Fractional Model of Brinkman-Type Nanofluid Flow with Fractional Order Fourier's and Fick's Laws

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-10-20 DOI:10.1142/s0218348x23401990

Saqib Murtaza, Poom Kumam, Zubair Ahmad, Kanokwan Sitthithakerngkiet, Thana Sutthibutpong

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引用次数: 0

Abstract

Nanofluids are used to achieve maximum thermal performance with the smallest concentration of nanoparticles and stable suspension in conventional fluids. The effectiveness of nanofluids in convection processes is significantly influenced by their increased thermophysical characteristics. Based on the characteristics of nanofluids, this study examines generalized Brinkman-type nanofluid flow in a vertical channel. Three different types of ultrafine solid nanoparticles such as GO, [Formula: see text], and [Formula: see text] are dispersed uniformly in regular water to form nanofluid. Partial differential equations (PDEs) are used to model the phenomena. Fick’s and Fourier’s laws of fractional order were then used to formulate the generalized mathematical model. The exact solution of the generalized mathematical model has been obtained by the joint use of Fourier sine and the Laplace transform (LT) techniques. The obtained solution is represented in Mittag-Leffler function. To analyze the behavior of fluid flow, heat and mass distribution in fluid, the obtained solution was computed numerically and then plotted in response to different physical parameters. It is worth noting from the analysis that the heat transfer efficiency of regular water has been improved by 25% by using GO nanoparticles, 23.98% by using [Formula: see text], and 20.88% by using [Formula: see text].

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基于分数阶傅里叶定律和菲克定律的brinkman型纳米流体流动分数阶模型

纳米流体用于在常规流体中以最小的纳米颗粒浓度和稳定的悬浮液获得最大的热性能。纳米流体在对流过程中的有效性受到其增加的热物理特性的显著影响。基于纳米流体的特性，研究了垂直通道中广义brinkman型纳米流体的流动。将氧化石墨烯、[公式:见文]、[公式:见文]等三种不同类型的超细固体纳米颗粒均匀分散在规则水中，形成纳米流体。用偏微分方程(PDEs)来模拟这种现象。然后使用分数阶菲克定律和傅立叶定律来制定广义数学模型。利用傅里叶正弦和拉普拉斯变换技术，得到了广义数学模型的精确解。得到的解用Mittag-Leffler函数表示。为了分析流体的流动行为、热量和质量分布，对得到的解进行了数值计算，并对不同物理参数下的解进行了绘图。从分析中值得注意的是，使用氧化石墨烯纳米颗粒可将普通水的换热效率提高25%，使用[公式:见文]可将换热效率提高23.98%，使用[公式:见文]可将换热效率提高20.88%。

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来源期刊

Fractals-Complex Geometry Patterns and Scaling in Nature and Society 数学-数学跨学科应用

CiteScore

7.40

自引率

23.40%

发文量

319

审稿时长

>12 weeks

期刊介绍： The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development and applications in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, engineering and technology, and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes. Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality. The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.