Computation of von Karman thermo-solutal swirling flow of a nanofluid over a rotating disk to a non-Darcian porous medium with hydrodynamic/thermal slip

Motivated by recent trends in spin coating operations in chemical engineering which are exploiting nanomaterials, the present article investigates theoretically and numerically the steady mass and heat transfer in von Karman swirling slip flow of a nanofluid from a rotating disk touching to a homogenous non-Darcy porous medium. The porous medium is simulated with a Darcy-Forchheimer-Brinkman model. To track the thermophoresis and Brownian movement of the nanoparticles, the Buongiorno nanoscale model is used. von Karman similarity variables are deployed to transform the partial differential conservation equations into a system of highly coupled, nonlinear, dimensionless ordinary differential equations (ODE's). These similarity boundary layer equations, i. e., continuity, momentum, energy and nanoparticle concentration (volume fraction), are solved with bvp4c shooting quadrature in MATLAB. Validation with earlier studies is included. Further verification with an Adams-Moulton predictor-corrector method is conducted. The influence of velocity (momentum) slip coefficient, thermal slip, Darcian bulk drag parameter (inverse permeability), Forchheimer inertial parameter, Brownian motion parameter m Schmidt number, thermophoresis parameter and Prandtl number on radial, tangential (azimuthal) and axial velocity components, temperature and nanoparticle concentration is visualized graphically. The distributions for skin friction component and Nusselt number are also computed. Radial, axial and tangential velocities are reduced with increasing Forchheimer inertial drag and hydrodynamic wall slip, whereas they are elevated with increasing permeability (decreasing inverse Darcy parameter). Thermal and nanoparticle concentration boundary layers are also markedly modified with an increment in Forchheimer inertial parameter, Schmidt number, Prandtl number, thermophoresis and Brownian motion parameters .