Magnetohydrodynamic Viscous Flow Separation in a Channel With Constrictions

Abstract

An analysis is made of the flow of an electrically conducting fluid in a channel with constrictions in the presence of a uniform transverse magnetic field. A solution technique for governing magnetohydrodynamic (MHD) equations in primitive variable formulation is developed. A coordinate stretching is used to map the long irregular geometry into a finite computational domain. The governing equations are discretized using finite difference approximations and the well-known staggered grid of Harlow and Welch is used. Pressure Poisson equation and pressure-velocity correction formulas are derived and solved numerically. It is found that the flow separates downstream of the constriction. With increase in the magnetic field, the flow separation zone diminishes in size and for large magnetic field, the separation zone disappears completely. Wall shear stress increases with increase in the magnetic field strength. It is also found that for symmetrically situated constrictions on the channel walls, the critical Reynolds number for the flow bifurcation (i.e., flow asymmetry) increases with increase in the magnetic field.

Magnetohydrodynamic effects on blood flow through an irregular stenosis

“…Interestingly, the wall shear stress increases when H is increased. Meanwhile, the value of wall shear stress is also increased with increase in parameter K , as can be seen from Figure 7 and the same observation also revealed from the works of Midya et al [4]. The effects on this flow characteristic are implied from the presence of magnetic field, which has retarded the flow, and it is produced from the Lorentz force arising out of the electric current flow at the tube axis.…”

“…They studied the flow analysis in the absence of electric and induced magnetic fields. Using similar assumptions, Midya et al [4] reported the results of MHD flow of a viscous fluid in channel with constrictions. They performed this study in the absence of body acceleration.…”

MHD Flow of Power-Law Fluids in Locally-Constricted Channels

“…3 represents the so-called Lorentz force as induced by the external magnetic field. 23) In the above equations we have, …”

“…23) To proceed any further, at this stage of the analysis, we have to decide on the constitutive equation of the fluid to be inserted into the momentum equations. For ease of analysis, and also because of the qualitative nature of the present work, we assume that the fluid of interest obeys the Generalized Newtonian (GN) fluid model.…”

“…Newtonian fluids [21][22][23] , but its effectiveness for the flow of blood through constricted arteries is still the subject of extensive studies. 24,25) Having said this, it should be mentioned that in a recent work, Ikbal et al 26) have numerically investigated the influence of a transverse magnetic field on the pulsatile flow of blood in a time-variant constricted artery using the same rheological model as used in the present work, i.e., the power-law model.…”