Hydromagnetic flow due to torsional oscillations of an infinite disk about a steady non-zero mean

The present investigation is the study of the laminar hydromagnetic flow due to torsional oscillations of an infinite disk about a steady non-zero mean in an electrically conducting fluid. Separate solutions have been obtained for the limiting cases of low and high frequency oscillations. The low frequency solution is obtained by expressing the flow functions in powers (ik) while for high frequencies, the flow functions are expressed in powers of $\text{(ik)}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$, where $\text{k =}\text{ω}\text{Ω}$ being the ratio of the frequency of oscillations ω to the mean disk-angular velocity Ω and i² = ?1. It is found that the oscillating part of the transverse shearing stress has a phase-lead while that of the radial shearing stress has a phase lag behind the disk oscillations. The phase-lead in the former case and phase-lag in the latter case decrease with the increase in the strength of the applied magnetic field.