Numerical study of heat transfer and viscous flow in a dual rotating extendable disk system with a non-Fourier heat flux model

Nonlinear, steady-state, viscous flow, and heat transfer between two stretchable rotating disks spinning at dissimilar velocities are studied with a non-Fourier heat flux model. A nondeformable porous medium is intercalated between the disks and the Darcy model is used to simulate matrix impedance. The conservation equations are formulated in a cylindrical coordinate system and via the von Karman transformations are rendered into a system of coupled, nonlinear ordinary differential equations. The emerging boundary value problem is controlled by number of dimensionless parameters, that is, Prandtl number, upper disk stretching, lower disk stretching, permeability, non-Fourier thermal relaxation, and relative rotation rate parameters. A perturbation solution is developed and the impact of selected parameters on radial and tangential velocity components, temperature, pressure, lower disk radial, and tangential skin friction components and surface heat transfer rate are visualized graphically. Validation of solutions with the homotopy analysis method is included. Extensive interpretation of the results is presented which are relevant to rotating disk bioreactors in chemical engineering.