Entropy optimization and Prandtl-Eyring non-Newtonian fluid flow with second-order slip conditions past a curved Riga sheet; numerical simulation

The non-Newtonian (NN) Prandtl-Eyring fluid (PEF) model can be used to optimize conditions for processing, ensure substance high quality and consistency, and anticipate melted polymer flow behavior. This paper looks into an intriguing feature of irreversibility estimation through NN-PEF flow over a curved Riga surface. The impact of second-order slip conditions, thermal radiation, and exponential heat source/sink are also elaborated. The flow equations of NN-PEF have been reformulated into a dimensionless representation of differential equations (DEs) with an application of similarity conversions. The obtained lowest-order differential equations are numerically solved through the PCM (parametric continuation method). For accuracy of the results, the outcomes are compared to both experimental and theoretical results. The relative percent error between the present findings and the published numerical results at Re = 5000 is 0.71094 %. The rate of heat transfer (W/m²K) enhances from 4238.0724 to 44390.4205 at Re = 1594 to 440. The relative error between published experimental and present results is about 0.0029 % at Re = 440, which ensures the reliability of the proposed model and applied methodology. The velocity field of PEF is significantly boosted with the positive variation in 1st and 2nd order slip parameters. The influence of the Brinkmann number and heat radiation factor is enhanced, while the consequences of the temperature ratio parameter drop the rate of entropy generation in the system.