The fluid flow through inclined plates has several applications in magneto-aerodynamics, materials processing and magnetohydrodynamic propulsion thermo-fluid dynamics. Inspired by these applications, the rate of entropy production in a bio-convective flow of a magnetohydrodynamic Williamson nanoliquid over an inclined convectively heated stretchy plate with the influence of thermal radiation, porous materials and chemical reaction has been deliberated in this paper. The presence of microorganisms aids in stabilizing the suspended nanoparticles through a bioconvection process. Also, the thermal radiation assumed an optically thick limit approximation. With the help of similarity transformations, the coupled partial differential equations are converted to nonlinear ordinary differential equations and the resulting model is numerically tackled using the shooting method. The influences of the determining thermo-physical parameters on the flow field are incorporated and extensively discussed. The major relevant outcomes of the present analysis are that the upsurge in values of Schmidt number decays the mass transfer characteristics, but the converse trend is depicted for boost up values of the thermophoresis parameter. Enhancement in bioconvection Peclet and Schmidt numbers deteriorates the microorganism density characteristics. Further, the upsurge in the Williamson parameter declines the Bejan number and irreversibility ratio.

The present work concentrates on the two-dimensional steady incompressible flow of an Oldroyd-8 constant fluid between vertical plates influenced by a magnetic field. The cross diffusive and second-order chemical reactions are incorporated into the study. The homotopy analysis method (HAM) is used to obtain the series solutions of the transformed system of nonlinear equations. The effects of these parameters on the dimensionless velocity, temperature, concentration, skin friction, and Nusselt and Sherwood numbers are also investigated for various values of relevant parameters affecting the flow and heat transfer phenomena. The most relevant outcomes of the present study are that enhancement in magnetic field strength undermines the flow velocity, temperature, and concentration establishing thinner related boundary layer. Another important outcome is that an increase in the Dufour parameter upsurges the rate of heat transfer at the wall y = 0 while peters out at y = 1. Finally, the second-order chemical reaction parameter reduces the concentration distribution. The novel outcomes of this investigation will be helpful in the field of the aerosol technology.