NATURAL-CONVECTION HEAT-TRANSFER IN INCLINED ENCLOSURES WITH MULTIPLE CONDUCTING SOLID PARTITIONS

Laminar natural convection heat transfer is studied in a tilted fluid system consisting of multiple layers of fluid separated by solid partitions with finite thickness and conductivity. A closed form solution is derived in the limit of a thin-layered system subject to a uniform heat flux from the sides and adiabatic boundary conditions at two ends. Results are obtained in terms of overall Nusselt number Nu as a function of Rayleigh number Ra, angle of inclination of the system PHI, solid to fluid conductivity ratio K, thickness of the fluid layers Z(i), thickness of the solid partitions t(i), and number of partitions N. The critical Rayleigh number for the onset of convection in a bottom-heated horizontal system is predicted. The results are compared with limiting cases of the problem and are in agreement. A numerical study of the same phenomenon is obtained by solving the complete system of governing equations using a finite difference formulation and a volume control method. Good agreement is found between the analytical predictions and the numerical simulation.