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Nonlinear stability theory is used to investigate free convection arising in a particular class of Horton–Rogers–Lapwood (HRL) problem. Time periodic modulation is imposed on either the temperature at the bounding surfaces or the gravitational field permeating the medium. The Brinkman model and the Boussinesq approximation govern the fluid flow. The energy formulation is followed and the Galerkin...
A typical plane parallel convective motion arising in an externally and internally heated slot filled with some porous material is considered. Temperature dependent diffusion coefficients and nonuniform distribution of volumetric heat sources across the slot are taken into account. Using Lyapunov direct method the perturbations are shown to be asymptotically and exponentially stable provided that...
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