A three-dimensional model and dimensionless scale analysis of the transient fluid dynamics and heat transfer in an inclined adiabatic water-filled enclosure with an immersed cylindrical cold sink is presented. The geometry represents an integral collector storage system with an immersed heat exchanger. The modeled enclosure has an aspect ratio of 6:1 and is inclined at to the horizontal. The heat exchanger is represented by a constant surface temperature horizontal cylinder positioned near the top of the enclosure. A scale analysis of the transient heat transfer process identifies four temporal periods: conduction, quasi-steady, fluctuating, and decay. It also provides general formulations for the transient Nusselt number, and volume-averaged water temperature in the enclosure. Insight to the transient fluid and thermal processes is provided by presentation of instantaneous flow streamlines and isotherm contours during each transient period. The flow field consists of two distinct zones. The zone above the cold sink is nearly stagnant. The larger zone below the sink is one of strong mixing and recirculation initiated by the cold plume formed in the boundary layer of the cylindrical sink. Correlations for the transient Nusselt number and the dimensionless volume-averaged tank temperature predicted from the model compare favorably to prior measured data. Fluid motion in the enclosure enhances heat transfer compared to that of a cylinder in an unbounded fluid.
Natural Convective Flow and Heat Transfer in a Collector Storage with an Immersed Heat Exchanger: Numerical Study
Su, Y., and Davidson, J. H. (March 4, 2005). "Natural Convective Flow and Heat Transfer in a Collector Storage with an Immersed Heat Exchanger: Numerical Study." ASME. J. Sol. Energy Eng. August 2005; 127(3): 324–332. https://doi.org/10.1115/1.1934735
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