Transitions and chaos for free convection in a rotating porous layer
The nonlinearity which is inherently present in centrifugally driven free convection in porous media raises the problem of multiple solutions in this type of system. Here we present a solution to the nonlinear problem by using a truncated Galerkin method to obtain a set of ordinary differential equations for the time evolution of the Galerkin amplitudes. It is demonstrated that Darcy's model, when extended to include the time derivative term and subject to appropriate scaling, provides the familiar Lorenz equations, although with different coefficients. The system of ordinary differential equations is solved by Adomian's decomposition method. We give some examples of convection solutions and resulting rates of heat transfer.
scientific article; zbMATH DE number 1291930