Convection In Nanofluid Layer Research Articles

On the Oscillatory Convective Instability in Nanofluid Layer with Temperature Dependent Viscosity

In the present paper, the problem of thermal convection in nanofluid layer heated from below with temperature dependent viscosity is studied mathematically for general boundary conditions, when the instability sets in as oscillatory convection. The expressions for Rayleigh numbers for exponential temperature dependent viscosity variation are derived using Galerkin method from the eigenvalue problem for each combination of rigid (the surfaces with non-slip condition) and dynamically free (the surfaces with stress free condition) boundaries. The effects of viscosity variation parameter, Lewis number, concentration Rayleigh number, modified diffusivity ratio and Prandtl number on the onset of oscillatory convection for each case of boundary conditions are investigated numerically. It is observed that the exponential variation of temperature dependent viscosity has stabilizing effect on the onset of oscillatory convection in nanofluid layer for each case of boundary conditions. However, the Lewis number and the concentration Rayleigh number have destabilizing effect on the onset of oscillatory convection.

Control strategy on the double-diffusive convection in a nanofluid layer with internal heat generation

The influences of feedback control and internal heat source on the onset of Rayleigh–Bénard convection in a horizontal nanofluid layer is studied analytically due to Soret and Dufour parameters. The confining boundaries of the nanofluid layer (bottom boundary–top boundary) are assumed to be free–free, rigid–free, and rigid–rigid, with a source of heat from below. Linear stability theory is applied, and the eigenvalue solution is obtained numerically using the Galerkin technique. Focusing on the stationary convection, it is shown that there is a positive thermal resistance in the presence of feedback control on the onset of double-diffusive convection, while there is a positive thermal efficiency in the existence of internal heat generation. The possibilities of suppress or augment of the Rayleigh–Bénard convection in a nanofluid layer are also discussed in detail.

Thermal Convection in a Nanofluid Layer with Thermorheological Effect

Thermorheological effect on the onset of convection in a horizontal nanofluid layer heated from below is studied for rigid-rigid, free-free and rigid-free boundaries by incorporating the effects of Brownian motion and thermophoresis. The viscosity of nanofluid is allowed to vary exponentially with temperature. The boundaries are considered to be isothermal and the normal flux of nanoparticle volume fraction is taken to be zero on the boundaries. The resulting eigenvalue problem is solved numerically by the Galerkin method and observed that the instability sets in only as stationary convection irrespective of the velocity boundary conditions. The stability characteristics of the system are strongly dependent on the viscosity parameter. At low values of the viscosity parameter, the variation in the critical Rayleigh number is found to be nominal but increases with increasing viscosity parameter, reaches a maximum and then decreases. Results also indicate that increase in the modified diffusivity ratio, concentration Rayleigh number, and Lewis number is to hasten the convection while the modified particle density increment has no observable effect on the onset of convection.

Effect of Internal Heat Source on the Onset of Convection in a Nanofluid Layer

Effect of internal heat source on the onset of convection in nanofluid layer heated from below is studied. The lower boundary and upper boundary are assumed to be rigid and free respectively. The two important effects namely the Brownian motion and thermophoresis have been included in the model of nanofluid. Linear stability analysis has been made to investigate the effect of internal heat source on the onset of convection. Galerkin method is used to obtain the analytical expression for Rayleigh number in the non-oscillatory mode and result are depicted graphically. It has been shown that the internal heat source, nanoparticle Rayleigh number and modified diffusivity ratio have a destabilizing effect depending upon the values of various nanofluid parameters.