A Realistic Study of the Rayleigh-B?nard Problem in the Newtonian Nanofluids with a Uniform Heat Source: Free-Free Case

The main purpose in this investigation is to use the Buongiorno mathematical model for studying the effect of an internal heat source which produces a constant volumetric heat on the onset of convective instability in a confined medium, filled of a newtonian nanofluid layer and heated from below, this layer is assumed to have a low concentration of nanoparticles. The linear study in the free - free case where the tangential stresses of viscous friction are zero on the boundaries, shows that the thermal stability depends of the volumetric heat delivered by the internal source, the Brownian motion, the thermophoresis and other thermophysical properties of nanoparticles. The studied problem will be solved analytically by converting our boundary value problem to an initial value problem, after this step we will approach the searched solutions with polynomials of high degree.