MAGNETIC CONVECTION IN A NONUNIFORMLY ROTATING LAYER OF CONDUCTIVE NANOFLUID IN AN EXTERNAL HELICAL MAGNETIC FIELD

Investigating the effects of Brownian diffusion and thermophoresis of nanoparticles on the forced convection of nanofluids in heat exchangers is a critical and relevant area of research. Many researchers [1] have investigated convective instability in nanofluids, considering the effects of Brownian diffusion and thermophoresis. There is currently a gap in the literature regarding magnetic convection in nonuniformly rotating media. This issue has been partially addressed in articles [2-4], focusing on various astrophysical applications. Paper [5] explored the idea of using metallic nanofluids for laboratory simulations of magnetorotational instability. The study specifically examined the influence of the Hall current on thermal instability in a nonuniformly rotating nanofluid layer subjected to a constant magnetic field. Using the local WKB approximation, in [6] was derived a dispersion equation describing the evolution of small perturbations in a thin nanofluid layer. Specifically, it was obtained a dispersion equation for magnetorotational instability (MRI) in the absence of a temperature gradient but with a gradient in nanoparticle concentration. For large Hall parameter values (), it was determined an expression for the critical Rossby number (), which defines the threshold for nonuniform rotation profiles (). The investigation of paper [5] led to the following conclusions: