Magnetohydrodynamic flow

What is it about?

The MHD flow produced by counter-rotation of the top and bottom disks in a truncated conical container having an aspect ratio (height/radius) =2, filled with a liquid metal, and submitted to a vertical temperature gradient (system heated from below) is studied. The bottom disk is rotating with a constant angular velocity Ω, and is maintained at a hot temperature Th, while the top disk is in counter-rotating ( Ωtop =4Ω ) and maintained at the cold temperature Tc. The governing Navier-Stokes, energy, and potential equations are solved by using the finite-volume method. Results are presented for various values of the Hartmann number, Ha, and Richardson numbers, Ri, in order to see their effects on the value of the critical Reynolds number, Recr (transition from axisymmetric to non-axisymmetric flow). It was observed that the Reynolds number is increased, the axisymmetric basic state loses stability and giving an asymmetric mode. The application of the magnetic field results to fluid deceleration and, thus, to flow stabilization. Finally, stability diagram (Re-Ha) has been established according to the numerical results of this investigation.

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Why is it important?

• When the critical value of Reynolds exceeds the critical value, the axisymmetric basic state loses stability and becomes an asymmetric flow. • increase in the values of Hartmann number, Ha reduces the axial velocity, suppress the fluid motion, and • It means that both fluid flow and heat transfer can be controlled via the magnetic field at a constant value of Richardson and Reynolds number confirming the phenomenon of flow stabilization by the application of the magnetic field.

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