Chebyshev spectral element method for natural convection in a porous cavity under local thermal non-equilibrium model

An accurate Chebyshev spectral element method is developed to simulate the natural convection in a porous cavity using the local thermal non-equilibrium model. Two horizontal walls of the cavity are adiabatic, while the left vertical wall is heated and the right side wall is cooled. The non-dimensional governing equations are derived based on the Darcy model and Boussinesq assumption. The validation test with exact solution verifies the high accuracy of the algorithm, and the numerical results for natural convection in porous square cavity reach an excellent agreement with reported solutions. Two physical problems are investigated: (1) Natural convection in porous cavity at different aspect ratios with fixed temperature on two vertical walls; (2) Natural convection in porous square cavity with temporal sinusoidal temperature on the hot wall and fixed temperature on the cold wall. The effects of aspect ratio and non-dimensional heat transfer characteristic parameters are analyzed.