Thermal Convection in a Vertical Slot with Lateral Heating

Abstract

Thermal convection of a fluid contained in a two-dimensional vertical rectangle under a uniform horizontal temperature gradient is studied with the aid of numerical simulations of the governing equations of motion. The velocity is assumed to satisfy the rigid boundary conditions (b.c.) on all the boundary walls whereas the temperature satisfies the isothermal and the adiabatic b.c. on the vertical and the horizontal side walls respectively. The Prandtl number Pr of the fluid is Pr = 0.71 and the aspect ratio A of the rectangle is taken as A=6. With increase of the Grashof number G characterizing the intensity of the thermal gradient, the motion successively exhibits different temporal behavior: steady \longrightarrow periodic \longrightarrow quasi-periodic with two fundamental frequencies \longrightarrow chaotic where the transition to chaos is caused by the disruption of the T²-torus due to the phase-locking. The spatial patterns associated with the above temporal oscillations are also given using the contour plots of the temperature field of the convection.