Instability in Three-Dimensional Magnetohydrodynamic Flows of an Electrically Conducting Fluid

The three-dimensional instability of an electrically conducting fluid between two parallel plates affected by an imposed transversal magnetic field is numerically investigated by a Chebyshev collocation method. The QZ method is utilized to obtain neutral curves of the linear instability. The details of instability are analyzed by solving the generalized Orr-Sommerfeld equation. The critical Reynolds number Rec, the stream-wise and span-wise critical wave numbers αc and βc are obtained for a wide range of Hartmann number Ha. The effects of Lorentz force and span-wise perturbation on three-dimensional instability are investigated. The results show that magnetic field would suppress the instability and critical Reynolds number tends to be larger than that for two-dimensional instability.

Bifurcation phenomena and control for magnetohydrodynamic flows in a smooth expanded channel

This work reports the effects of magnetic field on an electrically conducting fluid with low electrical conductivity flowing in a smooth expanded channel. The governing nonlinear magnetohydrodynamic （MHD） equations in induction- free situations are derived in the framework of MHD approximations and solved numerically using the finite-difference technique. The critical values of Reynolds number （based on upstream mean velocity and channel height） for symmetry breaking bifurcation for a sudden expansion channel （1：4） is about 36, whereas the value in the case of the smooth expansion geometry used in this work is obtained as 298, approximately （non-magnetic case）. The flow of an electrically conducting fluid in the presence of an externally applied constant magnetic field perpendicular to the plane of the flow is reduced significantly depending on the magnetic parameter （M）. It is expansion （1：4） is about 475 for the magnetic parameter M found that the critical value of Reynolds number for smooth = 2. The separating regions developed behind the smooth symmetric expansion are decreased in length for increasing values of the magnetic parameter. The bifurcation diagram is shown for a symmetric smoothly expanding channel. It is noted that the critical values of Reynolds number increase with increasing magnetic field strength.

Heat Transfer Analysis of MHD Power Law Nano Fluid Flow through Annular Sector Duct

Flow and heat transfer analysis of an electrically conducting MHD power law nano fluid is carried out through annular sector duct,under the influence of constant pressure gradient.Two types of nano particles(i.e.Cu and TiO2)are used in power law nano fluid.Strongly implicit procedure,(SIP)is used to simulate the discretized coupled algebraic equations.It has been observed that volume fraction of nano particles,ϕand magnetic field parameter,Ha are favourable for the heat transfer rate,however,both resist the fluid flow.Impact of applied uniform transverse magnetic field exceeds in the case of shear thickening fluids(i.e.n>1)by increasing the value of Ha as compared to that in shear thinning fluids(i.e.n<1).Therefore,enhancement in heat transfer rate is comparably more in shear thickening fluid.Furthermore,comparable limiting case study with published result is also carried out in this research paper.