Three-dimensional numerical simulation of natural convection in an inclined liquid-filled enclosure with an array of discrete heaters

A three-dimensional (3-D) numerical model is developed to investigate the effects of inclination on the heat transport processes in a liquid-filled rectangular enclosure of finite size. The interactions of flows tangential and normal to the heater surfaces in an inclined enclosure cause a slight oscillation in Nusselt number. Inclination has little effects on the average heat transfer characteristics except configurations close to the conduction case with heaters on top leading to a sharp decrease in Nusselt number. The critical Rayleigh number of 1708 is also observed in the present study regardless of inclinations. Heat transfer from discrete heaters is non-uniform. Maximum Nusselt number occurs at the heater leading edge and decreases towards the trailing edge. Correlations for the row average Nusselt number vs. Rayleigh number at various inclination angles are presented. By taking the average of the discrete heater array, the numerical results compared well with the empirical correlations obtained from a single heater plate in literature.