Discov Nano. 2026 Jun 11;21(1):257. doi: 10.1186/s11671-026-04713-4.
ABSTRACT
The findings of this study have significant implications for a wide range of engineering applications that include cooling of rotating disk surfaces, the optimization of chemical reactors, and the design of filtration systems, where the synergistic use of variable porous media and hybrid nanofluids offers a pathway to enhanced performance. Keeping these substantial applications in perspective, the present study examines the optimization of thermal transport in an unsteady Casson hybrid nanofluid flowing through a variable porous medium between two rotating disks. The flow is influenced by inertial effects, Joule heating, viscous dissipation, and time-dependent heat generation and absorption effects. The modeled equations are solved through the Homotopy Analysis Method (HAM) in dimensionless form. It is deduced in this investigation that axial velocity [Formula: see text] augments with growth in stretching parameter of the lower disk [Formula: see text], Reynolds number [Formula: see text] and suction factor [Formula: see text] while declines with augmentation in stretching parameter of the upper disk [Formula: see text]. Radial velocity [Formula: see text] augments on the interval [Formula: see text] and it declines on the range [Formula: see text] with growth in the stretching parameter of the lower disk [Formula: see text]. Tangential velocity [Formula: see text] augments with growth in suction parameter [Formula: see text] and angular velocity at the lower disk [Formula: see text], while it declines with growth in Reynolds numbe r[Formula: see text]. Thermal profiles [Formula: see text] augment with growth in Eckert number [Formula: see text], heat source parameter [Formula: see text], suction parameter r[Formula: see text] and stretching parameter of lower and upper disks [Formula: see text]. A close agreement is observed between the HAM solutions and the numerical Runge-Kutta shooting results, confirming the accuracy, reliability, and validity of the HAM-based solutions. For variations in Reynolds number in the range [Formula: see text] the percentage error in [Formula: see text] between HAM and Runge-Kutta shooting results are 0.0%, 2.4 × 10– 5%, 2.2 × 10– 5% and 1.5 × 10– 5%. Moreover, for the same range of [Formula: see text] the percentage error in [Formula: see text] between these results are 0.05 × 10– 5%, 1.3 × 10– 5%, 1.5 × 10– 5% and 1.7 × 10– 5%.
PMID:42274958 | DOI:10.1186/s11671-026-04713-4
