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Hartmann number
About: Hartmann number is a research topic. Over the lifetime, 2593 publications have been published within this topic receiving 61342 citations.
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TL;DR: In this paper, the authors considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli in the presence of a radial magnetic field and found that the induced magnetic field produced by the motion of an electrically conducting fluid is taken into account.
Abstract: In the present paper, we have considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli in the presence of a radial magnetic field. The induced magnetic field produced by the motion of an electrically conducting fluid is taken into account. The transport equations concerned with the considered model are first recast in the non-dimensional form and then unified analytical solutions for the velocity, induced magnetic field and temperature field are obtained for the cases of isothermal and constant heat flux on the inner cylinder of concentric annuli. The effects of the various physical parameters appearing into the model are demonstrated through graphs and tables. It is found that the magnitude of maximum value of the fluid velocity as well as induced magnetic field is greater in the case of isothermal condition compared with the constant heat flux case when the gap between the cylinders is less or equal to 1.70 times the radius of inner cylinder, while reverse trend occurs when the gap between the cylinders is greater than 1.71 times the radius of inner cylinder. These fields are almost the same when the gap between the cylinders is equal to 1.71 times the radius of inner cylinder for both the cases. It is also found that as the Hartmann number increases, there is a flattening tendency for both the velocity and the induced magnetic field. The influence of the induced magnetic field is to increase the velocity profiles.
37 citations
TL;DR: In this article, a stability analysis for the laminar flow of a layer of a viscous and electrically conducting fluid down an inclined plane in a transverse magnetic field is made.
Abstract: A stability analysis is made for the laminar flow of a layer of a viscous and electrically conducting fluid down an inclined plane in a transverse magnetic field. It is found that the effect of the magnetic field, revealed through the Hartmann number, is to stabilize the flow. A simpler and physically clearer approximate treatment of the same problem based on the principle of local balance is also given. The results agree quite satisfactorily with the exact analysis.
37 citations
TL;DR: The aspect ratio of the cone was found to be an excellent tool for heat transfer enhancement while 95% enhancements in the average Nusselt number were obtained.
Abstract: Effects of a rotating cone in 3D mixed convection of CNT-water nanofluid in a double lid-driven porous trapezoidal cavity is numerically studied considering magnetic field effects. The numerical simulations are performed by using the finite element method. Impacts of Richardson number (between 0.05 and 50), angular rotational velocity of the cone (between -300 and 300), Hartmann number (between 0 and 50), Darcy number (between 10 - 4 and 5 × 10 - 2 ), aspect ratio of the cone (between 0.25 and 2.5), horizontal location of the cone (between 0.35 H and 0.65 H) and solid particle volume fraction (between 0 and 0.004) on the convective heat transfer performance was studied. It was observed that the average Nusselt number rises with higher Richardson numbers for stationary cone while the effect is reverse for when the cone is rotating in clockwise direction at the highest supped. Higher discrepancies between the average Nusselt number is obtained for 2D cylinder and 3D cylinder configuration which is 28.5% at the highest rotational speed. Even though there are very slight variations between the average Nu values for 3D cylinder and 3D cone case, there are significant variations in the local variation of the average Nusselt number. Higher enhancements in the average Nusselt number are achieved with CNT particles even though the magnetic field reduced the convection and the value is 84.3% at the highest strength of magnetic field. Increasing the permeability resulted in higher local and average heat transfer rates for the 3D porous cavity. In this study, the aspect ratio of the cone was found to be an excellent tool for heat transfer enhancement while 95% enhancements in the average Nusselt number were obtained. The horizontal location of the cone was found to have slight effects on the Nusselt number variations.
37 citations
TL;DR: In this article, forced convection of Fe 3 O 4 -water nanofluid in a bifurcating channel was numerically studied under the influence of variable magnetic.
Abstract: In this study, forced convection of Fe 3 O 4 –water nanofluid in a bifurcating channel was numerically studied under the influence of variable magnetic. Galerkin residual finite element method was used for numerical simulations. Effects of various values of Reynolds number (between 100 and 500), Hartmann number (between 0 and 3), and solid nanoparticle volume fraction (between 0% and 4%) on the convective heat transfer characteristics were analyzed. It was observed that location and size of the re-circulation zones established in the walls of the bifurcating channel strongly influenced by the variable magnetic field and Reynolds number. Average Nusselt number versus Hartmann number showed different characteristics for hot walls of the vertical and horizontal branching channels. The average Nusselt number enhancements were in the range of 12–15% and 9–12% for hot walls of the branching channel in the absence and presence of magnetic field (at Hartmann number of 3).
37 citations
TL;DR: In this article, it was shown that nonaxisymmetric perturbations are unstable if the rotation rate and the Alfven frequency of the field are of the same order, almost independent of the magnetic Prandtl number Pm.
Abstract: The interaction of differential rotation and toroidal fields that are current-free in the gap between two corotating axially unbounded cylinders is considered. It is shown that nonaxisymmetric perturbations are unstable if the rotation rate and Alfven frequency of the field are of the same order, almost independent of the magnetic Prandtl number Pm. For the very steep rotation law \Omega\propto R^{-2} (the Rayleigh limit) and for small Pm the threshold values of rotation and field for this Azimuthal MagnetoRotational Instability (AMRI) scale with the ordinary Reynolds number and the Hartmann number, resp. A laboratory experiment with liquid metals like sodium or gallium in a Taylor-Couette container has been designed on the basis of this finding. For fluids with more flat rotation laws the Reynolds number and the Hartmann number are no longer typical quantities for the instability. For the weakly nonlinear system the numerical values of the kinetic energy and the magnetic energy are derived for magnetic Prandtl numbers \leq 1. We find that the magnetic energy grows monotonically with the magnetic Reynolds number Rm, while the kinetic energy grows with Rm/\sqrt{Pm}. The resulting turbulent Schmidt number, as the ratio of the `eddy' viscosity and the diffusion coefficient of a passive scalar (such as lithium) is of order 20 for Pm=1, but for small Pm it drops to order unity. Hence, in a stellar core with fossil fields and steep rotation law the transport of angular momentum by AMRI is always accompanied by an intense mixing of the plasma, until the rotation becomes rigid.
37 citations