Analysis of Magnetic Properties of Nano-Particles Due to a Magnetic Dipole in Micropolar Fluid Flow over a Stretching Sheet

• Main Authors: Liaqat Ali, Xiaomin Liu, Bagh Ali, Saima Mujeed, Sohaib Abdal, Shahid Ali Khan
• Format: Article
• Language: English
• Published: MDPI AG 2020-02-01
• Series: Coatings
• Subjects: nano-particles; magnetic dipole; finite element method (fem); viscous dissipation; micro-polar
• Online Access: https://www.mdpi.com/2079-6412/10/2/170

This article explores the impact of a magnetic dipole on the heat transfer phenomena of different nano-particles Fe (ferromagnetic) and Fe₃O₄ (Ferrimagnetic) dispersed in a base fluid (<inline-formula> <math display="inline"> <semantics> <mrow> <mn>60</mn> <mo>%</mo> </mrow> </semantics> </math> </inline-formula> water + <inline-formula> <math display="inline"> <semantics> <mrow> <mn>40</mn> <mo>%</mo> </mrow> </semantics> </math> </inline-formula> ethylene glycol) on micro-polar fluid flow over a stretching sheet. A magnetic dipole in the presence of the ferrities of nano-particles plays an important role in controlling the thermal and momentum boundary layers. The use of magnetic nano-particles is to control the flow and heat transfer process through an external magnetic field. The governing system of partial differential equations is transformed into a system of coupled nonlinear ordinary differential equations by using appropriate similarity variables, and the transformed equations are then solved numerically by using a variational finite element method. The impact of different physical parameters on the velocity, the temperature, the Nusselt number, and the skin friction coefficient is shown. The velocity profile decreases in the order Fe (ferromagnetic fluid) and Fe₃O₄ (ferrimagnetic fluid). Furthermore, it was observed that the Nusselt number is decreasing with the increasing values of boundary parameter <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <mi>&#948;</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>, while there is controversy with respect to the increasing values of radiation parameter <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <mi>N</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>. Additionally, it was observed that the ferromagnetic case gained maximum thermal conductivity, as compared to ferrimagnetic case. In the end, the convergence of the finite element solution was observed; the calculations were found by reducing the mesh size.