Uni-directional heat flux through the horizontal fluid layer with sinusoidal wall temperature at the top or bottom boundaries

Abstract

Infinite horizontal fluid layer is considered between the top and bottom walls. Either top or bottom wall temperature is sinusoidally oscillated in terms of the constant average temperature in an opposing horizontal wall. This is the system with no temperature difference between the top and bottom walls in time-averaged sense, as studied by Kalabin et al. for a square channel. The fluid is Newtonian and Boussinesq approximation is made. The fluid layer of height 1 versus the horizontal width 1 or 4 is adopted and numerical computations are carried out for Pr=1. The time-averaged Nusselt numbers computed both at top and bottom walls give the upward time-averaged heat flux without depending on the temperature oscillation either at the upper or lower walls. This is because the time-dependent convection plumes occur at the almost largest temperature of the bottom wall in comparison to the top wall. 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.