Magneto-Convection in Casson Nanofluids with Three Different Boundaries

Abstract

This paper is centered on the numerical and analytical solution of a non-Newtonian Casson nanofluid flow problem in the presence of vertical magnetic field. Brownian motion and thermophoretic forces are introduced due to the addition of nanoparticles and; the magnetic field adds an extra Lorentz’s force term along with Maxwell’s equations. Using Normal mode technique, the system of PDEs with the corresponding boundary conditions is reduced to a system of ODEs. The Galerkin-type weighted residual method is used to get a numerical solution for the formulated differential system. Numerical simulation is carried out to make the investigation helpful for practical applications like nano-drug delivery systems as in clinical and medical research, magnets are extremely important to create three-dimensional images of anatomical and diagnostic importance from nuclear magnetic resonance signals. Comparisons of the numerical results with previously published results are made and fine agreements are noted for the considered values of the parameters. The impact of magnetic field, Casson parameter and nanoparticle parameters are discussed for different types of boundary conditions (free–free, rigid-free and rigid–rigid). The system is found to be the most stable for more realistic rigid–rigid boundaries out of three different boundaries. For the purpose of numerical computations, blood has been considered as the Casson nanofluid. The novelty of the work lies in the fact that the strong stabilizing influence of Lorentz force on blood-based Casson nanofluid enables the red blood cells to pass through the blood in a more streamlined fashion which may play a significant role in human health, more specifically in the cardiovascular system. Further, although the Casson parameter hastens the onset of convection yet Casson fluids are more stable as compared to regular fluids.