Analysis of constant proportional Caputo operator on the unsteady Oldroyd‐B fluid flow with Newtonian heating and non‐uniform temperature

IF 2.3 4区 工程技术 Q1 MATHEMATICS, APPLIED
Muhammad Arif, Poom Kumam, Wiboonsak Watthayu
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引用次数: 0

Abstract

Abstract The Caputo operator has recently gained popularity as a widely used operator in fractional calculus. The purpose of this current research is to develop a new operator by combining the Caputo and proportional derivatives, resulting in the constant proportional Caputo (CPC) fractional operator. To demonstrate the dynamic behavior of this newly defined operator, it was applied to the unsteady Oldroyd‐B fluid model. Additionally, the research considered an Oldroyd‐B fluid in a generalized Darcy medium, considering non‐uniform temperature, radiation, and heat generation. Analytical solutions for the proposed model were obtained and presented in graphical form using the computational software MATHCAD. The impact of various physical parameters was also examined through graphical analysis of velocity and temperature profiles, as well as a comparison between isothermal and non‐uniform temperature. In conclusion, this research found that the CPC fractional operator effectively explains the dynamics of the Oldroyd‐B fluid model with stable and strong memory effects, compared to the classical model.
牛顿加热和非均匀温度下非定常oldyd - B流体流动的常比例Caputo算子分析
Caputo算子作为分数阶微积分中广泛应用的算子,近年来得到了广泛的应用。本研究的目的是将Caputo和比例导数相结合,开发出一种新的算子,得到恒定比例Caputo分数算子(CPC)。为了证明这一新定义的算符的动力学行为,将其应用于非定常Oldroyd‐B流体模型。此外,该研究考虑了广义达西介质中的Oldroyd - B流体,考虑了非均匀的温度、辐射和热量产生。利用计算软件MATHCAD得到了该模型的解析解,并以图形形式给出。通过速度和温度曲线的图形分析,以及等温和非均匀温度之间的比较,还检查了各种物理参数的影响。综上所述,与经典模型相比,CPC分数算子有效地解释了Oldroyd‐B流体模型的动力学,具有稳定且强的记忆效应。
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来源期刊
CiteScore
3.30
自引率
8.70%
发文量
199
审稿时长
3.0 months
期刊介绍: ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.
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