Statistical and numerical analysis of the flow of a special third grade fluid driven by a shrinking surface

Abstract

This paper explores the boundary layer flow and heat transfer characteristics of a special third-grade fluid over a shrinking surface, considering the effects of a magnetic field and thermal radiation. The mathematical formulation of the problem results in nonlinear PDEs, which are transformed into a system of coupled ODEs using Lie group analysis through a set of local similarity variables. The resulting ODEs are then solved numerically using MATLAB’s ‘bvp4c’ solver. Dual solutions are found within a specific range of suction and shrinking parameters. The sheet’s skin friction coefficient and heat transfer rates are analyzed for relevant physical parameters. The results show that the dual solutions bifurcate from a critical point, and no solutions are found beyond this point. A stability analysis is conducted to assess the stability of these two solutions based on the signs of the least eigenvalue. The least eigenvalues are determined numerically, indicating that the upper solution branch (USB) is stable. Thus, the features of the USB can be used to characterize the flow dynamics. Furthermore, multiple linear regression analysis is performed, and we successfully generate the estimated regression equations for the physical quantities for both solutions. The predicted results exhibit strong agreement with the numerical outcomes.