能和流动动力学之间的复杂相互作用。这些发现为改善现实世界中的热传递过程提供了有用的见解。