Abstract
The inspiration for this study is to explore the crucial impact of viscous dissipation (VISD) on magneto flow through a cross or secondary flow (CRF) in the way of streamwise. Utilizing the pertinent similarity method, the primary partial differential equations (PDEs) are changed into a highly nonlinear dimensional form of ordinary differential equations (ODEs). These dimensionless forms of ODEs are executed numerically by the aid of bvp4c solver. The impact of pertinent parameters such as the suction parameter, magnetic parameter, moving parameter, and viscous dissipation parameter is discussed with the help of plots. Dual solutions are obtained for certain values of a moving parameter. The velocities in the direction of streamwise, as well as cross-flow, decline in the upper branch solution, while the contrary impact is seen in the lower branch solution. However, the influence of suction on the velocities in both directions uplifts in the upper branch solution and shrinks in the lower branch solution. The analysis is also performed in terms of stability to inspect which solution is stable or unstable, and it is observed that the lower branch solution is unstable, whereas the upper branch one is stable.
Highlights
Introduction e investigations ofCRFS started after the pioneering research by Blasius [1] and Prandtl [2] on the laminar flow from a flat surface through a miniature viscosity
Jones [4] discussed the vital results involving the problem of cross or secondary flow (CRF), where he scrutinized the influence of sweepback on the boundary layer flow (BOUNLF). e three-dimensional flow past flat surface, as well as curved surfaces, was explored by Mager [5]
Weidman [7] found the outcomes of the flow over an exponentially stretching surface involving the power law at which CRFS is shaped via the activity of the transverse wall shearing
Summary
The linear stability analysis of the solutions achieved is carried out to test their stability. Because of such purpose, we cited the work concluded through the study of Merkin [33]. Using (27) into (22)–(26), we may achieve the following linearized eigenvalue problem: F′′′ + f0F′′ + Ff0′′ + βF′ − MF′ 0,. Because of the approach of linear stability analysis, the initial deceleration of disturbance, which is a physically reliable outcome (stable), is observed because of the positive coarse eigenvalue, while the initial development of disturbance is occurred owing to the negative coarse values which provide the unstable outcome. It is easy to note all of the positive smallest eigenvalues which indicates that the results achieved are stable and physically consistent. erefore, in the current problem, equations (28)–(32) are solved for the eigenvalue β with the new BC F′′ 1 by relaxing the condition that F′ ⟶ 0 as η ⟶ ∞
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