Numerical and experimental study of steady state free convection generated by constant heat flux in tilted hemispherical cavities

Steady-state natural convection taking place in hemispherical air-filled cavities is presented in this work. The circular base of the hemispherical cavity is the hot active wall subjected to a constant heat flux. The closing dome is maintained isothermal at a lower temperature and acts as a cold wall. This cavity can be inclined at an angle α between 0° (hot wall horizontal) and 90° (hot wall vertical) in steps of 15°. The problem is studied both experimentally and numerically. Measurements of thermal variables are taken on an experimental assembly at steady state in order to characterize the heat exchanges at the hot wall. The Rayleigh number resulting from the experimental parameters varies between 3.44 × 105 and 2.83 × 107. The numerical study covers a larger Ra range, between 104 and 5 × 107. Calculations performed using the finite volume method complement the experimental results by examining also the dynamic aspects. The mathematical model used is validated by measurements. Differences between the two approaches are found to be relatively low, always within the uncertainties of the experimental data. The comparison with previous published works dealing with the horizontal cavity is also satisfactory. The resulting thermal and dynamic fields are presented for all the angles treated. Correlations between average Nusselt and Rayleigh numbers are proposed to quantify the convective exchanges for engineering applications.