Impact of Radiation and Slip Conditions on MHD Flow of Nanofluid Past an Exponentially Stretched Surface

The paper’s energy equation places the radiation parameter R as a positive contribution to the coefficient of θ″ (see equations (9)–(10)), so increasing R increases the effective diffusion p, which, under the standard boundary conditions, raises the temperature profile and reduces the wall heat-flux magnitude; hence Re_x^{-1/2} Nu_x must decrease with R. In contrast, the paper asserts the opposite—claiming θ decreases and the Nusselt number increases with R (conclusion bullets and Table 4). Moreover, in the bvp4c transcription, the θ″-equation is miswritten: the coefficient multiplying θ″ in (9) is used as a multiplier rather than a divisor, and 4/3 is mistakenly replaced by 3/4; this inversion explains the incorrect R-trends (bvp4c Algorithm subsection). The model provides a correct comparison-principle proof (θ increases in R, decreases in δ), a coherent phase-plane uniqueness picture, and numerics consistent with the analysis. Key places in the PDF establishing these points: governing ODEs and BCs (equations (9)–(10)) ; definitions of the skin-friction and Nusselt scalings (equation (13)) and the erroneous bvp4c θ″ line ; narrative claims for the R-effect on θ and Nusselt in the results/conclusion sections .