Entropy and thermal performance on shape-based 3D tri-hybrid nanofluid flow due to a rotating disk with statistical analysis

Fluid flow across a rotating disk has significant technical and industrial applications, including rotors, turbines, fans, centrifugal pumps, spinning disks, viscometers, etc. The impact of different-shaped nanoparticles immersed in the fluid controlled the thermophysical characteristics of the fluid, which were utilized in several sectors to accelerate thermal advancement. In the present problem, the tri-hybrid nanofluid flows over a rotating disk with three different shapes, namely spherical, cylindrical, and platelets, respectively, for Al₂O₃, multi-layered carbon nanotubes, and graphene nanoparticles immersed in the base fluid water. Under convective conditions, the tri nanofluid’s thermal expansion is more significant when combined with Joule heating, Cattaneo-Christov heat flux, and nonlinear thermal radiation. The Galerkin Finite Element Method is used to solve the simplified form of PDEs after a similarity transformation is introduced to convert them into ODEs. The skin friction coefficient and the heat transfer rate are subjected to a quadratic regression analysis; the results are shown in tables. Compared to the base fluid, the Nusselt number reveals an improvement of around 5.72% for nanofluid, 7.35% for hybrid nanofluid, and 17.18% for tri-hybrid nanofluid when the strength of radiation parameter and Brinkman number is raised. Platelet-shaped nanoparticles observed a significant tendency to enhance the rate of heat transfer, which is more prominent for the tri-hybrid nanofluid than the hybrid and mono nanofluids. Each graph features a comparison of ternary hybrid, hybrid, and mono nanofluid with other significant physical parameters. It was noted that the entropy of the system significantly intensified with Reynolds number and temperature ratio, while it was controlled by radiation parameters. The uses of ternary nanofluids include energy storage devices, adsorbents, sensors, imaging, catalysts, therapeutic activity, and more.