Buoyancy-driven flow in an enclosure with time periodic boundary conditions

Abstract

The problem of laminar buoyancy-driven flow in a square cavity driven by a warm vertical wall, having a uniform surface temperature whose magnitude is changing periodically with time, is investigated numerically. The warm wall surface temperature varies sinusoidally, oscillating about a fixed mean temperature. The opposite cold wall is maintained at a constant temperature. Solutions are obtained for a number of different cases which illustrate the effects of the oscillating surface temperature on the fluid flow and the heat transfer through the enclosure. The transient solutions obtained are all periodic in time. The streamlines show that a weak secondary flow cell intermittently appears and then disappears in the upper corner of the enclosure near the hot driving wall, rotating in a direction opposite to the main flow. The instantaneous heat flux through the hot wall fluctuates greatly in time and over certain times heat removal occurs over a large segment of the hot driving surface. The effect of the periodically changing wall temperature is felt only partially into the enclosure and, overall, the time-averaged heat transfer across the enclosure is rather insensitive to the time-dependent boundary condition.