VISUALIZATION ANALYSIS OF NATURAL CONVECTION IN A POROUS ENCLOSURE USING THE CHEBYSHEV SPECTRAL COLLOCATION METHOD WITH TEMPERATURE-DEPENDENT THERMAL DIFFUSIVITY

Abstract

We studied the effects of temperature-dependent thermal diffusivity and aspect ratio on natural convection in a rectangular porous cavity. Thermal diffusivity is assumed to vary as a linear function of temperature.We used the Chebyshev spectral collocation method to solve coupled nonlinear partial differential equations. The domain of the problem is discretized by Chebyshev–Gauss–Lobatto collocation points, and time derivatives are discretized by a semi-implicit scheme with finite-difference approximation. We executed the treatment of variable thermal diffusivity using array multiplication in the computation and used the matrix diagonalization method to solve discretized equations. Results from the current study are compared with those available in the literature. Numerical solutions are visualized using the isotherm, streamline, and heatline for different values of Rayleigh number, thermal diffusivity coefficient, and aspect ratio. For the first time, the visualization tool of heatline is applied to a porous enclosure with temperature-dependent thermal diffusivity. On the basis of these results, the heat-transfer process across the enclosure was analyzed. We found that variable thermal diffusivity has a considerable influence on flow pattern and corresponding heat transfer in the enclosure.