Hartmann number

About: Hartmann number is a research topic. Over the lifetime, 2593 publications have been published within this topic receiving 61342 citations.

Role of induced magnetic field on MHD natural convection flow in vertical microchannel formed by two electrically non-conducting infinite vertical parallel plates

Abstract: The present work consists of theoretical investigation of MHD natural convection flow in vertical microchannel formed by two electrically non-conducting infinite vertical parallel plates. The influence of induced magnetic field arising due to the motion of an electrically conducting fluid is taken into consideration. The governing equations of the motion are a set of simultaneous ordinary differential equations and their exact solutions in dimensionless form have been obtained for the velocity field, the induced magnetic field and the temperature field. The expressions for the induced current density and skin friction have also been obtained. The effects of various non-dimensional parameters such as rarefaction, fluid wall interaction, Hartmann number and the magnetic Prandtl number on the velocity, the induced magnetic field, the induced current density, and skin friction have been presented in graphical form. It is found that the effect of Hartmann number and magnetic Prandtl number on the induced current density is found to have a decreasing nature at the central region of the microchannel.

Thermal analysis of Casson micropolar nanofluid flow over a permeable curved stretching surface under the stagnation region

Abstract: We consider a curved surface upon which the Casson micropolar nanofluid flow is discharged to understand the behavior of such flow and heat progression. The non-Newtonian fluid flow is controlled with the introduction of a magnetic force which is directed against the flow to alter the moment of flow. An increase in the numerical value of modified Hartmann number slows down the flow by adding discharge against the flow. Lorentz force produced by increasing the curve of the channel suppresses the flow velocity. The micropolar parameter reduces the drag and helps in increasing the fluid flow. Mathematical modeling of the problem is done by taking into account the conventional assumptions taken in fluid flow theories. The modeled equations are simplified by considering similar transformation variables used in the contemporary literature. Numerical result is obtained by using bvp4c solver used in MATLAB by allowing the acceptable tolerance level at 1e−4. Various tests are carried out to choose the best match of the parametric values which help in achieving the defined boundary conditions. The output of the various solutions is plotted under varying values of different parameters, and henceforth the changes occurred are noted and discussed. The behavior of velocity, microrotational, temperature and concentration profiles is observed by comparing the graphical and tabular values. The role of different physical quantities under different parametric assumptions for stretching/shrinking channel is also taken into account and highlighted.

A super-rotating shear layer in magnetohydrodynamic spherical Couette flow

Abstract: We consider axisymmetric magnetohydrodynamic motion in a spherical shell driven by rotating the inner boundary relative to the stationary outer boundary – spherical Couette flow. The inner solid sphere is rigid with the same electrical conductivity as the surrounding fluid; the outer rigid boundary is an insulator. A force-free dipole magnetic field is maintained by a dipole source at the centre. For strong imposed fields (as measured by the Hartmann number M), the numerical simulations of Dormy et al. (1998) showed that a super-rotating shear layer (with angular velocity about 50% above the angular velocity of the inner core) is attached to the magnetic field line [Cscr ] tangent to the outer boundary at the equatorial plane of symmetry. At large M, we obtain analytically the mainstream solution valid outside all boundary layers by application of Hartmann jump conditions across the inner- and outer-sphere boundary layers. We formulate the large-M boundary layer problem for the free shear layer of width M−1/2 containing [Cscr ] and solve it numerically. The super-rotation can be understood in terms of the nature of the meridional electric current flow in the shear layer, which is fed by the outer-sphere Hartmann layer. Importantly, a large fraction of the current entering the shear layer is tightly focused and effectively released from a point source at the equator triggered by the tangency of the [Cscr ]-line. The current injected by the source follows the [Cscr ]-line closely but spreads laterally due to diffusion. In consequence, a strong azimuthal Lorentz force is produced, which takes opposite signs either side of the [Cscr ]-line; order-unity super-rotation results on the equatorial side. In fact, the point source is the small equatorial Hartmann layer of radial width M−2/3 ([Lt ]M−1/2) and latitudinal extent M−1/3. We construct its analytic solution and so determine an inward displacement width O(M−2/3) of the free shear layer. We compare our numerical solution of the free shear layer problem with our numerical solution of the full governing equations for M in excess of 104. We obtain excellent agreement. Some of our more testing comparisons are significantly improved by incorporating the shear layer displacement caused by the equatorial Hartmann layer.