Asjad Muhammad Imran, Usman Muhammad, Ali Arfan, Awrejcewicz Jan, Bednarek Maksymilian
Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan.
Department of Mathematics, National University of Modern Languages (NUML), Islamabad 44000, Pakistan.
Nanomaterials (Basel). 2022 May 20;12(10):1745. doi: 10.3390/nano12101745.
In recent times, the loss of useful energy and solutions to those energy challenges have a wide scope in different areas of engineering. This work focuses on entropy analysis for unsteady viscoelastic fluids. The momentum boundary layer and thermal boundary layer are described under the effects of a magnetic field in the absence of an induced magnetic field. The study of a fractional model of Maxwell nanofluid by partial differential equation using Caputo time differential operator can well address the memory effect. Using transformations, the fractional ordered partial differential equations (PDEs) are transfigured into dimensionless PDEs. Numerical results for fractional Maxwell nanofluids flow and heat transfer are driven graphically. The Bejan number is obtained following the suggested transformation of dimensionless quantities like entropy generation. A mathematical model of entropy generation, Bejan number, Nusselt number and skin friction are developed for nanofluids. Effects of different physical parameters like Brickman number, Prandtl number, Grashof number and Hartmann number are illustrated graphically by MAPLE. Results depict that the addition of nanoparticles in base-fluid controls the entropy generation that enhances the thermal conductivity and application of magnetic field has strong effects on the heat transfer of fractional Maxwell fluids. An increasing behavior in entropy generation is noticed in the presence of source term and thermal radiation parameter.
近年来，有用能量的损失以及针对这些能量挑战的解决方案在不同工程领域具有广泛的范围。这项工作专注于非稳态粘弹性流体的熵分析。在不存在感应磁场的情况下，在磁场作用下描述动量边界层和热边界层。使用卡普托时间微分算子通过偏微分方程对麦克斯韦纳米流体的分数模型进行研究，可以很好地解决记忆效应。通过变换，将分数阶偏微分方程（PDEs）转化为无量纲PDEs。以图形方式给出了分数麦克斯韦纳米流体流动和传热的数值结果。根据诸如熵产生等无量纲量的建议变换获得贝扬数。为纳米流体建立了熵产生、贝扬数、努塞尔数和表面摩擦的数学模型。通过MAPLE以图形方式说明了不同物理参数如布里克曼数、普朗特数、格拉晓夫数和哈特曼数的影响。结果表明，在基液中添加纳米颗粒可控制熵产生，从而提高热导率，并且磁场的应用对分数麦克斯韦流体的传热有强烈影响。在存在源项和热辐射参数的情况下，注意到熵产生呈增加趋势。
