Sheikh Nadeem Ahmad, Ching Dennis Ling Chuan, Khan Ilyas, Sakidin Hamzah Bin
Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, 32610, Seri Iskandar, Perak, Malaysia.
Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia.
Sci Rep. 2022 Aug 18;12(1):14117. doi: 10.1038/s41598-022-18110-1.
The flow of fluid through porous media is of great importance in industry and other physical situations, Darcy's law is one of the most useful laws to describe such situation, however, the flows through a dense swarm of particles or through a very high porous media cannot be elaborated by this law. To overcome this difficulty, Brinkman proposed a new idea of Brinkman-type fluid in highly porous media. In this study, the Brinkman-type fluid flow is analyzed with hybrid nanoparticles (a hybridized mixture of clay and alumina), suspended in water taken as a base fluid under the effect of an applied magnetic field. The fluid motion is taken inside a vertical channel with heated walls. Free convection is induced due to buoyancy. The momentum and energy equations are written in dimensionless form using the non-dimensional variables. The energy equation is modified to fractional differential equations using the generalized Fourier's law and the Caputo fractional derivatives. The fractional model is solved using the Laplace and Fourier transformation. Variations in velocity and temperature are shown for various fractional parameter values, as well as charts for the classical model. For the volume fractions of nanoparticles, the temperature distribution increases, with maximum values of hybrid nanoparticles with the highest specified volume fractions. Moreover, due to hybrid nanoparticles, the rate of heat transfer is intensified.
流体在多孔介质中的流动在工业和其他物理情境中非常重要，达西定律是描述这种情况最有用的定律之一，然而，通过密集颗粒群或通过非常高孔隙率介质的流动不能用该定律来阐述。为克服这一困难，布林克曼提出了高孔隙率介质中布林克曼型流体的新观点。在本研究中，分析了混合纳米颗粒（粘土和氧化铝的混合混合物）悬浮在作为基液的水中，在施加磁场作用下的布林克曼型流体流动。流体运动发生在具有加热壁的垂直通道内。由于浮力引起自由对流。使用无量纲变量将动量和能量方程写成无量纲形式。利用广义傅里叶定律和卡普托分数阶导数将能量方程修改为分数阶微分方程。使用拉普拉斯变换和傅里叶变换求解分数阶模型。给出了各种分数参数值下的速度和温度变化，以及经典模型的图表。对于纳米颗粒的体积分数，温度分布增加，具有最高指定体积分数的混合纳米颗粒具有最大值。此外，由于混合纳米颗粒，传热速率增强。
