Coupling fluid dynamics and statistical inference: A casson MHD nanofluid model with Marangoni effects over an inclined surface

This study presents a numerical and statistical investigation of Casson magnetohydrodynamic (MHD) nanofluid flow with Marangoni convection over an inclined surface, incorporating several complex physical effects. The Casson fluid model accounts for shear-thinning behavior, while nanoparticle dynamics are captured through Buongiorno’s model, considering Brownian motion and thermophoresis. Additional phenomena such as thermal radiation, Joule heating, viscous dissipation, internal heat generation, and an Arrhenius-type chemical reaction with activation energy are also included. The governing nonlinear boundary layer equations, formulated via similarity transformations, are solved using the fourth-order Runge-Kutta methodology coupled with a shooting technique. To reinforce the numerical findings, statistical analysis is conducted through Pearson correlation coefficients and multiple linear regression. These techniques quantify the interrelationships among key dimensionless parameters and their influence on output quantities such as skin friction, Nusselt number, and Sherwood number. Diagnostic tools including residual plots, Q−Q plots, and leverage statistics are employed to verify model assumptions and assess statistical robustness. The results show that increasing magnetic field strength and Casson parameter suppresses fluid velocity due to enhanced resistive forces, while internal heat generation, radiation, and viscous dissipation significantly elevate the temperature field. Brownian motion and thermophoresis parameters are found to play opposing roles in nanoparticle concentration distribution. Weak multicollinearity among predictors also supports the stability of the regression models. This combined numerical statistical framework offers valuable insights into optimizing non-Newtonian nanofluid systems subjected to thermally and chemically complex conditions over inclined geometries.