Thermal instability in a nanofluid layer with a vertical magnetic field

The combined effect of a vertical magnetic field and the boundaries on the onset of convection in an electrically conducting nanofluid layer heated from below is investigated using linear stability theory. The employed model incorporates the effects of Brownian motion and thermophoresis. The boundaries are considered to be either rigid or free. The eigenvalue problem is solved analytically for free-free boundaries and numerically for rigid-rigid and lower-rigid and upper-free boundaries using the Galerkin technique. Numerical results are presented for alumina-water nanofluid.