Rayleigh-Bénard convection in rotating nanofluids layer of porous and nonporous with feedback control

Rayleigh–Bénard convection is the heat transfer process due to buoyancy effect involved that occurred in a horizontal plane of nanofluids layer heated from below. The model for nanofluids includes the mechanisms of Brownian motion and thermophoresis. The onset of Rayleigh–Bénard convection in a horizontal rotating nanofluids layer and in a horizontal nanofluids layer saturated in a rotating porous medium with feedback control, internal heat source, magnetic field, double–diffusive coefficients, porosity, anisotropic, viscosity variation and thermal conductivity variation parameters are investigated theoretically. The confining lower and upper boundary conditions of the nanofluids layer are assumed to be free–free, rigid–free and rigid–rigid. A linear stability analysis of Rayleigh–Bénard convection is used, then the eigenvalue is obtained numerically using the Galerkin method and solved using Maple software. The impact of the feedback control, rotation, internal heat source, magnetic field, double–diffusive coefficients, porosity, anisotropic, viscosity variation and thermal conductivity variation parameters on the onset of convection in nanofluids system are analyzed and presented graphically. It is found that the impact of increasing the effects of feedback control, rotation, magnetic field, Dufour, porosity, anisotropic and thermal conductivity variation parameters help to delay the onset of convection in the system, meanwhile elevating the effects of internal heat source, Soret and viscosity variation parameters hasten the instability of the system. Further, the lower and upper boundary conditions in the present investigation are obviously found to be more stable in rigid–rigid boundaries compared to free–free and rigid–free boundaries.

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