Validation of a magneto- and ferro-hydrodynamic model for non-isothermal flows in conjunction with Newtonian and non-Newtonian fluids

摘要

This work focuses on the validation of a magnetohydrodynamic (MHD) and ferrohydrodynamic(FHD) model for non-isothermal flows in conjunction with Newtonian and non-Newtonian fluids. The importance of this research field is to gain insight into the interaction ofnon-linear viscous behaviour of blood flow in the presence of MHD and FHD effects, becauseits biomedical application such as magneto resonance imaging (MRI) is in the centre of researchinterest. For incompressible flows coupled with MHD and FHD models, the Lorentz force anda Joule heating term appear due to the MHD effects and the magnetization and magnetocaloricterms appear due to the FHD effects in the non-linear momentum and temperature equations,respectively. Tzirtzilakis and Loukopoulos [1] investigated the effects of MHD and FHD forincompressible non-isothermal flows in conjunction with Newtonian fluids in a small rectangularchannel. Their model excluded the non-linear viscous behaviour of blood flows consideringblood as a Newtonian biofluid. Tzirakis et al. [2, 3] modelled the effects of MHD and FHD forincompressible isothermal flows in a circular duct and through a stenosis in conjunction withboth Newtonian and non-Newtonian fluids, although their approach neglects the non-isothermalmagnetocaloric FHD effects. Due to the fact that there is a lack of experimental data availablefor non-isothermal and non-Newtonian blood flows in the presence of MHD and FHD effects,therefore the objective of this study is to establish adequate validation test cases in order to assessthe reliability of the implemented non-isothermal and non-Newtonian MHD-FHD models.The non-isothermal Hartmann flow has been chosen as a benchmark physical problem to studyvelocity and temperature distributions for Newtonian fluids and non-Newtonian blood flows ina planar microfluidic channel. In addition to this, the numerical behaviour of an incompressibleand non-isothermal non-Newtonian blood flow has been investigated from computationalaspects when a dipole-like rotational magnetic field generated by infinite conducting wires. Thenumerical results are compared to available computational data taken from literature.