Near Continuum Flows Over a Rotating Disk

We analyze the near continuum flow created by a rotating disk facing a stagnant gas. The flow-field properties change from the traditional continuum solutions, due to the introductions of new velocity-slip and temperature-jump boundary conditions. To compute the velocity profiles, a self-similar transformation simplifies the Navier-Stokes equations into a system of ordinary differential equations. The introduction of new boundary conditions generates new parameters which can be adjusted at different degrees of rarefaction. Shooting methods are adopted to solve the differential equations with the new boundary conditions. Based on the solved velocity profiles, exact solutions for the temperature distribution are obtained. The gas temperature at the disk surface shifts towards the free stream temperature, while the heat flux between the gas and surface is reduced. Stream function solutions for the flow at the disk surface are presented to demonstrate the effects of the slip boundary conditions. The torque generated by the disk is obtained with different disk rotating speed, and the gas at the disk surface has different slip velocities.