Thermohydrodynamics of Bödewadt hybrid-nanofluid flow in a horizontal magnetic field

Abstract

Since disks, rotating or stationary, are integral in many thermal systems, such as rotating heat exchangers, thermoelectric coolers, solar energy systems, and geothermal plants, this study scrutinizes the thermohydrodynamics of rotating hybrid nanofluid flow over a stretchable disk at rest. Further, the shape of the nanoparticles and the choice of base fluid substantially impact the enhancement of the heat transfer rate in various such thermal systems. Therefore, the present investigation considers engineered colloids made of four distinct (sphere, cylinder, column, lamina) titania and copper nanoparticle shapes in two different base fluids: water and engine-oil. The problem is formulated mathematically in an externally applied horizontal magnetic field and incorporating a non-Fourier heat flux model in the presence of solar radiation. Analogous to the case of the conventional vertical magnetic field, a similarity solution is also possible when magnetic forces act horizontally, both towards and opposite to the direction of rotation. Thus, the governing partial differential equations (PDEs) are first reduced to a set of highly non-linear and coupled ordinary differential equations (ODEs) via similarity transformations. These resulting set of ODEs are then solved numerically using a rapid and efficient spectral quasilinearization method (SQLM). Obtained results show that lamina-shaped $Ti{O}_2-Cu$/ engine-oil hybrid-nanofluid is a better choice than the other shapes of nanoparticle suspension in water. The horizontally applied magnetic field exhibits a stronger influence on the flow and heat transfer characteristics when compared to a vertical magnetic field. Additionally increasing the thermal relaxation parameter ${\alpha }_t$ from 0.1 to 0.35, the Nusselt number boost by 24.44%, 23.41%, 22.54%, and 17.93% for sphere, cylinder, column, and lamina nanoparticles of $Ti{O}_2-Cu$/water hybrid nanofluid. In the case of $Ti{O}_2-Cu$/engine-oil hybrid-nanofluid augmenting ${\alpha }_t$ from 0.1 to 0.35, the Nusselt number rise by 23.95%, 22.83%, 21.82%, and 15.89% for sphere, cylinder, column, and lamina nanoparticles. Based on their increasing $NS$ and $Be$ values, the various shapes follow the sequence: lamina ¡ column ¡ cylinder ¡ sphere. Furthermore, entropy generation can be optimized through the augmentation of solar radiation factors $Q_{\text{SR}}$, $\delta$, along with the reduction of the magnetic interaction parameter $M$, and by a proper selection of nanoparticle’s shape. Interestingly, dual solutions are observed for the case of a shrinking disk, i.e., for $S<0$, and a linear temporal stability analysis reveals that only one of these two branches, namely the first solution branch, is stable and the second branch unstable.