Transitions and chaos for free convection in a rotating porous layer
type: Item
instance of: scholarly article
title: Transitions and chaos for free convection in a rotating porous layer
zbMATH Open document ID: 0935.76085
DOI: 10.1016/S0017-9310(97)00265-2
author: P. Vadasz
author: Shmuel Olek
published in: International Journal of Heat and Mass Transfer
publication date: 2000-05-09T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 76R10
Mathematics Subject Classification ID: 76E06
Mathematics Subject Classification ID: 37N10
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 76U05
zbMATH DE Number: 1291930
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: supercritical Rayleigh number
zbMATH Keywords: multiple solutions
zbMATH Keywords: truncated Galerkin method
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: Darcy's model
zbMATH Keywords: Lorenz equations
zbMATH Keywords: Adomian's decomposition method
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1291930