Abstract
The major aim of this work is to achieve a mathematical technique to scrutinize the nonlinear instability of a vertical cylindrical boundary separation of two streaming Reiner-Rivlin liquids. The system is portrayed by an unchanged longitudinal electric strength. Furthermore, the action of mass and heat transfer (MHT) and permeable media are also considered. The problem is not only of methodological interest but also of scientific and practical interest. To shorten the mathematical analysis, Hsieh's modulation together with the viscous potential theory (VPT) is employed. The nonlinear diagram is contingent on tackling the governing linear mechanism along with the nonlinear applicable border restrictions. A non-dimensional process produces several non-dimensional physical numbers. A linear dispersion equation is attained and the stability standards are theoretically governed and numerically established. The nonlinear stability procedure reveals a Ginzburg-Landau formula. Consequently, nonlinear stability stipulations are accomplished. Furthermore, by way of the Homotopy perturbation approach, along with the expanded frequency concept, an accurate perturbed technique of surface deflection is attained theoretically and numerically. To validate the theoretical outcomes, the analytical expression is confirmed through the Rung-Kutta of the fourth order. The stable and unstable zones are signified graphically displaying the influences of several non-dimensional numbers.