Influence of Hall current and microrotation on the boundary layer flow of an electrically conducting fluid: Application to Hemodynamics

Abstract In this study, a problem of micropolar fluid flow is analyzed taking into account the effect of Hall current. An external magnetic field is applied transverse to that of fluid flow. The partial differential equations of conservation of mass, linear momentum, angular momentum, energy and concentration are considered along with suitable boundary conditions in formulating the model for the physical problem and analyzing it theoretically. The problem is motivated towards exploring some novel information in the dynamics of blood flow, when the influence of Hall current and rotation of the microparticles of blood, for e.g. the erythrocytes and thrombocytes co-exist at the same platform. The governing equations are reduced to a system of non-linear ordinary differential equations by making use of similarity transformations. The resulting system of coupled non-linear ordinary differential equations is then solved by using a suitable numerical technique that involves the use of finite differences and Newton's linearization method. A parametric study illustrating the influences of the magnetic field, Hall current and the micropolarity of suspended microparticles has been carried out to investigate the variations in velocity, temperature and concentration profiles. The problem has an important bearing on some bio-engineering problems, where the biological conduits, cells and membranes are typically surrounded by fluids, which are electrically conducting (as in the case of blood) and the conduits, cells and membranes that are stretched constantly. The computational results reveal that the microrotation of erythrocytes in blood is enhanced due to the effect of Hall current, when blood flows in the arterial system.

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