Heat transfer analysis in a tilted cavity with rotation*

A heat transfer analysis of the natural convection in an inclined rotating cavity is presented. The top and bottom surfaces of the cavity are rigid and have fixed temperatures. The rotation axis passes orthogonally through the hot and cold surfaces. The heat transfer analysis is performed for different Taylor numbers and inclination angles (δ) of the cavity for longitudinal, transverse and oblique convective rolls solutions. The Nusselt number is obtained for the critical parameters of the onset of convection (Rayleigh number, wave number and roll orientation of oblique rolls) previously obtained from a linear stability analysis. Both unstable and stable thermal conditions are treated, with inclination angles of δ <90° (heated from below) and 90° < δ <= 120° (heated from above) respectively. Three dimensional non-linear numerical simulations are also presented for a Boussinesq fluid. The simulations are obtained using a spectral element method, considering periodic lateral boundaries and no-slip boundary conditions at the top and bottom surfaces.