Convective instability analysis of the flow due to a linearly shrinking sheet with uniform suction

We explore the linear stability of a two-dimensional flow induced due to streamwise linear shrinking of a flat surface. Dual solutions for mean flow are computed using MATLAB. A high-precision spectral numerical method is employed for the solution of the stability problem. By inspecting the neutral curves and conducting the energy analysis, it is shown that flows corresponding to both solutions are susceptible to linear instability triggered by Tollmien–Schlichting waves, particularly at large Reynolds numbers. However, the flow corresponding to the first solution achieves instability at higher Reynolds numbers in comparison to the flow corresponding to the second solution. The study shows that suction stabilizes the flow corresponding to the first solution. However, a reverse trend is observed for the flow corresponding to the second solution. These results are further corroborated through the energy analysis. An elevation in growth rates is observed by increasing suction for the second solution. In contrast, growth rates for the first solution diminish upon elevating suction.