Resonant response of fluid flow subjected to discrete heating elements

Two-dimensional calculation and theoretical analysis have been performed for laminar natural convection induced by two discrete heating elements flush mounted to one vertical wall of a square enclosure. Two cases are presented in this work. One is the upper elevation Heater-1 fluctuates its temperature as a sinusoidal function while the lower elevation Heater-2 maintains its temperature constant. The other case depicts the opposite situation of interchanging the boundary conditions of Heater-1 and Heater-2 in Case 1. A large range (0.01–10.0) of non-dimensional frequency is conducted numerically, and the results show the existence of resonance frequencies in both cases. Scale analysis over predicts the resonance frequency due to ignoring heat dissipation between the heaters. Mechanical details of the fluid flow and average heat transfer characteristics across Heater-1, Heater-2 and the centerline of the enclosure are scrutinized. The results indicate that in Case 1, the heat transfer of Heater-2 is little affected by the periodic change of temperature of Heater-1. However, the oscillatory behavior is largely intensified in Case 2 owing to the thermal wake generated on Heater-2 invigorating the global flow throughout the enclosure. The heatline concept, flow and temperature fields of the oscillating components are adopted to visualize the heat transport and fluid circulation.