Department of Physics, College of Science, King Faisal University, PO Box 400, Al Ahsa, 31982, Saudi Arabia.
Laboratory of Fluid Mechanics, Physics Department, Faculty of Science of Tunis, University of Tunis EI Manar, 2092, Tunis, Tunisia.
Sci Rep. 2021 Dec 3;11(1):20993. doi: 10.1038/s41598-021-00318-2.
The quest for high-performance of heat transfer components on the basis of accommodating shapes, smaller weights, lower costs and little volume has significantly diverted the industries for the enhancement of heat dissipation with variable thermal properties of fins. This manuscript proposes the fractional modeling of Fourier and non-Fourier heat transfer of longitudinal fin via non-singular fractional approach. The configuration of longitudinal fin in terms of one dimension is developed for the mathematical model of parabolic and hyperbolic heat transfer equations. By considering the Fourier and non-Fourier heat transfer from longitudinal fin, the mathematical techniques of Fourier sine and Laplace transforms have been invoked. An analytic approach is tackled for handling the governing equation through special functions for the fractionalized parabolic and hyperbolic heat transfer equations in longitudinal fin. For the sake of comparative analysis of parabolic verses hyperbolic heat conduction of fin temperature, we depicted the distinct graphical illustrations; for instance, 2-dimensional graph, bar chart, contour graphs, heat graph, 3-dimensional graphs and column graphs on for the variants of different rheological impacts of longitudinal fin.
追求基于适应形状、更小重量、更低成本和更小体积的高热传输性能的热传递组件，显著促使各行业采用可变热特性的翅片来增强散热。本文通过非奇异分数方法对纵向翅片的傅里叶和非傅里叶传热进行分数建模。针对抛物线和双曲线传热方程的数学模型，开发了纵向翅片的一维配置。通过考虑纵向翅片的傅里叶和非傅里叶传热，采用傅里叶正弦和拉普拉斯变换数学技术。通过特殊函数处理分数化抛物线和双曲线传热方程的控制方程，采用解析方法来处理控制方程。为了比较分析翅片温度的抛物线与双曲线热传导，我们绘制了不同的图形说明，例如二维图、条形图、等高线图、热图、三维图和柱形图，以展示纵向翅片不同流变影响的变体。
