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Stability Analysis of Natural Convection in Porous Cavities through Integral Transforms

L. S. de B. Alves
Renato Cotta
Organization: North Carolina State University
Department: Department of Physics
J. Pontes
Organization: Universidade Federal do Rio de Janeiro
Journal / Anthology

International Journal of Heat and Mass Transfer
Year: 2002
Volume: 45
Page range: 1185-1195

The onset of convection and chaos related to natual convection inside a porous cavity heated from below is investigated using the generalized integral transform technique (GITT). This eigenfunction expansion napproach generates an ordinary differential system that is adequately truncated in order to be handled by linear stablity analysis (LSA) as well as in full nonlinear form through the Mathematica sftware 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 trunctaion ordersare 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 behaviorfor increasing expansion orders is investigated.

*Science > Physics > Fluid Mechanics
*Science > Physics > Thermodynamics and Statistical Mechanics