Blowing and multiple slip effects on bio-nano-convection flow in porous media within the gap of a rotating cone-disc system

Abstract

Fluid flow inside the gap between a rotating cone and a disc has significant applications in bio-chemical engineering, biotechnological (biofuel) processing and materials science. In these areas, engineers are continuously exploring the combination of nanofluids, bioconvection mechanisms and other features (e.g. porous filtration materials) to optimize (flow) performance. Motivated by these applications, the present article describes a mathematical model for simulating nanofluid transport with bioconvection micro-organisms inside the conical gap between a rotating cone-disc system containing an incompressible, sparse Darcian porous medium. Buongiorno's two-component nanoscale model is deployed for the nanofluid and Kuznetsov gyrotactic bioconvection model utilized for the micro-organism self-propulsion. The mathematical model also features multiple walls slip effects and Stefan blowing boundary conditions. By employing coordinate transformations derived via group theory methods, the governing transport equations are transformed into a set of similarity equations with coupled boundary conditions. These transformed similarity equations are then solved numerically with an efficient finite difference method available in the MATLAB solver “bvp4c”. Some of the results reported are verified with special cases from the literature. Extensive graphical visualization of the key flow characteristics is included. Four physical cases are considered, namely the static disc with rotating cone, static cone with rotating disc, disc-cone in co-rotation, and disc-cone in counter rotation. Smaller gap angles are observed to intensify heat, NPVF transport rates and wall motile microorganism flux rates. Axial velocity attains the highest magnitude with large centrifugal force generated by the rotation of cone. Thermal slip induces a decrement in fluid temperature and associated thermal boundary layer thickness. Greater Stefan blowing leads to an increment in velocity components, fluid temperature, nanoparticle concentration (volume fraction) and gyrotactic microorganism concentration (density number) for all 4 cases examined.