Radial distribution effects of surface waviness on rotating disk flow and heat transfer in porous media

This study investigates the effects of radial placement of surface waviness on momentum and thermal transport in rotating disk boundary layers embedded in a porous medium. Rather than treating waviness solely as a geometric enhancement strategy, the present work focuses on identifying where along the disk surface waviness strongly alters the coupled transport processes and how porous resistance modulates these effects. Three different wavy surface profiles are defined: case I (constant amplitude), case II (amplitude proportional to radius), and case III (amplitude decreasing linearly with radius). The governing continuity, momentum, and energy equations are converted into a non-similar system using dimensionless variables and solved numerically with the Keller–Box method in MATLAB. Results show that cases I and II produce stronger effects than case III because surface waviness is present in the outer disk region, where rotational motion remains relatively strong even under porous resistance. Although Darcy effects reduce radial flow, circumferential motion persists near the outer radius, making this region more responsive to surface geometry. In case I, the constant waviness ensures continuous interaction across the entire disk, influencing both weak and strong flow regions and leading to noticeable changes in shear and heat transfer. In case II, waviness increases toward the outer radius, aligning maximum surface disturbance with the most dynamically active region, which enhances momentum and thermal transport. In contrast, case III places strong waviness near the center, where the flow is weak and still developing, while reducing it in the outer region where it would be most effective.