On the similarity formulation for convective Casson and Casson–Jeffrey nanofluid flow over linear and nonlinear stretching surfaces

This work examines the mathematical structure and validity of the similarity formulation presented in recent literature for Casson and Casson–Jeffrey nanofluid flow over linear and nonlinear stretching surfaces with convective boundary conditions. Starting from the standard dimensional model, the similarity reduction of the thermal and species Robin boundary conditions is derived explicitly. The resulting analysis establishes the dimensionless boundary conditions together with the associated thermal and mass-transfer Biot parameters, thereby completing the similarity formulation of the convective boundary-value problem. The reconstruction further shows that the similarity boundary conditions in the literature cannot be obtained from the governing dimensional model. In addition, reconstruction of the Arrhenius reaction term demonstrates that the dimensionless concentration variable necessarily remains a multiplicative factor in the reduced species equation, while several ambiguities in the notation of the dimensionless parameters are also identified. The mathematically justified derivation herein involving Casson and Casson–Jeffrey nanofluid models can be used for future research, and thus the work is both scientifically relevant and timely.