Natural convection in a periodically heated slot

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 α with the amplitude expressed in terms of a suitably defined Rayleigh number Ra_p. The maximum heat transfer takes place for the heating with the wave numbers α=0(1) as this leads to the most intense convection. The strength of convection decreases proportionally to α for small heating wave numbers, resulting in the heat transfer being dominated by periodic conduction with the Nusselt number decreasing proportionally to α². When α becomes large, the convection is confined to a thin layer adjacent to the lower wall with its strength decreasing proportionally to α^-3, with the temperature field above the convection layer loosing dependence on the horizontal direction.