Saranya Shekar, Al-Mdallal Qasem M, Javed Shumaila
Department of Mathematical Sciences, United Arab Emirates University, Al-Ain P.O. Box 15551, United Arab Emirates.
Nanomaterials (Basel). 2021 Jun 8;11(6):1512. doi: 10.3390/nano11061512.
A numerical treatment for the unsteady viscous-Ohmic dissipative flow of hybrid ferrofluid over a contracting cylinder is provided in this study. The hybrid ferrofluid was prepared by mixing a 50% water (H2O) + 50% ethylene glycol (EG) base fluid with a hybrid combination of magnetite (Fe3O4) and cobalt ferrite (CoFe2O4) ferroparticles. Suitable parameters were considered for the conversion of partial differential equations (PDEs) into ordinary differential equations (ODEs). The numerical solutions were established by expanding the unknowns and employing the truncated series of shifted Legendre polynomials. We begin by collocating the transformed ODEs by setting the collocation points. These collocated equations yield a system of algebraic equations containing shifted Legendre coefficients, which can be obtained by solving this system of equations. The effect of the various influencing parameters on the velocity and temperature flow profiles were plotted graphically and discussed in detail. The effects of the parameters on the skin friction coefficient and heat transfer rates were further presented. From the discussion, we come to the understanding that Eckert number considerably decreases both the skin friction coefficient and the heat transfer rate.
本研究提供了一种对混合铁磁流体在收缩圆柱面上非定常粘性 - 欧姆耗散流动的数值处理方法。混合铁磁流体是通过将50%的水（H₂O）+ 50%的乙二醇（EG）基液与磁铁矿（Fe₃O₄）和钴铁氧体（CoFe₂O₄）铁颗粒的混合组合相混合而制备的。考虑了合适的参数用于将偏微分方程（PDEs）转换为常微分方程（ODEs）。通过展开未知量并采用移位勒让德多项式的截断级数建立了数值解。我们首先通过设置配置点来配置变换后的ODEs。这些配置方程产生一个包含移位勒让德系数的代数方程组，通过求解这个方程组可以得到这些系数。以图形方式绘制并详细讨论了各种影响参数对速度和温度流动剖面的影响。进一步给出了这些参数对表面摩擦系数和传热速率的影响。从讨论中我们了解到，埃克特数会显著降低表面摩擦系数和传热速率。
