Hartmann number

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

The method of variably scaled radial kernels for solving two-dimensional magnetohydrodynamic (MHD) equations using two discretizations: The Crank–Nicolson scheme and the method of lines (MOL)

Abstract: MHD equations have many applications in physics and engineering. The model is coupled equations in velocity and magnetic field and has a parameter namely Hartmann. The value of Hartmann number plays an important role in the equations. When this parameter increases, using different meshless methods makes the oscillations in velocity near the boundary layers in the region of the problem. In the present paper a numerical meshless method based on radial basis functions (RBFs) is provided to solve MHD equations. For approximating the spatial variable, a new approach which is introduced by Bozzini et al. (2015) is applied. The method will be used here is based on the interpolation with variably scaled kernels. The methodology of the new technique is defining the scale function c on the domain Ω ⊂ R d . Then the interpolation problem from the data locations x j ∈ R d transforms to the new interpolation problem in the data locations ( x j , c ( x j ) ) ∈ R d + 1 (Bozzini et al., 2015). The radial kernels used in the current work are Multiquadrics (MQ), Inverse Quadric (IQ) and Wendland’s function. Of course the latter one is based on compactly supported functions. To discretize the time variable, two techniques are applied. One of them is the Crank–Nicolson scheme and another one is based on MOL. The numerical simulations have been carried out on the square and elliptical ducts and the obtained numerical results show the ability of the new method for solving this problem. Also in appendix, we provide a computational algorithm for implementing the new technique in MATLAB software.

Hall effects on MHD flow in a rotating system with heat transfer characteristics

Abstract: Closed-form solutions are derived for the steady magnetohydrodynamic (MHD) viscous flow in a parallel plate channel system with perfectly conducting walls in a rotating frame of reference, in the presence of Hall currents, heat transfer and a transverse uniform magnetic field A mathematical analysis is described to evaluate the velocity, induced magnetic field and mass flow rate distributions, for a wide range of the governing parameters Asymptotic behavior of the solution is analyzed for large M 2 (Hartmann number squared) and K 2 (rotation parameter) The heat transfer aspect is considered also with Joule and viscous heating effects present Boundary layers arise close to the channel walls for large K 2, ie strong rotation of the channel For slowly rotating systems (small K 2), Hall current parameter (m) reduces primary mass flow rate (Q x /R ρ v) Heat transfer rate at the upper plate (d θ/d η) η=1 decreases, while at the lower plate (d θ/d η) η=−1 increases, with increase in either K 2 or m For constant values of the rotation parameter, K 2, heat transfer rate at both plates exhibits an oscillatory pattern with an increase in Hall current parameter, m The response of the primary and secondary velocity components and also the primary and secondary induced magnetic field components to the control parameters is also studied graphically Applications of the study arise in rotating MHD induction machine energy generators, planetary and solar plasma fluid dynamics systems, magnetic field control of materials processing systems, hybrid magnetic propulsion systems for space travel etc