Natural convection simulations and numerical determination of critical tilt angles for a parallel plate channel

Three dimensional laminar unsteady natural convection flow of incompressible air between two inclined parallel plates is analyzed by using spectral methods. The channel that is periodical in streamwise and spanwise directions is heated from below. The motivation behind the study is to perform simulations for a domain representing a bottom heated, open ended and inclined enclosure that appears mostly in solar energy applications. The governing equations are solved using a pseudospectral solver in order to obtain velocity and temperature fields in the channel, accurately. Fourier series and Chebyshev polynomial expansions are used for the variables. The standard Boussinesq approximation is used to include density variation. Modified Adams–Bashforth/Crank–Nicolson semi-implicit time stepping is used for stability. By using the obtained temperature distribution between the plates, the local and the average Nusselt numbers (Nu) are calculated. The Nu values are correlated with the tilt angle for fixed Rayleigh numbers (Ra) or for a fixed Ra times cosine of the tilt angle. By observing the changes in flow structures, the critical tilt angles for air at which the maximum and the minimum heat fluxes occur are determined. There is a very good agreement with the present results and the available empirical correlations in the literature. Moreover, the present study also explores the instabilities beyond the lower and upper tilt angle limits of the experimental studies in the literature.