Abstract
The studies dealing with micropolar magnetohydrodynamic (MHD) flows usually ignore the micromagnetorotation (MMR) effect, by assuming that magnetization and magnetic field vectors are parallel. The main objective of the present investigation is to measure the effect of MMR and the possible differences encountered by ignoring it. The MHD planar Couette micropolar flow is solved analytically considering and by ignoring the MMR effect. Subsequently, the influence of MMR on the velocity and microrotation fields as well as skin friction coefficient, is evaluated for various micropolar size and electric effect parameters and Hartmann numbers. It is concluded that depending on the parameters’ combination, as MMR varies, the fluid flow may accelerate, decelerate, or even excite a mixed pattern along the channel height. Thus, the MMR term is a side mechanism, other than the Lorentz force, that transfers or dissipates magnetic energy in the flow direct through microrotation. Acceleration or deceleration of the velocity from 4% to even up to 45% and almost 15% deviation of the skin friction were measured when MMR was considered. The crucial effect of the micromagnetorotation term, which is usually ignored, should be considered for the future design of industrial and bioengineering applications.
Highlights
The model of micropolar fluids proposed by Eringen [1,2] is a mathematical theory, which accounts for the local microstructure of a fluid
The micropolar theory describes fluids with a wide variety of microstructure by assuming that their internal particles may rotate independent of their linear velocity [5,6]
The fully developed planar MHD micropolar Couette flow is analytically solved for various values of the magnetization effect parameter σm
Summary
The model of micropolar fluids proposed by Eringen [1,2] is a mathematical theory, which accounts for the local microstructure of a fluid. In the balance law of the angular momentum the internal rotation because of the magnetization has not been included, since magnetization was considered parallel to the magnetic field To this end, Shizawa et al [29] obtained a set of equations for micropolar fluids with good thermal and electrical conductivity including internal rotation. Shizawa et al [29] presented an analytical solution of the planar Couette micropolar flow with the MMR term, without emphasizing on the effect of the term in linear velocity and microrotation It appears that at most of the relevant literature where magnetization is considered, the MMR term is ignored in micropolar equations. The applications of this include magnetic targeted drug delivery systems [32], magnetic hyperthermia for thermal ablation of cancer cells [28], and lessening of bleeding in surgeries [33] to mention but a few
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