Aspect Ratio Effect on Natural Convection Flow in a Cavity Submitted to a Periodical Temperature Boundary

Abstract

The effect of aspect ratio on natural convection flow in a cavity submitted to periodic temperature boundary, is investigated numerically. The temperature of the heated wall is either maintained constant or varied sinusoidally with time while the temperature of the opposite vertical wall is maintained constant. The results are given for a range of varied parameters as Rayleigh number ͑5 ϫ 10 3 ഛ Raഛ 10 6 ͒, cavity aspect ratio ͑1/6ഛ A ഛ 8͒, and period of the sinusoidally heated wall ͑1 ഛ ഛ 1600͒. The amplitude of oscillation ͑a = 0.8͒ and the Prandtl number ͑Pr= 0.71͒ were kept constant. The results obtained in the steady state regime show that the heat transfer averaged over the cold wall is maximum when the aspect ratio is in the range 1 ഛ A ഛ 2. In the case of a periodic temperature boundary, it is shown that the deviation between the mean heat transfer and the heat transfer of the constant heated case is larger for shallow cavities.

Onset of Natural Convection and Transition Laminar-Oscillatory Convection Flow in Rayleigh-Bénard Configuration

“…In table 2, we have compared our results with those of Ben Cheikh [4]. A Good agreement has been obtained with two results.…”

“…In our study we found that the time dependent flow begins at around 16 Rac-1, it is the oscillatory mode. The critical value of this mode is Rac2= 4.58×10 4 . In order to view the physical oscillatory flow, we have chosen many arbitrary probes in the cavity.…”

“…Since, Rayleigh-Bé nard convection presents the evolution from the stationary state to the fully developed turbulent regime with many different flow patterns and sequences of bifurcations; it is widely investigated as the problems of different transition mechanisms in hydrodynamics [1][2]. Most of the published works covering natural convection in enclosures that exist today can be classified into two categories: differentially heated enclosures [3][4][5][6] and enclosures heated from below and cooled from above (Rayleigh Bé nard problems) [7]. Benchmark solutions related to differentially heated enclosures (first group) can be found in several numerical investigations [8].…”

Natural convection in an enclosure containing a sinusoidally heated cylindrical source

“…An additional verification of accuracy for the present code is shown in Table 2 for the unsteady condition and the case of a differentially heated vertical enclosure with Ra = 1.4 Â 10 5 and Pr = 7. We observe that the comparison was in good agreement with the results reported in the literatures [17,21].…”

“…Abourida et al [19] and El Ayachi et al [20] indicated that the heat transfer in a system could be enhanced by a proper choice of the considered parameters. Cheikh et al [21] concluded that the periodical heating case causes an increase of the mean heat transfer in comparison to the constant heating case. Liu et al [22] studied a square conducting body placed at the center of the enclosure.…”