Homann modeling of thermodynamic optimization on yield-stress nanofluid with radiation and bioconvection effects

The enquiry inspects the movement of bioconvection through a nanoliquid near the stagnant flow subject to a stretchable surface. The effects of convective flow condition, radiative flow with rate of heat generation/absorption and chemical reaction are considered in energy and concentration equations. A well-known Buongiorno’s nanofluid model is applied to examine the effects of Brownian movement and thermophoresis characteristics. Irreversible analysis of the proposed system is also carried out. The modeled formulations having partial differential equations (PDEs) are transmuted through suitable transformations. Further, the set of transmuted ordinary differential equations (ODEs) can be employed by the analytical method recognized as the homotopic technique. The significance of numerous important variables in represented equations has been visually illustrated along with pertinent physical outcomes. The outcomes indicate that the rate of flow reduces due to the rising values of the Casson fluid variable [Formula: see text] while the Bejan profile is increasing with a bigger estimation of [Formula: see text]. The augmentation in the thermal radiation [Formula: see text] and Biot number ([Formula: see text] improved in the temperature field. However, a reduction in motile density due to the larger magnitude of the Bioconvection Lewis number [Formula: see text]. Comparison has been endeavored in the results of past publications.