Analytical and numerical study of natural convection heat transfer in an inclined composite enclosure

Laminar natural convection heat transfer in inclined fluid layers divided by a partition with finite thickness and conductivity is studied analytically and numerically. The governing equations for the fluid layers are solved analytically in the limit of a thin layered system with constant flux boundary conditions. The study covers of the range of Ra from 10³ to 10⁷, from 0° to 180° and the thermal conductivity ratio of partition to fluid ratioK from 10^–2 to 10⁶. The Prandtl number was 0.72 (for air). Results are obtained in terms of an overall Nusselt number as a function of Rayleigh number, angle of inclination of the system, mid layer thickness, and mid layer thermal conductivity. The critical Rayleigh number for the onset of convection in a bottom-heated horizontal system is predicted. The results are compared with the numerical results obtained by solving the complete system of governing equations, using SIMPLER method, as well as with the limiting cases in the literature.