Weak nonlinear oscillatory convection in a nonuniform heating porous medium with throughflow

Palle Kiran (1)

1 Department of Applied Mathematics, School for Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India

A weak nonlinear stability analysis has been performed for the oscillatory mode of convection, heat and mass transports in terms of Nusselt, Sherwood numbers which are governed by the non−autonomous complex Ginzburg-Landau equation is calculated. The porous medium boundaries are heated sinusoidally with time. The basic state temperature is defined in terms steady and oscil-latory parts, where steady part show nonlinear throughflow effect on the system. The generalized Darcy model is employed for the momentum equation. The disturbances of the flow are expanded in power series of amplitude of modulation, which is assumed to be small and employed using normal mode technics. The effect of vertical throughflow is found to stabilize or destabilize the system depending on its direction. The time relaxation parameter λ 1 has destabilizing effect, while time retardation parameter λ 2 has stabilizing effect on the system. Three types of modulations has been analyzed, and found that, OPM, LBMO cases are effective on heat/mass transfer than IPM case. The effects of amplitude and frequency of modulation on heat/mass transports have been analyzed and depicted graphically. The study establishes that the heat/mass transports can be controlled effectively by a mechanism that is external to the system. Further, it is found that better results may obtain for oscillatory mode of convection.

Mots clés: Weak nonlinear theory; Complex Ginzburg-Landau equation; Thermal modulation; Through- flow; Oscillatory convection

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Palle Kiran. Weak nonlinear oscillatory convection in a nonuniform heating porous medium with throughflow. International Journal of Engineering and Mathematical Modelling, 2015, 2 (3), pp.63-78. ⟨hal-01186689⟩