| A Fourier-Chebyshev collocation spectral method is applied for solving two-dimensional pure radiation, pure natural convection, combined radiation-conduction, and combined radiation-convection problems. The method is also extended to solve three-dimensional Rayleigh-Benard convection and combined radiation convection problems. Three numerical techniques: the influence matrix, the time splitting, and the modified semi-implicit time splitting methods for handling the unknown pressure boundary conditions are analyzed in the two-dimensional cases. Compared with the results from the finite element and the finite difference methods, results obtained in this study are more effective and accurate. The modified semi-implicit time splitting method is chosen to simulate the three dimensional problems due to the computational efficiency. The results obtained in this study reveal that the addition of the radiative heat transfer increases the first and second critical Rayleigh number and stabilizes the flow for Rayleigh-Benard convective problems. |
