利用优化切比雪夫多项式和内点算法研究具有温度相关导热系数的双曲环形翅片

IF 0.9 Q2 MATHEMATICS
Mahdi Keshtkar, Elyas Shivanian
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引用次数: 0

摘要

本文讨论了热导率随温度变化的双曲型环形翅片问题。提出了一种新的求解方法。为了达到这一目的,将控制方程转化为一个等价问题,该等价问题的边界条件便于应用第一类改进版的切比雪夫多项式。这些基于切比雪夫多项式的函数构造了具有未知权值的近似级数解。优化问题的数学表达式由一个无监督误差组成,该误差通过内点法的权值调整最小化。通过对优化问题施加公差约束,验证了试逼近解的正确性。此外,更准确地讨论了翅片尺寸、表面对流特性和导热系数参数对翅片热性能的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
To study the hyperbolic annular fin with temperature dependent thermal conductivity via optimized Chebyshev polynomials with interior point algorithm

In this paper, the problem of an annular fin of hyperbolic profile with temperature dependent thermal conductivity is discussed. A novel intelligent computational approach is developed for searching the solution. In order to achieve this aim, the governing equation is transformed into an equivalent problem whose boundary conditions are such that they are convenient to apply reformed version of Chebyshev polynomials of the first kind. These Chebyshev polynomials based functions construct approximate series solution with unknown weights. The mathematical formulation of optimization problem consists of an unsupervised error which is minimized by tuning weights via interior point method. The trial approximate solution is validated by imposing tolerance constrained into optimization problem. Furthermore, a more accurate discussion of the effect of fin dimensions, surface convection characteristics and the thermal conductivity parameter on the thermal performance of the fin is graphically presented.

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来源期刊
Afrika Matematika
Afrika Matematika MATHEMATICS-
CiteScore
2.00
自引率
9.10%
发文量
96
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