Abstract
This chapter investigates the convective instability in a horizontal porous annulus subjected to quasi-periodic (QP) gravitational modulation having two incommensurate frequencies. The porous matrix is supposed to be filled by an incompressible fluid. The model we consider includes the heat equation and the hydrodynamic equations under Darcy law and Boussinesq approximation. The derived model with the temperature-stream function is solved numerically using the alternate direction implicit method. The main objective is to examine the influence of the QP modulation on the transition from unicellular to bicellular flow regime, corresponding to a substantial change in the thermo-convective regime flow. Numerical simulations are conducted for some values of the amplitudes and frequencies of the modulation and the radius ratio of the annulus. Results showed that the thermo-convective instability in the QP regime is greatly influenced by radius ratio and the amplitudes of the QP gravitational modulation. The effect of the frequencies ratio on the critical Rayleigh number is also examined showing that for certain values of parameters, the maximum critical Rayleigh number is reached when the frequency ratio is equal to \(\sqrt{3}\) (QP gravitational modulation) and the minimum is obtained when the frequency ratio is equal to 3 (periodic gravitational modulation).
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Belabid, J., Allali, K., Belhaq, M. (2019). Convection in a Horizontal Porous Annulus with Quasi-Periodic Gravitational Modulation. In: Belhaq, M. (eds) Topics in Nonlinear Mechanics and Physics. Springer Proceedings in Physics, vol 228. Springer, Singapore. https://doi.org/10.1007/978-981-13-9463-8_14
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