COMPATIBILITY AND GENERALIZED GROUP APPROACH FOR NOVEL SOLUTIONS IN NONLINEAR FLUID DYNAMICS: APPLICATIONS TO REMARKABLE PRANDTL BOUNDARY LAYER EQUATIONS

An effective compatibility criterion is implemented to ensure that higher-order nonlinear ordinary differential equations align with a linear first-order ordinary differential equation. The proposed methodology facilitates the derivation of necessary and sufficient compatibility conditions, enabling precise solutions for ordinary differential equations of higher-order. Additionally, a connection is established with the compatibility analysis of generalized groups. Employing the compatibility and generalized group approach, novel solutions are developed for the Prandtl boundary layer equations in scenarios involving two-dimensional and radial flows with uniform mainstream velocity. Consideration is given to various physical aspects of the Prandtl boundary layer theory. By applying the necessary and sufficient compatible conditions, new closed-form solutions are generated for diverse nonlinear problems, demonstrating the practical application of Prandtl's boundary layer theory. Consequently, the outcomes attained are particularly relevant for investigating exact solutions to nonlinear problems related to the boundary layer theory of both Newtonian and non-Newtonian fluids.