Rayleigh-Bénard Convection for Nanofluids for More Realistic Boundary Conditions (Rigid-Free and Rigid-Rigid) Using Darcy Model

Abstract

In this article, Rayleigh-Bénard convection for nanofluids for more realistic boundary conditions (rigid-free and rigid-rigid) under the influence of the magnetic field is investigated. Presence of nanoparticles in base fluid has introduced one additional conservation equation of nanoparticles that incorporates the effect of thermophoretic forces and Brownian motion and the inclusion of magnetic field has introduced Lorentz’s force term in the momentum equation along with Maxwell’s equations. The solution of the Eigen value problem is found in terms of Rayleigh number by implementing the technique of normal modes and weighted residual Galerkin approximation. It is found that the stationary as well as oscillatory motions come into existence and heat transfer takes place through oscillatory motions. The critical Rayleigh number for alumina water nanofluid has an appreciable increase in its value with the rise in Chandrasekhar number and it increases moderately as we move from rigid-free to both rigid boundaries. The effect of different nanofluid parameters on the onset of thermal convection for two types of boundaries is investigated.

Keywords

• Darcy’s law
• Brownian motion
• Magneto-convection
• Chandrasekhar number