Transient Convection in a Two- Dimensional Square Cavity 

An interferometric study of transient natural convection in a long air-filled square cavity is reported. The top and bottom walls of the cavity are maintained at uniform temperatures at all times in an unstably stratified configuration. Three different Rayleigh numbers namely have been considered. The orientation of the light beam is maintained parallel to the longest dimension of the cavity. The fringes thus obtained reveal depth-averaged isotherm patterns in the cavity at various instants of time. The image is filtered and the fringes are thinned using image processing operations. Subsequently, the local and average heat transfer parameters in t he experimental setup have been computed. Results of the present study of show that the onset of flow in the cavity is bicellular. However, the flow is unicellular for the most part of the transient. The flow becomes increasingly vigorous with time and the average Nusselt number of the cavity is a maximum at steady state.

Buouancy- driven flow in an air-filled cavity heated from below is a problem of fundamental as well as practical importance. A summary of experimental and theoretical result including several correlations for buoyancy-dominated flow is presently available [89]. These results pertain essentially to steady-state situations, with only a few numerical results being available for transient convection. One of the principal difficulties associated with transient flows is the measurement of the wall heat flux. Energy balance methods require careful accounting of losses and are simple to use only after steady state has been reached. In contrast to this, optical methods of measurement have several advantages. These include non-intrusiveness, absence of inertia while following transient, and the ability of a light beam to scan a flow field rather than the flow property at a point. Besides they can be used for qualitative as well as quantitative analysis of the problem at hand since the fringe spacing or the fringe thickness, however, places a lower limit on the length scales that can be resolved by the image.

Interferometric study of natural convection in a two-dimension cavity whose side walls are heated has been reported earlier [108]. A similar study for a horizontal cylindrical annulus has also been described [109]. The study that comes closest to the present work is that of Eckert and Carlson [110] where the effect of wall conduction on natural convection in a square cavity has been presented using interferometry. The bottom-heated/top-cooled configurations is one of the several arrangements considered in Eckert and Carlson [110]. Features such as plume formation and fringe symmetry about the vertical plane have been observed and these are similar to the results obtained in the present work. However, there are significant differences arising from initial and boundary conditions and in the data reduction procedures.

Figure 4.38: (a) Flow patterns in an infinite fluid layer and a square cavity; (b) schematic of the test cell.

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