No abstract

We study the electrically conducting fluid stability of magnetohydrodynamic flow between parallel plates by Chebyshev collocation method by applied transverse magnetic field. Temporal growth is obtained by the governing equations. The results show that the dominating factor is the change in shape of the undisturbed velocity profile caused by the magnetic field, which depends only on the Hartmann number. The stability equations is solved by QZ-algorithm to find the eigenvalue problem. The numerical calculation show that Magnetic field with particular magnitude destabilizes Couette flow while other magnitude stabilize the flow. It is also analyzed that Rec decreases rapidly to the minimum value for Hartmann number Ha greater than 3.887 and increases steadily from Hartmann number Ha (>5.559). It is observed that critical Reynolds number Rec is larger as Hartmann number decreases from Ha=3.887. The two critical Reynolds numbers in the elliptic curves are found for different values of Hartmann number.

This study is concerned with the existence and uniqueness results for fuzzy differential equations (FDEs). The existence result of FDEs in the space of linear correlated (LC) fuzzy number with LC-differentiability is the goal of this work. Linear FDEs of first order in the space of LC-fuzzy number mostly have many solutions and sometimes have no solutions. Existence theory insures the existence of unique solution of FDEs. Therefore, we propose to study the existence results of LC-fuzzy solution of FDEs of first order. The existence criteria for the unique LC-fuzzy solution for both symmetric and nonsymmetric basic fuzzy number will be studied in this work. Some examples are given to show the usability of the criteria for a unique LC-fuzzy solution. The plots of the fuzzy solutions of examples are also provided.

This study investigates the linear stability of the Hartmann layers of an electrically conductive fluid between parallel plates under the impact of a transverse magnetic field. The corresponding Orr–Sommerfeld equations are numerically solved using Chebyshev’s pseudo-spectral method with Chebyshev polynomial expansion. The QZ algorithm is applied to find neutral linear instability curves. Details of the instability are evaluated by solving the generalized Orr–Sommerfeld system, allowing growth rates to be determined. The results confirm that a magnetic field provides a stabilizing impact to the flow, and the extent of this impact is demonstrated for a range of Reynolds numbers. From numerical simulations, it is observed that a magnetic field with a specific magnitude stabilizes the Hartmann flow. Further, the critical Reynolds number increases rapidly when the Hartmann number is greater than 0.7. Finally, it is shown that a transverse magnetic field overcomes the instability in the flow.