Holographic interferometric study of natural convective heat transfer in vertical rectangular enclosures

Abstract

Natural convective flows, induced by buoyancy forces on the fluid, in rectangular enclosures are important in many engineering applications such as thermal insulation of buildings, double-glazed windows and in flat plate solar collectors. A dimensional analysis of the physical situation shows that the flow and heat transfer arising in such circumstances are uniquely defined by the three dimensionless parameters: Flow Rayleigh number RaRaRa, Fluid Prandtl number PrPrPr, and the enclosure aspect ratio (height-to-width ratio) H/LH/LH/L. In the present work, heat transfer in a water-filled vertical rectangular enclosure of moderate aspect ratios has been studied using holographic interferometric technique. A holographic interferometer based on double-exposure holography with diffuse back illumination has been designed and fabricated. This instrument was employed to obtain the interference fringe pattern of the convective flow generated within the differentially heated vertical walls of the enclosure. The infinite-fringe spacing technique which maps the isothermal contours, in the form of constant phase planes, was found very convenient for visualization of flow pattern and for the data reduction from the interferograms. The interferograms were scanned on a microdensitometer to obtain local and average heat transfer coefficients. Experiments were performed for aspect ratio ranging from 0.86 to 15.8 and Rayleigh numbers ranging from 1.25�41.25 \times 10^41.25�4 to 2.75�62.75 \times 10^62.75�6 and results are presented in the form of isotherms, temperature profiles and local Nusselt number plots. The isotherms show the flow regimes developed in the cavity and the important features of flow such as the extent of thermal boundary layers and occurrence of secondary flow in the cavity are seen. The local Nusselt number was found to be a strong function of aspect ratio for aspect ratios less than 2.5 and the calculated average Nusselt number increases monotonically as the aspect ratio is decreased within the range studied (0.86 < H/L < 7.6). One of the important inferences drawn from the local Nusselt number variation plots is the significant drop in local Nusselt number at the departure corner. Finally, the variation of average heat transfer coefficient as a function of Rayleigh number has been discussed for two aspect ratios (2.5 and 6.0). There is an excellent qualitative agreement between the numerically predicted isotherms as reported in the literature and those obtained during the present study. The average Nusselt number values obtained for different aspect ratios compare well (within 10%) with those calculated from the correlation reported by MacGregor and Emery (Trans. of ASME, J. Heat Transfer, pp. 391, August 1969).