Influence of magnetic field on the onset of nanofluid convection induced by purely internal heating

This note considers the effect of magnetic field on the onset of convection in a nanofluid layer induced by purely uniform internal heating. The nanofluid layer bounded between two rigid surfaces and also incorporates the effect of Brownian motion along with thermophoresis. The zero nanoparticle flux condition under the thermophoretic effects is considered at the boundaries. The stability condition are found for two sets of thermal boundary conditions namely, case (i) both boundaries isothermal and case (ii) lower insulated and upper isothermal using the higher order Galerkin method. The purely internal heating problem shows that there is no applied temperature difference across the layer and so the external Rayleigh number is no longer appropriate. Therefore, here the relevant parameter is an internal Rayleigh number, one based on the heat source strength. It is found that the critical internal Rayleigh number increases with an increase in the magnetic Chandrasekhar number, while decreases with an increase in the Lewis number, the nanoparticle Rayleigh number and the modified diffusivity ratio. A comparative study between the previously published results and the present results for a special case is found to be in good agreement.