Implication of Bio-convection and Cattaneo-Christov heat flux on Williamson Sutterby nanofluid transportation caused by a stretching surface with convective boundary

This theoretical and computational analysis reveals the thermal characteristics for the flow of Williamson Sutterby nanofluid through the Darcy–Forchheimer sponge medium over an extending surface. The Cattaneo-Christov heat flux, radiation heat flux, and convective boundary are taken into account. Moreover the impacts of bio-convection of self-propelled micro-organisms and electromagnetic fields are considered. The amalgamation of Sutterby–Williamson with slight homogeneous diffusion of nano-particles and micro-organism exposes the novelty of this work. The principal objective pertains to avoid the possible settling of nano-entities to given effective heat transportation. The physical problem is formulated in the form of partial differential equations which are then altered to a system of ordinary differential equations. The influences of emerged parameters on the physical quantities of interest are evaluated by utilizing the Runge–Kutta method. The parameters of Sutterby fluid, inertia friction and porosity decelerate the flow but the parameters of electric field and mixed convection are directly responsible to promote the velocity of fluids. It is noted that fluid accelerates for Williamson model λ≠0. The parameter of the electric field, Brownian motion, radiations, thermophoresis, and Eckert number raises the temperature of the fluid. The heat transfer rate at the surface recedes in magnitude for larger b (Cattaneo-Christov diffusion). The motile density number increases with the upsurge values of Lb, Pe and Ω. Two sets of graphical outputs are presented for Williamson fluid parameter λ(λ=0,λ=0.5).