Numerical solutions development for radiating flow of rheological nanoliquid invoking entropy optimization

• Magnetohydrodynamic bioconvection entropy induced flow of Power-law nanomaterial is considered. • Thermo-diffusion and diffusion thermo effects are discussed. • Random movement and thermophoresis diffusions are discussed. • Numerical results is computed through finite difference method. Thermal transport in rheological nanoliquid flow is very significant for electronic cooling equipment, heat exchange, cooling and heating system of buildings, nuclear reactor coolant, defense system, petroleum and engineering industries. In view of such considerations the bioconvective magnetohydrodynamic (MHD) reactive flow of power-law nanoliquid is considered. Porous space is analyzed through Darcy-Forchheimer relation. Significance of thermal enhancement is deliberated by random movement and thermophoresis diffusions. Thermal radiation, magnetohydrodynamics, heat source and dissipation are considered in energy expression. Entropy optimization with motile microorganism and chemical reaction is discussed. Thermo-diffusion and diffusion-thermo characteristics are considered. Related dimensionless partial differential systems (PDE's) are obtained through adequate variables. Computational simulations are developed by finite difference method (FDM). Interpretation of sundry parameters on entropy rate, microorganism field, liquid flow, concentration and thermal distribution is organized. It is found that larger Hartmann number corresponds to rise entropy rate and temperature whereas velocity reduces. Higher radiation lead to enhancement of temperature and entropy rate. Larger estimation of random movement and Eckert number intensify thermal field and Nusselt number. Reverse trends for concentration and thermal field through thermophoresis variable are noticed. Higher bioconvective Schmidt number decay microorganism field. Higher thermal transport rate is observed for heat generation and Dufour impact. Concentration enhances for Soret number, whereas reverse trend for Sherwood number is witnessed. Increasing effect of entropy rate for Brinkman number is detected.