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Non-linear spectral analysis of Rayleigh-Benard convection in a high-porosity medium

Thangaraj R. P.

International Journal of Applied Mechanics and Engineering

2002

Vol. 7, no 4

1305-1328

A local non-linear stability analysis using the spectral method is made of the Rayleigh-Benard situation in a high-porosity porous medium. The series expansion solution so obtained is valid for a large range of imposed temperature differences and yields a quantitative estimate of the heat transport by convection. Streamline patterns and mean temperature distributions have been obtained. The temperature distributions show that at the middle of the fluid-filled porous layer a layer of isothermal mean temperature develops, thus limiting the major heat transport to thermal boundary layers. The damping nature of porous media on heat transport is also clearly brought out.

The effect of non-uniform basic temperature gradient on the convective instability of a fluid layer sandwiched between two porous layers with general velocity and thermal conditions

Thangaraj R. P.

International Journal of Applied Mechanics and Engineering

2001

Vol. 6, no 1

35-52

The stability of a horizontal fluid layer bounded on either side by porous layers with different permeabilities is examined for different non-uniform basic temperature gradients using general velocity and thermal conditions at the boundaries. In the case of sudden heating and cooling, analytical solutions are obtained using single-term Galerkin expansion. Numerical solutions are obtained for all possible combinations of basic temperature gradients and boundary conditions in respect of velocity and temperature. General conclusion about the thermal depth and the destabilizing effects of the basic temperature gradients are presented. The classical results of free-free, rigid-free and rigid-rigid boundaries with isothermal or adiabatic boundaries are recovered as limiting cases of the present study.