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.

This article focused on framing the features of melting heat transfer on magnetohydrodynamic (MHD) Casson fluid flow in a porous medium influenced by thermal radiation. The present model is employed to simulate the viscoelastic behavior of fluid in the porous regime. Firstly, the governing partial differential equations are converted into ordinary differential equations via suitable similarity transformation and then solved the developed nonlinear equations by using Runge-Kutta Fehlberg-45 order method. A detailed analysis of certain parameters on the velocity, temperature, skin friction coefficient, and reduced Nusselt number are illustrated and examined. The results indicate that enlargement in M and Ω decline velocity profile but an opposite trend for temperature. Furthermore, an increment in R and M e results in uphill Nusselt number. The results of the present analysis are compared with the available works in particular situations and more agreement has been observed.