Natural convection in a rectangular enclosure with sinusoidal temperature distributions on both side walls

A two-dimensional steady and laminar natural convection in an air-filled (Pr=0.7) rectangular enclosure is investigated numerically. The horizontal walls are thermally insulated and the vertical side walls have two spatially varying sinusoidal temperature distributions of different amplitudes and phases. The governing equations in primitive variables are discretized by the finite-volume method and solved by the SIMPLE algorithm. The fluid flow and heat transfer characteristics are systematically investigated over a wide range of Rayleigh number (Ra=10(3)-10(6)), amplitude ratio (epsilon = 0-1), phase deviation (phi=0-pi), and aspect ratio (Ar=0.25-4). The results show that the natural-convection heat transfer in enclosures with two sinusoidal temperature distributions on the side walls is superior to that with a single sinusoidal temperature profile on one side wall.