In,. J. Heat Mass Transfer. Vol. 32, No. 8, pp. 1517-1527, 1989 cm17-9310/89 $3.oo+o.oLl Printedin Great Britain 0 1989 Pergamon Press plc An experimental study of heat transfer in a vertical annulus with a rotating inner cylinder K. S. BALL,? B. FAROUK and V. C. DIXIT Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, PA 19104, U.S.A. (Received 25 August 1988 and inJinal form 6 January 1989) Abstract-The results of an experimental study of the convective flows engendered within the annular gap between concentric vertical cylinders are presented. The inner cylinder is rotating and heated, while the outer cylinder is stationary and cooled. Stationary horizontal endplates are used to seal the annulus, forming an enclosure. The working fluid is air. Of particular interest is the accurate prediction of the heat transfer rates, which are intimately linked to the structure of the flow field. In rotating systems, the existence of hydrodynamic instabilities may lead to a variety of secondary flows as the parameters describing the system are varied. Along with each transition in a flow, the transport mechanisms are altered, and usually result in markedly changed rates ofheat and momentum transport. Experiments are conducted to determine the interdependence between the heat transfer mechanism and the structure of the secondary flows. Specifically, a parametric study of the mean heat transfer rate across the annular gap is performed, as well as a qualitative study (using smoke visualization techniques) of the secondary flow characteristics of the rotating system. The results provide a qualitative description of the transition from a buoyancy-dominated flow regime to one dominated by rotation. A correlation for the heat transfer rate as a function of the rotational Reynolds number and radius ratio is obtained in the forced convection limit. zyxwvutsrqponmlkjihg INTRODUCTION HEAT AND mass transfer from rotating cylindrical bodies occurs in many practical applications, the most common being the cooling of conventional rotating machinery, such as electrical motors and turbines [I]. The development of new rotating devices has further stimulated interest in this area. Among these are clini- cal blood oxygenators [2], gas centrifuges [3], and ‘barrel reactors’ used in the chemical vapor deposition (CVD) process [4]. Also, rotating heat exchangers operating in a variety of different ways are being intro- duced in the chemical, automotive, and nuclear indus- tries. Buoyant rotating flows also occur in nature (e.g. oceanic and atmospheric circulation), and provide useful models for study [5]. In spite of its technological importance, little work has been directed toward the study of heat transfer within rotating cylindrical annuli. The isothermal flow configuration, in contrast, has been the subject of much research. It is widely known that a critical speed of rotation exists, above which appears a stable, secondary mean flow consisting of regularly spaced toroidal vortices. This flow is commonly referred to as Taylor-Couette or Taylor-vortex flow, and results from an inherent hydrodynamic instability. A com- prehensive review of the general Taylor problem is provided by DiPrima and Swinney [6]. A considerable amount of research has also been conducted for the natural convection problem (with no rotation). The recent paper by Weidman and Mehrdadtehranfar [7] TPresent address: Division of Applied Mathematics, Brown University, Providence, RI 02912, U.S.A. investigates the stability of the natural convection flow in a tall annulus using the flow visualization technique, and also provides a good review of previously pub- lished results. The first efforts to study the combined problem with rotation and heat transfer were primarily exper- imental, and were usually coupled with an axial flow through the annular gap [8-141. Global heat transfer rates across the annular gap were reported, cor- responding to the different flow regimes which were observed. However, these studies were limited to the forced convection regime, and no effort was made to quantify the magnitude of the buoyancy effects (such as reporting values of the cylinder surface tem- peratures or the Grashof number). Furthermore, the role of the radius ratio as a parameter in this problem was neglected, and therefore some discrepancies between the heat transfer measurements in the studies cited above could not be explained. Later theoretical studies focused on the stability of the circular Couette flow in the presence of a radial temperature gradient [15-l 71. With the inner cylinder rotating, it was concluded that a positive gradient of temperature across the annular gap (i.e. a heated outer cylinder and a cooled inner cylinder) is destabilizing, while a negative temperature gradient is stabilizing. This can be explained by noting that a greater cen- trifugal force is exerted on a heavier (cooler) fluid particle. Thus, fluid particles adjacent to a cooled inner cylinder would have a greater tendency to be displaced by the rotating flow. In these analyses, the gravity force (buoyancy) was neglected. Walowit et al. [17] justified this seemingly severe restriction by noting that in the conduction regime (Gr & 103), natu- ral convection has little effect on the heat transfer, and 1517 BMT 32:8-I