**2. Grooved Rotating-Disk System Configuration**

The schematic of a simplified open grooved two-disk system model is presented in Figure 1. The flow field in the gap is described by a cylindrical coordinate system (*r*, θ and *z*), indicating the radial, the azimuthal, and the axial coordinates, respectively. The disk with the radial grooves rotates axially with an angular velocity ω, and the stationary disk is ungrooved. There is a gap H between two disks. The groove area is defined by the groove number Ng and the circumferential angle of each single groove. The groove depth of the textured disk is h, and *r*1 and *r*2 represent the inner and the outer radii of the disks, respectively. A dimensionless radial location *r*/*r*2 is defined to analyze the parameter effects.

An oil volumetric flow rate *Q,* which is assumed to be a constant temperature (320 K), is prescribed at the inner radius surface as the inlet boundary condition, while an ambient pressure is prescribed at the outer radius surface as the outlet boundary condition. For the heat transfer process, the thermal effect of the system is coupled in the model by considering the heat conduction of disks and the heat convection between fluid and disks. In spite of a rather small gap and the viscous shear of the fluid, the viscous heating effect of oil is omitted, since the oil is supplied continuously at the inner radius, and the heat of viscous friction is taken away. The stationary ungrooved disk is assumed to be a heat source with a constant heat flux uniformly distributed on the surface. A stationary wall boundary condition is specified on the surface of the stationary disk. The surface of the rotating grooved disk is specified as an adiabatic wall boundary condition with a constant angular speed.

**Figure 1.** Schematic of the grooved rotating-disk system.

#### **3. Grooved Rotating-Disk System Modeling**
