Upward heat flux through the horizontal fluid layer of water with sinusoidal wall temperature at the top or bottom boundary

Either top or bottom wall temperature of an infinite horizontal fluid layer at Pr=6 is sinusoidally oscillated with constant average temperature on the opposing horizontal wall. This is a system with no temperature difference between the top and bottom walls in a time-averaged sense, as studied by Kalabin et al. for a square channel. The fluid is water, and the Boussinesq approximation is made. The computational region of height 1 and horizontal width 1 is adopted and numerical computation is carried out. The results show that the fluctuating Nusselt numbers computed at both the top and bottom walls give positive time-averaged values for two different frequencies computed. Time-dependent convection plumes occur when the bottom wall temperature becomes higher than the top wall temperature. The time-averaged heat flux is always positive, i.e., upward, even if the time-averaged temperature difference is zero between the top and bottom walls. This holds even if the oscillating temperature is on either the top or bottom wall. Two periods of temperature oscillation give one period of oscillation in flow and Nu, at least for the parameters studied.