Khan Ziad, Srivastava Hari Mohan, Mohammed Pshtiwan Othman, Jawad Muhammad, Jan Rashid, Nonlaopon Kamsing
Department of Mathematics, University of Swabi, Swabi 23561, Khyber Pakhtunkhwa, Pakistan.
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W3R4, Canada.
Math Biosci Eng. 2022 Sep 26;19(12):14116-14141. doi: 10.3934/mbe.2022658.
An analysis of steady two-dimensional boundary layer MHD (magnetohydrodynamic) nanofluid flow with nonlinear thermal radiation across a horizontally moving thin needle was performed in this study. The flow along a thin needle is considered to be laminar and viscous. The Rosseland estimate is utilized to portray the radiation heat transition under the energy condition. Titanium dioxide (TiO$ 2 $) is applied as the nanofluid and water as the base fluid. The objective of this work was to study the effects of a magnetic field, thermal radiation, variable viscosity and thermal conductivity on MHD flow toward a porous thin needle. By using a suitable similarity transformation, the nonlinear governing PDEs are turned into a set of nonlinear ODEs which are then successfully solved by means of the homotopy analysis method using Mathematica software. The comparison result for some limited cases was achieved with earlier published data. The governing parameters were fixed values throughout the study, i.e., $ k_1 $ = 0.3, $ M $ = 0.6, $ F_r $ = 0.1, $ \delta\mu $ = 0.3, $ \chi $ = 0.001, $ Pr $ = 0.7, $ Ec $ = 0.5, $ \theta_r $ = 0.1, $ \epsilon $ = 0.2, $ Rd $ = 0.4 and $ \delta_k $ = 0.1. After detailed analysis of the present work, it was discovered that the nanofluid flow diminishes with growth in the porosity parameter, variable viscosity parameter and magnetic parameter, while it upsurges when the rate of inertia increases. The thermal property enhances with the thermal conductivity parameter, radiation parameter, temperature ratio parameter and Eckert number, while it reduces with the Prandtl number and size of the needle. Moreover, skin friction of the nanofluid increases with corresponding growth in the magnetic parameter, porosity parameter and inertial parameter, while it reduces with growth in the velocity ratio parameter. The Nusselt number increases with increases in the values of the inertia parameter and Eckert number, while it decliens against a higher estimation of the Prandtl number and magnetic parameter. This study has a multiplicity of applications like petroleum products, nuclear waste disposal, magnetic cell separation, extrusion of a plastic sheet, cross-breed powered machines, grain storage, materials production, polymeric sheet, energy generation, drilling processes, continuous casting, submarines, wire coating, building design, geothermal power generations, lubrication, space equipment, biomedicine and cancer treatment.
本研究对具有非线性热辐射的稳态二维边界层磁流体动力学（MHD）纳米流体绕水平移动细针的流动进行了分析。沿细针的流动被认为是层流和粘性的。利用罗斯兰估计来描述能量条件下的辐射热传递。以二氧化钛（TiO₂）作为纳米流体，水作为基液。这项工作的目的是研究磁场、热辐射、可变粘度和热导率对MHD流向多孔细针流动的影响。通过使用合适的相似变换，将非线性控制偏微分方程转化为一组非线性常微分方程，然后使用Mathematica软件通过同伦分析方法成功求解。在一些有限情况下的比较结果与早期发表的数据一致。在整个研究过程中，控制参数为固定值，即k₁ = 0.3、M = 0.6、Fr = 0.1、δμ = 0.3、χ = 0.001、Pr = 0.7、Ec = 0.5、θr = 0.1、ε = 0.2、Rd = 0.4和δk = 0.1。在对本工作进行详细分析后发现，纳米流体流动随着孔隙率参数、可变粘度参数和磁参数的增加而减小，而随着惯性率的增加而增加。热特性随着热导率参数、辐射参数、温度比参数和埃克特数的增加而增强，而随着普朗特数和针的尺寸减小。此外，纳米流体的表面摩擦力随着磁参数、孔隙率参数和惯性参数的相应增加而增加，而随着速度比参数的增加而减小。努塞尔数随着惯性参数和埃克特数的增加而增加，而随着普朗特数和磁参数的更高估计值而减小。本研究有多种应用，如石油产品、核废料处理、磁细胞分离、塑料片材挤出、混合动力机器、谷物储存、材料生产、聚合物片材、能源发电、钻井过程、连铸、潜艇、电线涂层、建筑设计、地热能发电、润滑、太空设备、生物医学和癌症治疗。
