ON LAMINAR FREE-CONVECTION IN INCLINED RECTANGULAR ENCLOSURES

A class of problems of natural convection in tilted boxes is studied b y analytical and numerical methods. The convection is assumed to be dr iven by uniform fluxes of heat (or mass) at two opposing walls, the re maining walls being perfect insulators. Disregarding end-region effect s, an exact analytical solution is derived for the state which occurs after initial transients have decayed. This state is steady except for a spatially uniform, linear growth in the temperature (or the species concentration) which occurs whenever the fluxes are not equal. It is characterized by a uni-directional flow, a linear stratification and w all-to-wall temperature profiles which, except for the difference in a bsolute values due to the stratification, are the same at each cross-s ection. The mathematical problem is in essence nonlinear and multiple solutions are found in some parameter regions. The Benard limit of hor izontal orientation and heating from below is found to give a first bi furcation for which the steady states both before and after the bifurc ation are obtained analytically. For a tilted Benard-type problem, a s teady state with top-heavy stratification is found to exist and compet e with a more natural solution. The analytical solution is verified us ing numerical simulations and a known approximate solution for a verti cal enclosure at high Rayleigh numbers. The presented solution admits arbitrary Rayleigh numbers, inclination angles and heat fluxes. Some r estrictions on its validity are discussed in the paper.