Due to the various recent technological advancements and applications to human existence and productivity in industries, engineering, medicine, electronics, and others, researchers and scientists have devoted substantial attention to studies on microchannel flow systems, entropy generation, nanofluids, and generally nanotechnology in the past decades. Numerous applications have found Casson fluids to be one of the most commonly used non-Newtonian fluids. This study analyzes the variational influence of linear and nonlinear thermal radiation on Casson ternary hybrid nanofluid flow through an inclined micro-porous channel. The modeled equations for the flow system of the Casson ternary hybrid nanofluid \(Al_2 O_3\text {-}TiO_2\text {-}CuO\text {-}C_2 H_6 O_2\) were numerically analyzed using the Chebyshev collocation technique to scrutinize the impacts of different associated physical flow parameters including Hartmann number, Casson parameter, thermal radiation parameter, Forchheimer coefficient, Darcy number, heat source parameter, nanoparticles volume fraction, and Brinkmann number, on the velocity field, temperature profile, and entropy generation, illustrated through graphs and tables taking Rosseland’s linear and nonlinear heat flux into consideration. The iterative computations were done using a developed pseudocode implemented on the Wolfram language tool MATHEMATICA 11.0 software. Analyses showed that the internal heat source is more prominent in nonlinear thermal radiation than linear thermal radiation. Increasing the volume fraction of nanoparticles decelerates the fluid flow. This investigation finds its applications in various fields, including biomedical engineering, electronics cooling, chemical and process engineering, aerospace and automotive engineering, printing and coating technologies, pharmaceutical and cosmetic industries, sensors and actuators, and others.
