Radiative heat and mass transfer of second-grade nanofluid slip flow with variable thermal properties

The behavior of second-grade nanofluid is investigated in this work using entropy formation, thermal radiation, and changing thermal conductivity. The objective of this study is to provide deeper insights into how these variables influence fluid flow characteristics and heat transfer in nanofluid. To assess their impact on fluid dynamics and thermal behavior, the Tomson–Troian velocity slip condition and temperature slip boundary conditions are incorporated to examine mass and heat transport. The governing partial differential equations are simplified and effectively analyzed by transforming them into a collection of ordinary differential equations employing stream functions and similarity transformations. The shooting approach is used to produce numerical solutions for the physical phenomena, with the addition of the Newton–Raphson and Keller-box scheme for improved accuracy and convergence. This method also assesses the impact of physical parameters on temperature, velocity, and mass transfer sketches graphically for a clear understanding of their behavior. These parameters include heat production, variable thermal conductivity, the second-grade fluid parameter, the Eckert number, the Brownian motion, the Prandtl number, thermophoresis, and the Lewis number. This study found that the raising parameter for variable thermal conductivity enhances both temperature and velocity profiles. For the maximum second-grade fluid parameter, the temperature profile diminishes, while the velocity profile exhibits an upward trend. The Eckert number enhances the concentration and temperature profiles. The velocity profile of second-grade nanofluid decreases with increasing Prandtl numbers. Higher temperature-dependent density results in the greatest fluid temperature and concentration values. Greater Brownian motion results in improved mass and heat transmission magnitudes. The Sherwood number, Nusselt number, and skin friction coefficient decrease as the Prandtl number rises, but increase when the Lewis number rises.