Mixed Bioconvective Flow of Williamson Nanofluid Over a Rough Vertical Cone

This paper investigates the mixed bio-convection in a flow of Williamson nanofluid with liquid oxygen diffusion. The main innovation is to study the bio-convection and surface roughness in a flow of non-Newtonian Williamson nanofluid via a nonsimilar approach. The applications of bio-convection in boundary layer analysis include biological sciences, drugs and biotechnology, wastewater treatment, biofuels processing, and food production. The nonlinear coupled partial differential equations are the governing equations of the given problem. Mangler’s nonsimilar transformations are utilized to get a non-dimensional form of governing equations. For mathematical simplifications, implicit finite difference scheme and Quasilinearization technique are used. Further, an analysis is carried out for various controlled parameters, and the results are depicted through graphs. The heat transfer rate for nanofluid is approximately about 4% more than that of Williamson nanofluid. Moreover, the heat transfer rate for a permeable surface (suction case) is about 44% more than for an impermeable surface. The wall suction augments the mass transfer rate of liquid oxygen, and it is about 140% for rough surface compared to the smooth surface. Microorganism’s density in the fluid is more for lower values of bio-convection Lewis and Peclet numbers. The microorganism’s density number enhances by about 78% when the value of the Peclet number increases from 1 to 2. The results are compared to earlier published papers and have an excellent agreement with each other.