Heat Transfer Due to Natural Convection in a Periodically Heated Slot

Abstract

Heat transfer resulting from the natural convection in a fluid layer contained in an infinite horizontal slot bounded by solid walls and subject to a spatially periodic heating at the lower wall has been investigated. The heating produces sinusoidal temperature variations along one horizontal direction characterized by the wave number خ± with the amplitude expressed in terms of a suitably defined Rayleigh number Rap. The maximum heat transfer takes place for the heating with the wave numbers خ±â€‰= 0(1) as this leads to the most intense convection. The intensity of convection decreases proportionally to خ± when خ±â†’0, resulting in the temperature field being dominated by periodic conduction with the average Nusselt number decreasing proportionally to خ±2. When خ±â†’âˆ‍, the convection is confined to a thin layer adjacent to the lower wall with its intensity decreasing proportionally to خ±âˆ’3. The temperature field above the convection layer looses dependence on the horizontal direction. The bulk of the fluid sees the thin convective layer as a “hot wall.â€‌ The heat transfer between the walls becomes dominated by conduction driven by a uniform vertical temperature gradient which decreases proportionally to the intensity of convection resulting in the average Nusselt number decreasing as خ±âˆ’3. It is shown that processes described above occur for Prandtl numbers 0.001 < Pr < 10 considered in this study.