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存在扩散效应时的分数阶 Brinkman 流分析。

Analysis of fractionalized Brinkman flow in the presence of diffusion effect.

作者信息

Abbas Shajar, Ramzan Muhammad, Inam Inamullah, Saleem Salman, Nazar Mudassar, Abduvalieva Dilsora, Al Garalleh Hakim

机构信息

Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan.

Department of Civil Engineering, Engineering Faculty, Laghman University, Mehtarlam, Afghanistan.

出版信息

Sci Rep. 2024 Sep 28;14(1):22507. doi: 10.1038/s41598-024-72785-2.

DOI:10.1038/s41598-024-72785-2
PMID:39341809
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11439061/
Abstract

A vertical plate experiences a dynamic flow of fractionalized Brinkman fluid governed by fluctuating magnetic forces. This study considers heat absorption and diffusion-thermo effects. The novelty of model is the fractionalized Fourier's and Fick's laws. The problem is solved using the constant proportional Caputo derivative and Laplace transform method. The resulting non-dimensional equations for temperature, mass, and velocity fields are solved and compared visually. We explore the influence of various parameters like the fractional order, heat absorption/generation (Q), chemical reaction rate (R), and magnetic field strength (M) through informative graphs. Additionally, we contrast the velocity fields of fractionalized and regular fluids. The visualizations reveal that diffusion-thermo and mass Grashof number enhance fluid velocity, while chemical reaction and magnetic field tend to suppress it. For the interest of engineering, physical quantities such as Sherwood number, skin friction, and Nusselt number are computed. The present study satisfying all initial and boundary condition can be reduced to to previous published work which shows the validity of present work.

摘要

一块垂直平板经历由波动磁力控制的分数阶 Brinkman 流体的动态流动。本研究考虑了热吸收和扩散 - 热效应。该模型的新颖之处在于分数阶傅里叶定律和菲克定律。使用常数比例 Caputo 导数和拉普拉斯变换方法求解该问题。求解了温度、质量和速度场的无量纲方程，并进行了可视化比较。我们通过信息图表探究了分数阶、热吸收/生成（Q）、化学反应速率（R）和磁场强度（M）等各种参数的影响。此外，我们对比了分数阶流体和常规流体的速度场。可视化结果表明，扩散 - 热和质量格拉晓夫数会提高流体速度，而化学反应和磁场则倾向于抑制它。出于工程目的，计算了诸如舍伍德数、表面摩擦力和努塞尔数等物理量。本研究满足所有初始条件和边界条件，可简化为先前发表的工作，这表明了本研究的有效性。

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