Regression analysis of thermophysical effects in casson nano fluid flow: Entropy generation, magnetic induction, and mixed convection in an inclined geometry

This article examines the enhancement of entropy generation in Casson’s non-Newtonian fluid flow, affected by an induced magnetic field and mixed convection, within an inclined pipe, considering the significant roles of Brownian motion and Thermophoresis. Temperature control in biomedical devices, polymer processing, geothermal systems, energy-efficient heat exchangers, electronic cooling, and industrial flows, including magnetic and non-Newtonian fluid dynamics, are a few uses for this study. A computational model for non-linear ODEs is developed to obtain numerical results for the flow problem. The results are compared to the fourth-order Runge-Kutta technique to ensure their validity. Several factors influencing fluid dynamics, mass transfer, and heat transfer are examined using graphical and tabular representations. Expressions for the Bejan number, coefficient of skin-friction, and the mass and heat transfer rates are also calculated. The results clearly show that concentration reaches a numerical maximum near the wall as the inclination angle rises. It is also noted that the Bejan number reaches a local maxima value when r is around 0.3. A quadratic regression model is implemented to calculate skin friction coefficients value as well as mass and energy transfer rates to better understand evolving physical quantities relevant to engineering.