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2 International Journal of Applied Mechanics and Engineering

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Double diffusive convection in a high porosity anisotropic porous medium with externally regulated darcy and brinkman frictions

Siddheshwar P. G., Vanishree R. K.

International Journal of Applied Mechanics and Engineering

2011

Vol. 16, no 4

1147-1168

A linear stability analysis is performed on the double diffusive porous system using the Rayleigh-Ritz technique. The condition for direct and Hopf bifurcations is obtained as a function of the parameters of the problem. A unique feature in this problem is that Darcy and Brinkman friction are temperature-dependent and hence are amenable to regulation. The study reveals that this external regulation of convection results in a preference for stationary convection over oscillatory mode. A low-porosity medium results for "finger" and "diffusive" instabilities are also discussed in the case of constant viscosity liquids.

Combined effect of temperature and gravity modulations on the onset of convection in an anisotropic porous medium

Vanishree R. K.

International Journal of Applied Mechanics and Engineering

2010

Vol. 15, no 1

267-291

The combined effect of time-periodic boundary temperature (TBT, also called temperature modulation) and time-periodic body force (TBF, also called gravity modulation) of small amplitude on convection in an anisotropic porous medium is investigated by making a linear stability analysis. A regular perturbation method is used to arrive at an expression for the correction Rayleigh number that throws light on the possibility of sub-critical motions. With respect to synchronous TBT and TBF for moderate frequency values, the role of the Prandtl number, horizontal porous parameter, mechanical and thermal anisotropy parameters and the Brinkman number in inducing sub-critical instability is delineated. An asymptotic analysis is also presented for small and large frequencies. A comparison is made between the effects of temperature, gravity and combined (temperature + gravity) modulations on convection. The problem illustrates a method of regulating convection.