Numerical investigation of thermal performance in unsteady Casson hybrid nanofluid flow across rotating disks under variable Darcy resistance and Joule heating

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 \ f( η ) \ augments with growth in stretching parameter of the lower disk ( α ₁ ) , Reynolds number ( Re ) and suction factor ( S ) while declines with augmentation in stretching parameter of the upper disk ( α ₂ ) . Radial velocity \ f^( η ) \ augments on the interval 0 η 0.3 and it declines on the range 0.3<η 1.0 with growth in the stretching parameter of the lower disk ( α ₁ ) . Tangential velocity \ g( η ) \ augments with growth in suction parameter ( S ) and angular velocity at the lower disk ( Ω ₁ ) , while it declines with growth in Reynolds numbe r ( Re ) . Thermal profiles \ Θ ( η ) \ augment with growth in Eckert number ( Ec ) , heat source parameter ( H ) , suction parameter r ( S ) and stretching parameter of lower and upper disks ( α ₁\,\,& \,\,α ₂ ) . 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 0.0 Re 3.0 the percentage error in f^( 0 ) 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 ( Re ) the percentage error in Θ ( 0 ) between these results are 0.05 × 10− 5%, 1.3 × 10− 5%, 1.5 × 10− 5% and 1.7 × 10− 5%.