Anwar Talha, Kumam Poom, Khan Ilyas, Watthayu Wiboonsak
Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand.
KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand.
Entropy (Basel). 2020 Mar 31;22(4):401. doi: 10.3390/e22040401.
This article analyzes heat transfer enhancement in incompressible time dependent magnetohydrodynamic (MHD) convective flow of Oldroyd-B nanofluid with carbon nanotubes (CNTs). Single wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs) are immersed in a base fluid named Sodium alginate. The flow is restricted to an infinite vertical plate saturated in a porous material incorporating the generalized Darcy's law and heat suction/injection. The governing equations for momentum, shear stress and energy are modelled in the form of partial differential equations along with ramped wall temperature and ramped wall velocity boundary conditions. Laplace transformation is applied to convert principal partial differential equations to ordinary differential equations first and, later, complex multivalued functions of Laplace parameter are handled with numerical inversion to obtain the solutions in real time domain. Expression for Nusselt number is also obtained to clearly examine the difference in rate of heat transfer. A comparison for isothermal wall condition and ramped wall condition is also made to analyze the difference in both profiles. A graphical study is conducted to analyze how the fluid profiles are significantly affected by several pertinent parameters. Rate of heat transfer increases with increasing volume fraction of nanoparticle while shear stress reduces with elevation in retardation time. Moreover, flow gets accelerated with increase in Grashof number and Porosity parameter. For every parameter, a comparison between solutions of SWCNTs and MWCNTs is also presented.
本文分析了含有碳纳米管（CNTs）的Oldroyd-B纳米流体在不可压缩、时间相关的磁流体动力学（MHD）对流流动中的传热增强情况。单壁碳纳米管（SWCNTs）和多壁碳纳米管（MWCNTs）被浸没在一种名为海藻酸钠的基液中。流动被限制在一个无限大的垂直平板上，该平板饱和于一种采用广义达西定律并考虑热抽吸/注入的多孔材料中。动量、剪应力和能量的控制方程以偏微分方程的形式建立，并带有斜坡壁面温度和斜坡壁面速度边界条件。首先应用拉普拉斯变换将主要偏微分方程转换为常微分方程，然后通过数值反演处理拉普拉斯参数的复多值函数，以获得实时域中的解。还得到了努塞尔数的表达式，以清楚地检验传热速率的差异。还对等温壁面条件和斜坡壁面条件进行了比较，以分析两种情况下的差异。进行了图形研究，以分析几个相关参数如何显著影响流体剖面。传热速率随着纳米颗粒体积分数的增加而增加，而剪应力随着延迟时间的增加而减小。此外，随着格拉晓夫数和孔隙率参数的增加，流动加速。对于每个参数，还给出了SWCNTs和MWCNTs解之间的比较。
