Heat transfer and flow transitions of a thermal plume generated by a heating element on the enclosure bottom wall

Abstract

Abstract The two-dimensional buoyancy-induced flow above a heating horizontal element in the center of the bottom of a rectangular enclosure filled with air is numerically studied using the thermal lattice Boltzmann equation method with two distribution functions. The heating element has a higher temperature than that of the remaining walls. The width and height of the enclosure are 5 and 10 times the length of the heating element respectively. The flow is space and time symmetric if after a transient, the flow is symmetric with respect to the vertical axis of the enclosure and is time independent. A suitable quantity, here called the asymmetry, is zero when the flow is time and space symmetric, positive and constant when the first symmetry is lost, and positive and time dependent when both symmetries are broken. Flow transitions are studied as the Rayleigh number, R a , changes in a large interval, 1000 ≤ R a ≤ 350 000 . Eight flow transitions were found, the first ones related to the space and time symmetries. When both symmetries are broken, additional flow transitions were found by studying the Fourier power spectrum of the asymmetry, which allows the identification of the fundamental frequency and the appearance of harmonics and other frequencies. The average Nusselt number as a function of R a is also studied and a transition in their relationship is found at the appearance of harmonics, giving way to two different correlations.