Effects of Magnetic Field and Internal Heat Generation on the onset of Rayleigh-Bénard Convection in Nanofluid

Abstract

The present paper deals with a Rayleigh-Bénard convection in a micropolar fluid, confined between two horizontal surfaces subjected to an imposed time-periodic boundary temperature (ITBT) along with internal heating effects. In the case of ITBT, the temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent oscillatory part. The temperature of both walls is modulated in this case. The disturbance is expanded in terms of power series of amplitude of convection, which is assumed to be small. The Venezian approach is adopted in arriving at the critical Rayleigh number, correction Rayleigh number and wave number for small amplitude of ITBT. Three cases of oscillating temperature field are examined: (a) symmetric, so that the wall temperatures are modulated in phase, (b) asymmetric, corresponding to out-of phase modulation and (c) only the lower wall is modulated. The temperature modulation is shown to give rise to sub-critical motion. The shift in the critical Rayleigh number is calculated as a function of frequency and it is found that it is possible to advance or delay the onset of convection by time modulation of the wall temperatures. It is shown that the system is more stable when the boundary temperatures are modulated in out-of-phase.