非定常薄膜内加热辐射流动的解析解

IF 0.7 Q2 MATHEMATICS Muenster Journal of Mathematics Pub Date : 2023-05-12 DOI:10.1155/2023/5612023
Ahsan Ali Naseer, M. Safdar, S. Taj, M. U. Ali, A. Zafar, Kwanghyok Kim, Jong Hyuk Byun
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引用次数: 0

摘要

本研究确定了具有内部加热和热辐射的随时间变化的薄膜流体流动的微分方程的李点对称性,以构造不变量。这些不变量用于推导相似变换,将流动方程简化为只有一个自变量的方程组。采用同伦分析方法解析求解简化方程组。新的相似变换和相应的解析解综合考虑了多种物理条件下的流动动力学和传热。这些解以图形的形式展示了内加热时辐射热通量的变化对流动动力学和传热性能的影响。此外,利用得到的解析同伦解,用图形描述了在不同非定常参数和普朗特数下流体动力学的变化。
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Analytical Solutions for Unsteady Thin Film Flow with Internal Heating and Radiation
This study determines Lie point symmetries for differential equations that mathematically express a time-dependent thin film fluid flow with internal heating and thermal radiation to construct invariants. These invariants are used in the derivation of similarity transformations for reducing the flow equations into systems of equations that possess only one independent variable. The homotopy analysis method is employed to analytically solve the reduced system of equations. The new similarity transformations and the corresponding analytical solutions comprehensively consider flow dynamics and heat transfer under multiple physical conditions. These solutions are presented graphically to demonstrate the effects of variations in the radiative heat flux with internal heating on the flow dynamics and heat transfer properties. Moreover, the variations in fluid dynamics are described graphically using the obtained analytical homotopy solution under different values of the unsteadiness parameter and Prandtl number.
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