Stability analysis of natural convection in porous cavities through integral transforms

Programa de Engenharia Metalúrgica e de Materiais, EE, COPPE, Universidade Federal do Rio de Janeiro, Cidade Universitária, Cx. Postal 68503, Rio de Janeiro, RJ, 21945-970, Brazil
International Journal of Heat and Mass Transfer (Impact Factor: 2.38). 03/2002; 45(6):1185-1195. DOI: 10.1016/S0017-9310(01)00231-9


The onset of convection and chaos related to natural convection inside a porous cavity heated from below is investigated using the generalized integral transform technique (GITT). This eigenfunction expansion approach generates an ordinary differential system that is adequately truncated in order to be handled by linear stability analysis (LSA) as well as in full nonlinear form through the Mathematica software system built-in solvers. Lorenz's system is generated from the transformed equations by using the steady-state solution to scale the potentials. Systems with higher truncation orders are solved in order to obtain more accurate results for the Rayleigh number at onset of convection, and the influence of aspect ratio and Rayleigh number on the cell pattern transition from n to n+2 cells (n=1,3,5,…) is analyzed from both local and average Nusselt number behaviors. The qualitative dependence of the Rayleigh number at onset of chaos on the transient behavior and aspect ratio is presented for a low dimensional system (Lorenz equations) and its convergence behavior for increasing expansion orders is investigated.

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Available from: Leonardo Alves, Feb 02, 2015
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    • "The main feature of this method relies on the following steps: stepwise approximation of the eddy diffusivity and wind speed, the Laplace transform application to the advection-diffusion equation, semi-analytical solution of the set of linear ordinary equation resulting for the Laplace transform application and construction of the pollutant concentration by the numerical Laplace transform inversion. The GITT is a well-known hybrid method that had solved a wide class of direct and inverse problems mainly in the area of heat transfer and fluid mechanics (Cotta, 1993; Cotta and Mikhailov, 1997; Cheroto et al., 1999; Alves et al., 2002; Magno et al., 2002; Neto et al., 2002 and Cotta et al., 2003). "
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