A unified compatibility method for exact solutions of non-linear flow models of Newtonian and non-Newtonian fluids

•Compatibility criteria are established for higher order ordinary differential equations to be compatible with lower order ordinary differential equations.•A connection is made with generalized groups through conditional symmetries.•New exact solutions of non-linear flow problems arising in the study of Newtonian and non-Newtonian fluids are derived.

Criteria are established for higher order ordinary differential equations to be compatible with lower order ordinary differential equations. Necessary and sufficient compatibility conditions are derived which can be used to construct exact solutions of higher order ordinary differential equations subject to lower order equations. We provide the connection to generalized groups through conditional symmetries. Using this approach of compatibility and generalized groups, new exact solutions of non-linear flow problems arising in the study of Newtonian and non-Newtonian fluids are derived. The ansatz approach for obtaining exact solutions for non-linear flow models of Newtonian and non-Newtonian fluids is unified with the application of the compatibility and generalized group criteria.