Ali Aamir, Khan Hajra Safdar, Saleem Salman, Hussan Muhammad
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Kamra Road, Attock 43600, Pakistan.
Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia.
Nanomaterials (Basel). 2022 Nov 2;12(21):3872. doi: 10.3390/nano12213872.
Nanofluids have gained prominence due to their superior thermo-physical properties. The current paper deals with MHD nanofluid flow over a non-linear stretchable surface of varying thickness in the presence of an electric field. We investigated the effects of nanometer-sized copper (Cu) particles in water (base fluid) as a nanofluid, as well as non-linear thermal radiation, variable fluid viscosity, Joule heating, viscous dissipation, and non-uniform heat flux. The current study's aim is influenced by the immense applications in industry and machine building. It has been observed that linear stretching sheets have been extensively used in heat transfer research. Moreover, no effort has been made yet to model a non-linear stretching sheet with variable thickness. Furthermore, the effects of electromagnetohydrodynamics (EMHD) boundary-layer flow of a nanofluid with the cumulative impact of thermal radiation, variable viscosity, viscous dissipation, Joule heating, and variable heat flux have been investigated. Sheets with variable thicknesses are practically significant in real-life applications and are being used in metallurgical engineering, appliance structures and patterns, atomic reactor mechanization and paper production. To investigate the physical features of the problem, we first examined the model and identified all the physical properties of the problem. This problem has been formulated using basic laws and governing equations. The partial differential equations (PDEs) that govern the flow are converted into a system of non-dimensional ordinary differential equations (ODE's), using appropriate transformations. The Adam-Bashforth predictor-corrector technique and Mathematica software are utilized to numerically solve the resulting non-dimensionalized system. The interaction of various developing parameters with the flow is described graphically for temperature and velocity profiles. It is concluded that the velocity of nanoparticles declines as the intensity of the magnetic field increases. However, the temperature of the nanomaterials rises, as increasing the values of the electric field also increases the velocity distribution. The radiation parameter enhances the temperature field. The temperature of the fluid increases the occurrence of space- and time-dependent parameters for heat generation and absorption and radiation parameters.
由于其优异的热物理性质,纳米流体已受到广泛关注。本文研究了在电场作用下,磁流体动力学(MHD)纳米流体在具有不同厚度的非线性可拉伸表面上的流动。我们研究了纳米尺寸的铜(Cu)颗粒在水(基液)中作为纳米流体的影响,以及非线性热辐射、可变流体粘度、焦耳热、粘性耗散和非均匀热通量。当前研究的目的受到工业和机械制造中大量应用的影响。据观察,线性拉伸片材已广泛用于传热研究。此外,尚未有人尝试对具有可变厚度的非线性拉伸片材进行建模。此外,还研究了纳米流体的电磁流体动力学(EMHD)边界层流动,以及热辐射、可变粘度、粘性耗散、焦耳热和可变热通量的累积影响。具有可变厚度的片材在实际应用中具有重要意义,并且正在用于冶金工程、电器结构和图案、原子反应堆机械化和造纸生产。为了研究该问题的物理特性,我们首先检查了模型并确定了该问题的所有物理性质。这个问题是根据基本定律和控制方程来表述的。使用适当的变换,将控制流动的偏微分方程(PDEs)转换为无量纲常微分方程(ODE's)系统。利用亚当 - 巴什福斯预测 - 校正技术和Mathematica软件对所得的无量纲化系统进行数值求解。以图形方式描述了各种发展参数与流动对温度和速度分布的相互作用。结果表明,随着磁场强度的增加,纳米颗粒的速度下降。然而,纳米材料的温度升高,因为电场值的增加也会增加速度分布。辐射参数增强了温度场。流体温度增加了热生成、吸收以及辐射参数中与空间和时间相关的参数的出现。