Reliability of two-dimensional steady magnetized Jeffery fluid over shrinking sheet with chemical effect

Abstract

Abstract A numerical framework is established for a two-dimensional steady flow of the magnetized Jeffery fluid model over elongated/shrinking sheets, with potential applications such as coating sheets, food products, fiber optics, drilling fluids, and the manufacturing processes of thermoplastic polymers. The model also demonstrates the influence of chemical reaction, magnetic field, and stability analysis which provide a novel contribution to this study. To ensure the ease and effectiveness of this analysis, we transform the set of difference equations governing the system into ordinary equations using the similarity transformation. The reliability of the solution is examined by using stability analysis. The Navier–Stokes equations have been transformed into self-similar equations by adopting appropriate similarity transformations and subsequently solved numerically using the bvp4c (three-stage Labatto-three-A formula) approach. The comparison between the derived asymptotic solutions and previously documented numerical results is quite remarkable. The self-similar equations display a duality of solutions within a limited range of the shrinking parameter, as observed from the data. For each stretching scenario, there is a unique solution. Hence, an examination of temporal stability has been conducted through linear analysis to establish the most fundamentally viable solution. The determination of stability in the analysis is based on the sign of the smallest eigenvalue, which indicates whether a solution is unstable or stable. The analysis of stability reveals that the first solution, which describes the primary flow, remains stable. Through the utilization of graphs, we thoroughly examine and discuss the influence of emerging factors. The numerical results obtained from this analysis demonstrate multiple solutions within a certain range of M 1 ≥ M ci {M}_{1}\ge {M}_{{ci}} , i = 1 , 2 , 3 i=1,2,3 , and no solution in the range M 1 < M ci {M}_{1}\lt {M}_{{ci}} . M ci {M}_{{ci}} denotes the critical values, which increase as the quantities of Sc {\rm{Sc}} increase from 0.3 to 0.9. Similarly, multiple solutions exist for λ ≥ λ ci \lambda \ge {\lambda }_{{ci}} , i = 1 , 2 , 3 i=1,2,3 , and no solution in the range λ < λ ci \lambda \lt {\lambda }_{{ci}} is observed.