A Comprehensive Study of Nonlinear Stretching Sheet in Stagnation Point Flow of Casson Fluid: Unveiling New Similarity Transformations

Abstract

Abstract This paper introduces novel similarity transformations to solve governing equations, addressing a common limitation in prior stretching sheet research. Past studies often employed similarity transformations with the variable η as a function of single independent variable, introducing errors due to overlooking two or more independent variables in the governing equations. Our newly derived transformations rectify this by incorporating all relevant independent variables, enhancing precision by converting differential equations that are partial into ordinary differential equations. This study explores the motion of a Casson fluid close to a point of stagnation along a nonlinearly stretched sheet, focusing on understanding the fluid's behavior in this specific configuration. To solve the modified equations resulting from the intricate interactions of the Casson fluid, a numerical method is developed utilizing shooting technique along with the 4-5th order Runge-Kutta Fehlberg scheme. The findings provide valuable perspectives on the behavior of Casson fluids in these circumstances, highlighting the thorough comprehension facilitated by the improved accuracy of the applied transformations.