Linear stability analysis for the hartmann flow with interfacial slip

We study linear stability of the Hartmann flow with the interfacial slip between the flowing liquid and the solid wall using the slip length model. To address the effect of the slip length, the eigenvalue problem for the modified Orr-Sommerfeld equation is solved by a MATLAB code using the Chebyshev collocation method. The flow stability is addressed for both symmetric and asymmetric slip conditions, using linear modal and non-modal stability analyses. Using the modal stability analysis, it has been demonstrated that the magnetic field stabilizes the flow, while the increase in slip length significantly increases the critical Reynolds number even for very small slip lengths if compared to the thickness of the Hartmann layer. The non-modal stability analysis, at sub-critical Reynolds numbers, suggests that the slip hardly affects the transient energy growth.