Effect of internal-heating on weakly non-linear stability analysis of Rayleigh–Bénard convection under g-jitter

Appl. Math. Mech.-Engl. Ed.

2015

A non-autonomous complex Ginzburg-Landau equation (CGLE) for the finite amplitude of convection is derived, and a method is presented here to determine the amplitude of this convection with a weakly nonlinear thermal instability for an oscillatory mode under throughflow and gravity modulation. Only infinitesimal disturbances are considered. The disturbances in velocity, temperature, and solutal fields are treated by a perturbation expansion in powers of the amplitude of the applied gravity field. Throughflow can stabilize or destabilize the system for stress free and isothermal boundary conditions. The Nusselt and Sherwood numbers are obtained numerically to present the results of heat and mass transfer. It is found that throughflow and gravity modulation can be used alternately to heat and mass transfer. Further, oscillatory flow, rather than stationary flow, enhances heat and mass transfer.

Section: Introductionsupporting

confidence: 74%

Throughflow and g-jitter effects on binary fluid saturated porous medium

Appl. Math. Mech.-Engl. Ed.

2015

“…The effect of increasing Pr for lower values there is enhancement in the heat and mass transfer further increment in it no effect is found (Bhadauria et al 2013, Bhadauria andKiran 2014a,f …”

Section: Discussionmentioning

confidence: 96%

“…studied thermally or gravity modulated non-linear stability problem in a rotating viscous fluid layer, using Ginzburg-Landau equation for stationary mode of convection. Bhadauria et al (2013) studied internal heating effects weak nonlinear Rayleigh-Bénard convection under gravity modulated, using Ginzburg-Landau equation for stationary mode of convection.…”

Section: Introductionmentioning

confidence: 99%

Weak Nonlinear Double Diffusive Magneto-Convection in a Newtonian Liquid under Gravity Modulation

Bhadauria

2015

JAFM

A theoretical analysis of thermo-convective instability in an electrically conducting two component fluid layer is carried out when the gravity field vary with time in a sinusoidal manner. Newtonian liquid is considered between two horizontal surfaces, under a constant vertical magnetic field. The disturbance is expanded in terms of power series of amplitude of convection, which is assumed to be small. We use the linear matrix differential operator method to find the Ginzburg-Landau amplitude equation for the modulated problem. Use the solution of the Ginzburg-Landau equation in quantifying the amount of heat and mass transports in terms of Nusselt and Sherwood numbers. It is found that, the effect of magnetic field is to stabilize the system. Effect of various parameters on the heat and mass transport is also discussed. Further, it is found that the heat and mass transports can be controlled by suitably adjusting frequency and amplitude of gravity modulation.

“…The literature on internal heating is much less extensive than that on external heating. Some latest studies are due to Bhadauria et al [22], Bhadauria [23] and Bhadauria et al ([24], [25], [26]). …”

Section: Introductionmentioning

confidence: 99%

Nonlinear thermal convection in a layer of nanofluid under G-jitter and internal heating effects

Bhadauria

MATEC Web of Conferences

Belhaq

2014

Abstract. This paper deals with a mathematical model of controlling heat transfer in nanofluids. The time-periodic vertical vibrations of the system are considered to effect an external control of heat transport along with internal heating effects. A weakly non-linear stability analysis is based on the five-mode Lorenz model using which the Nusselt number is obtained as a function of the thermal Rayleigh number, nano-particle concentration based Rayleigh number, Prandtl number, Lewis number, modified diffusivity ratio, amplitude and frequency of modulation. It is shown that modulation can be effectively used to control convection and thereby heat transport. Further, it is found that the effect of internal Rayleigh number is to enhance the heat and nano-particles transport.