Dibjyoti Mondal, Abhijit Das

Abstract: Since non-Newtonian fluids are often encountered in engineering devices, the nonlinear boundary layer equations governing the flow and heat transfer properties of a non-Newtonian Williamson fluid over a stretching (c>0) or shrinking (c<0) sheet near the stagnation point are analyzed using two closely interrelated approaches. First, employing the shooting argument, it is proved that a unique solution exists when c∈ (-1,∞) and second, using the BVP4C solver in MATLAB, two different solution branches are reported on the interval [cT,-1], where cT is the bifurcation point. The cT values become more negative with increasing values of the Williamson parameter λ, marking the broadening of the solution range. Furthermore, the first solution branch continues for large positive values of c, whereas the second branch seems to cease at F''(0)=0 as c→-1. The smallest eigenvalue computed using temporal stability analysis of these solutions is found to be positive for the first branch, indicating that this branch is physically stable. These findings are relevant to various industrial processes involving non-Newtonian fluids, such as polymer processing and coating applications. Finally, an asymptotic expression is derived to provide insights into the behavior of large c.

Keywords: Williamson fluid, Existence-Uniqueness, Dual solutions, Stability analysis, Asymptotic analysis.

Date Published: December 1, 2025
DOI: 10.11159/jffhmt.2025.040

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